Internet Engineering Task Force R. Guerin/S. Kamat/A. Orda
INTERNET DRAFT IBM/IBM/Technion
T. Przygienda/D. Williams
Lucent/IBM
30 January 1998
QoS Routing Mechanisms and OSPF Extensions
draft-guerin-qos-routing-ospf-03.txt
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Abstract
This memo describes extensions to the OSPF [Moy97] protocol to
support QoS routes. The focus of this document is on the algorithms
used to compute QoS routes and on the necessary modifications to OSPF
to support this function, e.g., the information needed, its format,
how it is distributed, and how it is used by the QoS path selection
process. Aspects related to how QoS routes are established and
managed are also briefly discussed. The goal of this document is
to identify a framework and possible approaches to allow deployment
of QoS routing capabilities with the minimum possible impact to the
existing routing infrastructure.
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Contents
Status of This Memo i
Abstract i
1. Introduction 1
1.1. Overall Framework . . . . . . . . . . . . . . . . . . . . 1
1.2. Simplifying Assumptions . . . . . . . . . . . . . . . . . 2
2. Path Selection Information and Algorithms 4
2.1. Metrics . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Advertisement of Link State Information . . . . . . . . . 5
2.3. Path Selection Algorithms . . . . . . . . . . . . . . . . 6
2.3.1. Exact Pre-Computed QoS Paths (BF) . . . . . . . . 7
2.3.2. On-Demand Computation of QoS Paths (Dijkstra) . . 12
2.3.3. Exact & Approximate Pre-Computed QoS paths
(Dijkstra) . . . . . . . . . . . . . . . . 13
2.4. Extracting Forwarding Information from Routing Table . . 16
3. Establishment and Maintenance of QoS Routes 16
4. OSPF Protocol Enhancements 18
4.1. QoS -- Optional Capabilities . . . . . . . . . . . . . . 18
4.2. Encoding Resources as Extended TOS . . . . . . . . . . . 19
4.2.1. Encoding bandwidth resource . . . . . . . . . . . 20
4.2.2. Encoding Delay . . . . . . . . . . . . . . . . . 23
4.3. Packet Formats . . . . . . . . . . . . . . . . . . . . . 23
4.4. Calculating the Inter-area Routes . . . . . . . . . . . . 23
4.5. Open Issues . . . . . . . . . . . . . . . . . . . . . . . 23
A. Pseudocode for BF Algorithm 24
B. Pseudocode for On-Demand Dijkstra Algorithm 26
C. Pseudocode for Precomputed Dijkstra Algorithm 28
D. Zero-Hop Edges 30
E. Explicit Routing Support 31
F. Computational Complexity 33
G. Extension: Handling Propagation Delays 35
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H. Accounting for Link Metric Inaccuracy in Path Selection 36
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1. Introduction
In this document we describe a set of proposed additions to the
OSPF routing protocol (the additions are built on top of OSPF
V2 [Moy97]) to support Quality-of-Service (QoS) routing in IP.
In particular, we discuss the metrics required to support QoS,
the associated link advertisement mechanisms, the path selection
algorithm, as well as aspects of route establishment. Our goals are
to define an approach which while achieving the goals of improving
performance for QoS flows (likelihood to be routed on a path capable
of providing the requested QoS), does so with the least possible
impact on the existing OSPF protocol. Given the inherent complexity
of QoS routing, achieving this goal obviously implies trading-off
``optimality'' for ``simplicity'', but we believe this to be required
in order to facilitate deployment of QoS routing capabilities.
1.1. Overall Framework
We consider a network (1) that supports both best-effort packets and
packets with QoS guarantees. The way in which the network resources
are split between the two classes is irrelevant to our proposal,
except for the assumption that each QoS capable router in the network
is able to dedicate some of its resources to satisfy the requirements
of QoS packets. QoS capable routers are also assumed to be able to
identify and advertise the amount of their resources that remain
available for additional QoS flows. In addition, we limit ourselves
to the case where all the routers involved support the QoS extensions
described in this document, i.e., we do not consider the problem
of establishing a route in a heterogeneous environment where some
routers are QoS-capable and others are not. Furthermore, in this
document we focus on the case of unicast flows, although many of the
additions we define are applicable to multicast flows as well.
We assume that a flow with QoS requirements will specify them
in some fashion that is accessible to the routing protocol. For
example, this could correspond to the arrival of an RSVP [RZB+97]
PATH message, whose TSpec is passed to routing together with the
destination address. After processing such a request, the routing
protocol returns a path that it deems the most suitable given the
flow's requirements. Depending on the scope of the path selection
process, this returned path could range from simply identifying the
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1. In this document we commit the abuse of notation of calling a
``network'' the interconnection of routers and networks through which
we attempt to compute a QoS path.
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best next hop, i.e., traditional hop-by-hop routing, to specifying
all intermediate nodes to the destination, i.e., an explicit route.
Note that this decision impacts the operation of the path selection
algorithm as it translates into different requirements in order
to construct and return the appropriate path information. Note
also that extension to multicast paths will impact differently a
hop-by-hop and an explicit route based approach.
For simplicity, we will describe the path computation algorithm
assuming hop-by-hop routing. Extensions to support explicit routing
are discussed in appendix E.
In this document, we focus on the aspect of selecting an appropriate
path based on information about link metrics and flow requirements.
There are obviously many other aspects that need to be specified in
order to define a complete proposal for QoS routing. For example,
we incorporate a rather simplistic high level admission control
policy based on the path length. High level admission control is
important because often admitting a flow even when a feasible path
is found is not desirable if it will result in an inefficient use of
network resources. Another aspect concerns controlling the overhead
of additional link state updates caused by more frequent changes to
link metrics without adversely affecting the performance of path
selection. We present a brief discussion of various alternatives
that trade accuracy of link state information with protocol overhead
in Section 2.2. A discussion of some approaches to account for the
metric inaccuracies in path selection is deferred to Appendix H.
Management of QoS paths is yet another aspect of a complete solution.
Specifically, once a suitable path has been identified for a flow, it
may be desirable to keep the path assigned (pinned) to the flow as
long as it is deemed adequate in order to avoid frequent oscillations
and routing instability. A brief discussion of path management is
provided in Section 3 and the reader is referred to [GKH97] for
further details of one solution to this problem.
1.2. Simplifying Assumptions
In order to achieve our goal of a minimal impact to the existing
protocol, we impose certain restrictions on the range of requirements
the QoS path selection algorithm needs to deal with directly.
Specifically, a policy scheme is used to a priori prune from
the network, those portions that would be unsuitable given the
requirements of the flow. This limits the ``optimization'' performed
by the path selection to a containable set of parameters, which helps
keep complexity at an acceptable level. Specifically, the path
selection algorithm will focus on selecting a path that is capable of
satisfying the bandwidth requirement of the flow, while at the same
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time trying to minimize the amount of network resources that need to
be allocated to support the flow, i.e., minimize the number of hops
used.
This focus on bandwidth is adequate in most instances, but does not
fully capture the complete range of potential QoS requirements. For
example, a delay-sensitive flow of an interactive application could
be put on a path using a satellite link, if that link provided a
direct path and had plenty of unused bandwidth. This would clearly
be an undesirable choice. Our approach to preventing such poor
choices, is to assign delay-sensitive flows to a policy that would
eliminate from the network all links with high propagation delay,
e.g., satellite links, before invoking the path selection algorithm.
In general, each existing policy would present to the path selection
algorithm its correspondingly pruned network topology, and the same
algorithm would then be used to generate an appropriate path.
Another important aspect in minimizing the impact of QoS routing
is to develop a solution that has the smallest possible computing
overhead. Additional computations are unavoidable, but it is
desirable to keep the total cost of QoS routing at a level comparable
to that of traditional routing algorithms. In this document, we
describe several alternatives to the path selection algorithm,
that represent different trade-offs between simplicity, accuracy,
and computational cost. In particular, we specify algorithms
that generate exact solutions based either on pre-computations or
on-demand computations. We also describe algorithms that allow
pre-computations at the cost of some loss in accuracy, but with
possibly lower complexity or greater ease of implementation. It
should be mentioned, that while several alternative algorithms are
described in this document, the same algorithm needs to be used
consistently within a given routing domain. This requirement can
be relaxed when explicit routing is used as the responsibility
of selecting a QoS path lies with a single entity, the origin of
the request, which ensures consistency. Hence, it may then be
possible for each router to use a different path selection algorithm.
However, in general, the use of a common path selection algorithm is
recommended, if not necessary, for proper operation.
The rest of this document is structured as follows. In Section 2,
we describe the path computation process and the information it
relies on. In Section 3, we briefly review some issues associated
with path management and their implications. In Section 4, we go
over the extensions to OSPF that are needed in order to support the
path selection process of Section 2. Finally, several appendices
provide details on the different path selection algorithms described
in Section 2 and outline several additional work items.
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2. Path Selection Information and Algorithms
This section describes several path selection algorithms that
can be used to generate QoS capable paths based on different
trade-offs between accuracy, computational complexity, and ease of
implementation. In addition, the section also covers aspects related
to the type of information, i.e., metrics, on which the algorithms
operate, and how that information is made available, i.e., link state
advertisements. The discussion on these topics is of a generic
nature, and OSPF specific details are provided in Section 4.
2.1. Metrics
As stated earlier, the process of selecting a path that can satisfy
the QoS requirements of a new flow relies on both the knowledge of
the flow's requirements and characteristics, and information about
the availability of resources in the network. In addition, for
purposes of efficiency, it is also important for the algorithm to
account for the amount of resources the network has to allocate in
order to support a new flow. In general, the network prefers to
select the ``cheapest'' path among all paths suitable for a new flow.
Furthermore, the network may also decide not to accept a new flow
for which it identified a feasible path, if it deems the cost of the
path to be too high. Accounting for these aspects involves several
metrics on which the path selection process is based. They include:
- Link available bandwidth: As mentioned earlier, we assume that
most QoS requirements are derivable from a rate-related quantity,
termed ``bandwidth''. We further assume that associated with
each link is a maximal bandwidth value, e.g., the link physical
bandwidth or some fraction thereof that has been set aside for
QoS flows. Since for a link to be capable of accepting a new
flow with given bandwidth requirements, at least that much
bandwidth must be still available on the link, the relevant link
metric is, therefore, the (current) amount of available (i.e.,
unallocated) bandwidth.
- Hop-count: This quantity is used as a measure of the path cost
to the network. A path with a smaller number of hops (that can
support a requested connection) is typically preferable, since
it consumes fewer network resources. While, as a general rule,
each edge in the graph on which the path is computed should be
counted as one hop, some edges, specifically those that connect
a transit network to a router, should not be taken into account.
(See Appendix D for a detailed explanation.)
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- Policy: As previously discussed, policies are used to identify
the set of links in the network that need to be considered when
running the path selection algorithm. In particular, policies
are used to prune from the network links whose performance or
other characteristics are incompatible with the requirements of a
flow.
A specific policy example of special importance is the
elimination of high latency links when considering path selection
for delay sensitive flows. The use of policies to handle
specific requirements allows considerable simplification in
the optimization task to be performed by the path selection
algorithm.
2.2. Advertisement of Link State Information
It is assumed that each router maintains an updated database of the
network topology, including the current state (available bandwidth)
of each link. As mentioned, the distribution of link state (metrics)
information is based on extending OSPF mechanisms. However, in
addition to how link state information is distributed, another
important aspect is when such distribution is to take place.
One option is to mandate periodic updates, where the period of
updates is determined based on a tolerable corresponding load on the
network and the routers. The main disadvantage of such an approach
is that major changes in the bandwidth available on a link could
remain unknown for a full period and, therefore, result in many
incorrect routing decisions. Ideally, one would want routers to have
the most current view of the bandwidth available on all links in the
network, so that they can make the most accurate decision on which
path to select. Unfortunately, this then calls for very frequent
updates, e.g., close to every time the available bandwidth of a link
changes, which is neither scalable nor practical.
In general, we are faced with a trade-off between the protocol
overhead of frequent updates and the accuracy of the network state
information that the path selection algorithm depends on. We
outline below a few possible link state update policies that strike a
practical compromise.
The basic idea is to trigger link state advertisements only when
there is a significant change in the value of metrics since the last
advertisement. The notion of significance of a change can be based
on an ``absolute'' scale or a ``relative'' one. An absolute scale
means partitioning the range of values that a metric can take into
equivalence classes and triggering an update whenever the metric
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changes sufficiently to cross a class boundary (2). A relative
scale, on the other hand, triggers updates when the percentage change
in the metric value exceeds a predefined threshold.
In either of the above two approaches, the value of a metric
advertised in an LSA could either be the actual value or a quantized
one according to some rule. Thus, these design decisions introduce
a certain degree of inaccuracy where an advertised value of a link
metric implicitly indicates a range of potential current values
of the metric. The path selection algorithm that we describe in
the next subsection operates on the advertised available bandwidth
values. Potential enhancements to the path selection algorithm
that seek to account for the inaccuracies in link metrics that are
introduced due to the update trigger policies will be described in
Appendix H.
Even though the update triggering mechanisms described above seek to
reduce protocol traffic by not advertising small changes to metrics,
the only direct means of controlling this overhead is through a hold
down timer that enforces a minimum spacing between two successive
updates. This introduces an additional degree of inaccuracy in the
topology database where even the boundaries of the potential range
of values for a given advertised metric value become fuzzy. Further
research is needed to effectively account for such inaccuracies
during path selection.
2.3. Path Selection Algorithms
There are several aspects to the path selection algorithms. The
main ones include the optimization criteria it relies on, the exact
topology on which it is run, and when it is invoked.
As mentioned before, invocation of the path selection algorithm can
be either per flow setup, or when warranted by changes in link states
when the algorithm used allows precomputation of paths (more on this
below).
The topology on which the algorithm is run is, as with the standard
OSPF path selection, a directed graph where vertices (3) consist of
routers and networks (transit vertices) as well as stub networks
(non-transit vertices). When computing a path, stub networks are
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2. Some hysteresis mechanism can be added to suppress updates when the
metric value oscillates around a class boundary.
3. In this document, we use the terms node and vertex interchangeably.
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added as a post-processing step, which is essentially similar to
what is done with the current OSPF routing protocol. In addition,
for each policy supported on a router, the topology used by the
path selection algorithm is correspondingly pruned to reflect the
constraints imposed by the policy, and in some instances the flow
requirements.
The optimization criteria used by the path selection are reflected
in the costs associated with each interface in the topology and how
those costs are accounted for in the algorithm itself. As mentioned
before, the cost of a path is a function of both its hop count and
the amount of available bandwidth. As a result, each interface
has associated with it a metric, that corresponds to the amount of
bandwidth which remains available on this interface. This metric
is combined with hop count information to provide a cost value,
in a manner that depends on the exact form of the path selection
algorithm. It will, therefore, be detailed in the corresponding
sections below, but all the different alternatives that are described
share a common goal. That is, they all aim at picking a path with
the minimum possible number of hops among those that can support
the requested bandwidth. When several such paths are available,
the preference is for the path whose available bandwidth (i.e., the
smallest value on any of the links in the path) is maximal. The
rationale for the above rule is the following: we focus on feasible
paths (as accounted by the available bandwidth metric) that consume
a minimal amount of network resources (as accounted by the hop-count
metric); and the rule for selecting among these paths aims at
balancing load as well as maximizing the likelihood that the required
bandwidth will indeed be available.
It should be noted that standard routing algorithms are typically
single objective optimizations, i.e., they may minimize the
hop-count, or maximize the path bandwidth, but not both. Double
objective path optimization is a more complex task, and, in
general, it is an intractable problem [GJ79]. Nevertheless, as
we will see, because of the specific nature of the two objectives
being optimized (bandwidth and hop count), the complexity of our
proposed algorithm(s) is competitive with even that of standard
single-objective algorithms. For readers interested in a thorough
treatment of the topic, connected with insights into the connection
between the different algorithms, linear algebra and modification of
metrics, [Car79] is recommended.
2.3.1. Exact Pre-Computed QoS Paths (BF)
In this section, we describe a path selection algorithm, that for a
given network topology and link metrics (available bandwidth) allows
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us to pre-compute all possible QoS paths, and also has a reasonably
low computational complexity. Specifically, the algorithm allows
us to pre-compute for any destination a minimum hop count path with
maximum bandwidth, and has a computational complexity comparable to
that of a standard shortest path algorithm (4).
The path selection algorithm is based on a Bellman-Ford (BF) shortest
path algorithm that is adapted to compute paths of maximum available
bandwidth for all hop counts. It is a property of the BF algorithm
that, at its h-th iteration, it identifies the optimal (in our
context: maximal bandwidth) path between the source and each
destination, among paths of at most h hops. In other words, the
cost of a path is a function of its available bandwidth, i.e., the
smallest available bandwidth on all links of the path, and finding
a minimum cost path amounts to finding a maximum bandwidth path.
However, we also take advantage of the fact that the BF algorithm
progresses by increasing hop count, to essentially get for free the
hop count of a path as a second optimization criteria.
Specifically, at the kth (hop count) iteration of the algorithm,
the maximum bandwidth available to all destinations on a path of
no more than k hops is recorded (together with the corresponding
routing information). After the algorithm terminates, this
information enables us to identify for all destinations and bandwidth
requirements, the path with the smallest possible number of hops and
sufficient bandwidth to accommodate the new request. Furthermore,
this path is also the one with the maximal available bandwidth among
all the feasible paths with at most these many hops. This is because
for any hop count, the algorithm always selects the one with maximum
available bandwidth.
We now proceed with a more detailed description of the algorithm
and the data structure used to record routing information, i.e.,
the QoS routing table that gets built as the algorithm progresses
(pseudo-code for the algorithm can be found in Appendix A). As
mentioned before, the algorithm operates on a directed graph
consisting only of transit vertices (routers and networks), with
stub-networks subsequently added to the path(s) generated by the
algorithm. The metric associated with each edge in the graph is the
bandwidth available on the corresponding interface. Let us denote
by bn;mthe available bandwidth on the edge between vertices n and
m. The vertex corresponding to the router where the algorithm is
being run, i.e., the computing router, is denoted as the ``source
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4. See Appendix F for a more comprehensive discussion on the aspect of
computational complexity.
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node'' for the purpose of path selection. The algorithm proceeds to
pre-compute paths from this source node to all possible destination
networks and for all possible bandwidth values. At each (hop count)
iteration, intermediate results are recorded in a QoS routing table,
which has the following structure:
The QoS routing table:
- a Kx H matrix, where K is the number of destinations (vertices
in the graph) and H is the maximal allowed (or possible) number
of hops for a path.
- The (n;h) entry is built during the hth iteration (hop count
value) of the algorithm, and consists of two fields:
* bw: the maximum available bandwidth, on a path of at most h
hops between the source node (router) and destination node
n;
* neighbor: this is the routing information associated with
the h (or less) hops path to destination node n, whose
available bandwidth is bw. In the context of hop-by-hop
path selection (5), the neighbor information is simply the
identity of the node adjacent to the source node on that
path. As a rule, the ``neighbor'' node must be a router and
not a network (see Appendix D), the only exception being
the case where the network is the destination node (and the
selected path is the single edge interconnecting the source
to it).
Next, we provide additional details on the operation of the algorithm
and how the entries in the routing table are being updated as the
algorithm proceeds. For simplicity, we first describe the simpler
case where all edges count as ``hops'', and later explain how
zero-hop edges (see Appendix D for further details) are handled.
When the algorithm is invoked, the routing table is first initialized
with all bw fields set to 0 and neighbor fields cleared. Next, the
entries in the first column (which corresponds to one-hop paths) of
the neighbors of the computing router are modified in the following
way: the bw field is set to the value of the available bandwidth
on the direct edge from the source. The neighbor field is set to
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5. Modifications to support explicit routing are discussed in
Appendix E.
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the identity of the neighbor of the computing router, i.e., the next
router on the selected path.
Afterwards, the algorithm iterates for at most H iterations
(considering the above initial iteration as the first). H can be
either the maximum possible hop count of any path, i.e., an implicit
value, or it can be set explicitly in order to limit path lengths to
some maximum value (6) to better control worst case complexity.
At iteration h, we first copy column h-1 into column h. In
addition, the algorithm keeps a list of nodes that changed their
bw value in the previous iteration, i.e., during the (h - 1)-th
iteration. The algorithm then looks at each link (n;m) where n is
a node whose bw value changed in the previous iteration, and checks
the maximal available bandwidth on an (at most) h-hop path to node
m whose final hop is that link. This amounts to taking the minimum
between the bw field in entry (n;h - 1) and the link metric value
bn;mkept in the topology database. If this value is higher than the
present value of the bw field in entry (m;h), then a better (larger
bw value) path has been found for destination m and with at most h
hops. The bw field of entry (m;h) is then updated to reflect this
new value. In the case of hop-by-hop routing, the neighbor field
of entry (m;h) is set to the same value as in entry (n;h - 1). This
records the identity of the first hop (next hop from the source) on
the best path identified thus far for destination m and with h (or
less) hops.
We conclude by outlining how zero-hop edges are handled. At each
iteration h (starting with the first), whenever an entry (m;h) is
modified, it is checked whether there are zero-cost edges (m;k)
emerging from node m, which is the case when m is a transit network
(see Appendix D). In that case, we attempt to improve the entry of
node k that corresponds to the h-th hop, i.e., entry (k;h) (rather
than entry (k;h + 1)), since the edge (m;k) should not count as an
additional hop. As with the regular operation of the algorithm, this
amounts to taking the minimum between the bw field in entry (m;h)
and the link metric value bm;kkept in the topology database. If
this value is higher than the present value of the bw field in entry
(k;h), then the bw field of entry (k;h) is updated to this new value.
In the case of hop-by-hop routing, the neighbor field of entry (k;h)
is set, as usual, to the same value as in entry (m;h) (which is also
the value in entry (n;h- 1)).
----------------------------
6. This maximum value should be larger than the length of the minimum
hop-count path to any node in the graph.
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Note that while for simplicity of the exposition, the issue of equal
cost, i.e., same hop count and available bandwidth, is not detailed
in the above description, it is straightforward to add this support.
It only requires that the neighbor field be expanded to record the
list of next (previous) hops, when multiple equal cost paths are
present.
Addition of Stub Networks
As was mentioned earlier, the path selection algorithm is run
on a graph whose vertices consist only of routers and transit
networks and not stub networks. This is intended to keep the
computational complexity as low as possible as stub networks can
be added relatively easily through a post-processing step. This
second processing step is similar to the one used in the current OSPF
routing table calculation [Moy97], with some differences to account
for the QoS nature of routes.
Specifically, after the QoS routing table has been constructed, all
the router vertices are again considered. For each router, stub
networks whose link appears in the router's link advertisements will
be processed to determine QoS routes available to them. The QoS
routing information for a stub network is similar to that of routers
and transit networks and consists of an extension to the QoS routing
table in the form of an additional row. The columns in that new row
again correspond to paths of different hop counts, and contain both
bandwidth and next hop information. We also assume that an available
bandwidth value has been advertised for the stub network. As before,
how this value is determined is beyond the scope of this document.
The QoS routes for a stub network S are constructed as follows:
Each entry in the row corresponding to stub network S has its bws
field initialized to zero and its neighbor set to null. When stub
network S is found in the link advertisement of router V, the value
bw(S,h) in the hth column of the row corresponding to stub network S
is updated as follows:
bw(S,h) = min ( bw(S,h) ; min ( bw(V,h) , b(V,S) ) ),
where bw(V,h) is the bandwidth value of the corresponding column
for the QoS routing table row associated with router V, i.e.,
the bandwidth available on an h hop path to V, and b(V,S) is the
advertised available bandwidth on the link from V to S. The above
expression essentially states that the bandwidth of a h hop paths to
stub network S is updated using a path through router V, only if the
minimum of the bandwidth of the h hop path to V and the bandwidth on
the link between V and S is larger than the current value.
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Update of the neighbor field proceeds similarly whenever the
bandwidth of a path through V is found to be larger than or equal
to the current value. If it is larger, then the neighbor field
of V in the corresponding column replaces the current neighbor
field of S. If it is equal, then the neighbor field of V in the
corresponding column is concatenated with the existing field for S,
i.e., the current set of neighbors for V is added to the current set
of neighbors for S.
2.3.2. On-Demand Computation of QoS Paths (Dijkstra)
In the previous section, we described an algorithm that allows
pre-computation of QoS routes. However, it may be feasible in
some instances, e.g., limited number of requests for QoS routes,
to instead perform such computations on-demand, i.e., upon receipt
of a request for a QoS route. The benefit of such an approach is
that depending on how often recomputation of pre-computed routes is
triggered, on-demand route computation can yield better routes by
using the most recent link metrics available. Another benefit of
on-demand path computation is the associated storage saving, i.e.,
there is no need for a QoS routing table. This is essentially the
standard trade-off between memory and processing cycles.
In this section, we briefly describe how a standard Dijkstra
algorithm can, for a given destination and bandwidth requirement,
generate a minimum hop path that can accommodate the required
bandwidth and also has maximum bandwidth. Because the Dijkstra
algorithm is already used in the current OSPF route computation,
only differences from the standard algorithm are described. Also,
while for simplicity we do not consider here zero-hop edges (see
Appendix D), the modification required for supporting them is
straightforward.
The algorithm essentially performs a minimum hop path computation,
on a graph from which all edges, whose available bandwidth is less
than that requested by the flow triggering the computation, have been
removed. This can be performed either through a pre-processing step,
or while running the algorithm by checking the available bandwidth
value for any edge that is being considered (pseudo-code for the
algorithm can be found in Appendix B). Another modification to a
standard Dijkstra based minimum hop count path computation, is that
the list of equal cost next (previous) hops which is maintained as
the algorithm proceeds, needs to be sorted according to available
bandwidth. This is to allow selection of the minimum hop path with
maximum available bandwidth. Alternatively, the algorithm could also
be modified to, at each step, only keep among equal hop count paths
the one with maximum available bandwidth. This would essentially
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amount to considering a cost that is function of both hop count and
available bandwidth.
2.3.3. Exact & Approximate Pre-Computed QoS paths (Dijkstra)
This section outlines a Dijkstra-based algorithm that allows
pre-computation of QoS routes for all destinations and bandwidth
values. The benefit of using a Dijkstra-based algorithm is a
greater synergy with existing OSPF implementations. paths is to
consecutively compute shortest path spanning trees starting from
a complete graph and removing links with less bandwidth than the
threshold used in the previous computation. This yields paths with
possibly better bandwidth but of course more hops. Despite large
number of Dijkstra computations involved, several optimizations such
as incremental spanning tree computation can be used and allow for
efficient implementations in terms of complexity as well as storage
since the structure of computed paths leans itself towards path
compression [ST83]. Details including measurements and applicability
studies can be found in [Prz95].
A variation of this theme is to trade the ``accuracy'' of the
pre-computed paths, (i.e., the paths being generated may be of a
larger hop count than needed) for the benefit of using a modified
version of Dijkstra shortest path algorithm and also saving on some
computations. This loss in accuracy comes from the need to rely on
quantized bandwidth values, that are used when computing a minimum
hop count path. In other words, the range of possible bandwidth
values that can be requested by a new flow is mapped into a fixed
number of quantized values, and minimum hop count paths are generated
for each quantized value. For example, one could assume that
bandwidth values are quantized as low, medium, and high, and minimum
hop count paths are computed for each of these three values. A new
flow is then assigned to the minimum hop path that can carry the
smallest quantized value, i.e., low, medium, or high, larger than or
equal to what it requested. We restrict our discussion here to this
``quantized'' version of the algorithm and present its pseudo-code in
Appendix C.
Here too, we discuss the elementary case where all edges count as
``hops'', and note that the modification required for supporting
zero-hop edges is straightforward.
As with the BF algorithm, the algorithm relies on a routing table
that gets built as the algorithm progresses. The structure of the
routing table is as follows:
The QoS routing table:
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- a K x Q matrix, where K is the number of vertices and Q is the
number of quantized bandwidth values.
- The (n;q) entry contains information that identifies the
minimum hop count path to destination n, that is capable of
accommodating a bandwidth request of at least bw[q] (the qth
quantized bandwidth value). It consists of two fields:
* hops: the minimal number of hops on a path between the
source node and destination n, that can accommodate a
request of at least bw[q] units of bandwidth.
* neighbor: this is the routing information associated with
the minimum hop count path to destination node n, whose
available bandwidth is at least bw[q]. With a hop-by-hop
routing approach, the neighbor information is simply the
identity of the node adjacent to the source node on that
path.
The algorithm operates again on a directed graph where vertices
correspond to routers and transit networks. The metric associated
with each edge in the graph is as before the bandwidth available on
the corresponding interface, where bn;mis the available bandwidth
on the edge between vertices n and m. The vertex corresponding to
the router where the algorithm is being run is selected as the source
node for the purpose of path selection, and the algorithm proceeds to
compute paths to all other nodes (destinations).
Starting with the highest quantization index, Q, the algorithm
considers the indices consecutively, in decreasing order. For each
index q, the algorithm deletes from the original network topology
all links (n;m) for which bn;m< bw[q], and then runs on the remaining
topology a Dijkstra-based minimum hop count algorithm (7) between
the source node and all other nodes (vertices) in the graph. Note
that as with the Dijkstra used for on-demand path computation, the
elimination of links such that bn;m < bw[q] could also be performed
while running the algorithm.
After the algorithm terminates, the q-th column in the routing table
is updated. This amounts to recording in the hops field the hop
count value of the path that was generated by the algorithm, and by
updating the neighbor field. As before, the update of the neighbor
----------------------------
7. Note that a Breadth-First-Search (BFS) algorithm
[CLR90] could also be used. It has a lower complexity, but would not
allow reuse of existing code in an OSPF implementation.
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field depends on the scope of the path computation. In the case
of a hop-by-hop routing decision, the neighbor field is set to the
identity of the node adjacent to the source node (next hop) on the
path returned by the algorithm. However, note that in order to
ensure that the path with the maximal available bandwidth is always
chosen among all minimum hop paths that can accommodate a given
quantized bandwidth, a slightly different update mechanism of the
neighbor field needs to be used in some instances. Specifically,
when for a given row, i.e., destination node n, the value of the
hops field in column q is found equal to the value in column q + 1
(here we assume q < Q), i.e., paths that can accommodate bw[q] and
bw[q+ 1] have the same hop count, then the algorithm copies the value
of the neighbor field from entry (n;q+ 1) into that of entry (n;q).
Addition of Stub Networks
This proceeds in a manner very similar to that of Section 2.3.1,
except for some minor variations reflecting differences in the
structure of the QoS routing table. Specifically, the columns of
the QoS routing table now correspond to quantized bandwidth values,
and the bw field of a column entry has been replaced by a hops
field. Hence, the QoS routes for a stub network S are constructed
as follows:
Each entry in the row corresponding to stub network S has its hops
field initialized to zero and its neighbor set to null. When stub
network S is found in the link advertisement of router V, the value
hops(S,q) in the qth column of the row corresponding to stub network
S is updated as follows:
hops(S,q) = hops(V,q) IF (hops(V,q) <= hops(S,q) AND b(V ,S) >=
bw[q]),
where bw[q] is the qth quantized bandwidth value, and b(V,S) is
the advertised available bandwidth on the link from V to S. The
above expression essentially states that the hop count of the path
to stub network S capable of supporting a bandwidth allocation
of bw[q], is updated using a path through router V, only if the
corresponding path through V has fewer hops than the current one,
and the bandwidth on the link between V and S is larger than bw[q].
Update of the neighbor field proceeds similarly whenever the path
through router V capable of supporting a bandwidth allocation of
bw[q], is found to yield a hop count smaller than or equal to the
current value. If it is smaller, then the neighbor field of V in
the corresponding column replaces the current neighbor field of S.
If it is equal, then the neighbor field of V in the corresponding
column is concatenated with the existing field for S, i.e., the
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current set of neighbors for V is added to the current set of
neighbors for S.
2.4. Extracting Forwarding Information from Routing Table
When the QoS paths are precomputed, the forwarding information for
a flow with given destination and bandwidth requirement needs to be
extracted from the routing table. The case of hop-by-hop routing is
much simpler compared to explicit routing. This is because, only the
next hop needs to be returned instead of an explicit route.
Specifically, assume a new request to destination, say, d, and with
bandwidth requirements B. The index of the destination vertex
identifies the row in the QoS routing table that needs to be checked
to generate a path. How the row is searched to identify a suitable
path depends on which algorithm was used to construct the QoS routing
table. If the Bellman-Ford algorithm of Section 2.3.1 is used, the
search proceeds by increasing index (hop) count until an entry is
found, say at hop count or column index of h, with a value of the
bw field which is equal to or larger than B. This entry points
to the initial information identifying the selected path. If the
Dijkstra algorithm of Section 2.3.3 is used, the first quantized
value bBsuch that Bb B is first identified, and the associated
column then determines the first entry in the QoS routing table that
identifies the selected path. The next hop information is then
directly retrieved from the neighbor information of the first entry
pointed to in the QoS routing table.
If the path computation algorithm stores multiple equal cost paths,
then some degree of load balancing can be achieved at the time
of path selection. A next hop from the list of equivalent next
hops can be chosen in a round robin manner, or randomly with equal
probability or randomly with a probability that is weighted by the
actual available bandwidth on the local interface.
The case of explicit routing is discussed in Appendix E.
3. Establishment and Maintenance of QoS Routes
In this section, we briefly review issues related to how QoS paths
are established and maintained. For both, there are functional and
protocol aspects that need to be covered. We primarily address the
functional aspects here and point to other references that address
the protocol aspects.
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The goal of QoS routing is to select paths for flows with QoS
requirements, in such a manner as to increase the likelihood that the
network will indeed be capable of satisfying them. The use of QoS
routing algorithms such as the ones described in this document have a
number of implications above and beyond what is required when using
standard routing algorithms.
First, a specific mechanism needs to be used to identify flows with
QoS requirements, so that they can be assigned to the corresponding
QoS routing algorithm. The RSVP protocol [RZB+97] can be used
for this purpose. Specifically, RSVP PATH messages serve as the
trigger to query QoS routing. Second, because of variations in
the availability of resources in the network, routes between the
same source and destination and for the same QoS, may often differ
depending on when the request is made. However, it is important
to ensure that such changes are not always reflected on existing
paths. This is to avoid potential oscillations between paths and
limit changes to cases where the initial selection turns out to be
inadequate.
As a result, some state information needs to be associated with a
QoS route to determines its current validity, i.e., should the QoS
routing algorithm be queried to generate a new and potentially better
route, or does the current one remain adequate. We say that a path
is ``pinned'' when its state specifies that QoS routing need not be
queried anew, while a path is considered ``unpinned'' otherwise.
The main issue is then to define how, when, and where route pinning
and unpinning is to take place. In our context, where the RSVP
protocol is used as the vehicle to request QoS routes, we also want
this process to be as synergetic as possible with the existing RSVP
state management. In particular, our goal is to support pinning and
unpinning of routes in a manner consistent with RSVP soft states
while requiring minimal changes to the RSVP processing rules.
It should be noted that some changes are unavoidable, especially
to the interface between RSVP and routing. Specifically,
QoS routing requires, in addition to the current source and
destination addresses, at a minimum, knowledge of the flow's traffic
characteristics (TSpec), and possibly also service types (as per the
information in the Adspec), PHOP, IP TTL value, etc.
A broad RSVP-routing interface that enables this is described in
[GKR97]. Use of such an interface in the context of reserving
resources along an explicit path with RSVP is discussed in [GLG+97].
Details of path management and a means of avoiding loops in case of
hop-by-hop path set up can be found in [GKH97].
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4. OSPF Protocol Enhancements
As stated above, a goal of this work is to limit the additions to the
existing OSPF V2 protocol, while still providing the required level
of support for QoS based routing. To this end, all of the existing
OSPF mechanisms, data structures, advertisements, and data formats
remain in place. The purpose of this section of the document is to
list the enhancements to the OSPF protocol to support QoS as outlined
in the previous sections.
4.1. QoS -- Optional Capabilities
The OSPF Options field is present in OSPF Hello packets, Database
Description packets and all LSAs. The Options field enables OSPF
routers to support (or not support) optional capabilities, and to
communicate their capability level to other OSPF routers. Through
this mechanism, routers of differing capabilities can be mixed with
an OSPF routing domain. Currently, RFC 2178 [Moy97] specifies the
following 5 bits in the options octet:
+-----------------------------------------------+
| * | * | DC | EA | N/P | MC | E | * |
+-----------------------------------------------+
Note that the least significant bit (`T' bit) that was used to
indicate TOS routing capability in the older OSPF specification
[Moy94] has been removed. In this context, the current OSPF
specification [Moy97] states that:
``The TOS routing option has been deleted from OSPF. This action
was required by the Internet standards process, due to lack of
implementation experience with OSPF's TOS routing. However, for
backward compatibility the formats of OSPF's various LSAs remain
unchanged, maintaining the ability to specify TOS metrics in
router-LSAs, summary-LSAs, ASBR-summary-LSAs, and AS-external-LSAs.''
We propose to reclaim the `T' bit as an indicator of router's QoS
routing capability. In fact, QoS capability can be viewed as an
extension of the TOS-capabilities and QoS routing as a form of
TOS-based routing. A router sets this bit in its hello packets to
indicate that it is capable of supporting such routing. When this
bit is set in a router or summary links link state advertisement, it
means that there are QoS fields to process in the packet. When this
bit is set in a network link state advertisement it means that the
network described in the advertisement is QoS capable.
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We need to be careful in this approach so as to avoid confusing any
old style (i.e., RFC 1583 based) TOS routing implementations. The
TOS metric encoding rules of QoS fields introduced further in this
section will show how this is achieved. Additionally, unlike the
RFC 1583 specification that unadvertised TOS metrics be treated to
have same cost as TOS 0, for the purpose of computing QOS routes,
unadvertised TOS metrics (on a hop) indicate lack of connectivity for
the specific TOS metrics (for that hop).
4.2. Encoding Resources as Extended TOS
Introduction of QoS should ideally not influence the compatibility
with existing OSPFv2 routers. To achieve this goal, necessary
extensions in packet formats must be defined in a way that either
is understood by OSPFv2 routers, ignored or in the worst case
``gracefully'' misinterpreted. Encoding of QoS metrics in the
TOS field which fortunately enough is longer in OSPF packets
than officially defined in [Alm92], allows us to mimic the new
facility as extended TOS capability. OSPFv2 routers will either
disregard these definitions or consider those unspecified. Specific
precautions are taken to prevent careless OSPF implementations
from influencing traditional TOS routing when misinterpreting the
extension introduced.
For QoS resources, 32 combinations are available through the use
of the fifth bit in TOS fields contained in different LSAs. Since
[Alm92] defines TOS as being four bits long, this definition never
conflicts with existing values. Additionally, to prevent naive
implementations that do not take all bits of the TOS field in OSPF
packets into considerations, the definitions of the `QoS encodings'
is aligned in their semantics with the TOS encoding. Only bandwidth
and delay are specified as of today and their values map onto
`maximize throughput' and `minimize delay' if the most significant
bit is not taken into account. Accordingly, link reliability and
jitter could be defined later if necessary.
OSPF encoding RFC 1349 TOS values
___________________________________________
0 0000 normal service
2 0001 minimize monetary cost
4 0010 maximize reliability
6 0011
8 0100 maximize throughput
10 0101
12 0110
14 0111
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16 1000 minimize delay
18 1001
20 1010
22 1011
24 1100
26 1101
28 1110
30 1111
OSPF encoding `QoS encoding values'
-------------------------------------------
32 10000
34 10001
36 10010
38 10011
40 10100 bandwidth
42 10101
44 10110
46 10111
48 11000 delay
50 11001
52 11010
54 11011
56 11100
58 11101
60 11110
62 11111
Representing TOS and QoS in OSPF.
4.2.1. Encoding bandwidth resource
Given the fact that the actual metric field in OSPF packets only
provides 16 bits to encode the value used and that links supporting
bandwidth ranging into Gbits/s are becoming reality, linear
representation of the available resource metric is not feasible. The
solution is exponential encoding using appropriately chosen implicit
base value and number bits for encoding mantissa and the exponent.
Detailed considerations leading to the solution described are not
presented here but can be found in [Prz95].
Given a base of 8, the 3 most significant bits should be reserved for
the exponent part and the remaining 13 for the mantissa. This allows
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a simple comparison for two numbers encoded in this form, which is
often useful during implementation.
The following table shows bandwidth ranges covered when using
different exponents and the granularity of possible reservations.
exponent
value x range (2^13-1)*8^x step 8^x
-------------------------------------------------
0 8,191 1
1 65,528 8
2 524,224 64
3 4,193,792 512
4 33,550,336 4,096
5 268,402,688 32,768
6 2,147,221,504 262,144
7 17,177,772,032 2,097,152
Ranges of Exponent Values for 13 bits,
base 8 Encoding, in Bytes/s
The bandwidth encoding rule may be summarized as: ``represent
available bandwidth in 16 bit field as a 3 bit exponent (with assumed
base of 8) followed by a 13 bit mantissa as shown below
0 8 16
| | |
-----------------
|EXP| MANT |
-----------------
and advertise 2's complement of the above representation.''
Thus, the above encoding advertises a numeric value that is
2^16 -1 -(exponential encoding of the available bandwidth):
This has the property of advertising a higher numeric value for lower
available bandwidth, a notion that is consistent with that of cost.
Although it may seem slightly pedantic to insist on the property
that less bandwidth is expressed higher values, it has, besides
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consistency, a robustness aspect in it. A router with a poor OSPF
implementation could misuse or misunderstand bandwidth metric as
normal administrative cost provided to it and compute spanning trees
with a ``normal'' Dijkstra. The effect of a heavily congested link
advertising numerically very low cost could be disastrous in such
a scenario. It would raise the link's attractiveness for future
traffic instead of lowering it. Evidence that such considerations
are not speculative, but similar scenarios have been encountered, can
be found in [Tan89].
Concluding with an example, assume a link with bandwidth of 8
Gbits/s = 1024^3 Bytes/s, its encoding would consist of an exponent
value of 6 since 1024^3 = 4; 096 * 8^6, which would then have a
granularity of 8^6 approx. 260 kBytes/s. The associated binary
representation would then be %(110) 0 1000 0000 0000% or 53,248 (8).
The bandwidth cost (advertised value) of this link when it is idle,
is then the 2's complement of the above binary representation,
i.e., %(001) 1 0111 1111 1111% which corresponds to a decimal
value of (2^16 - 1) - 53;248 = 12;287. Assuming now a current
reservation level of of 6;400 Mbits/s = 200 * 1024^2, there remains
1;600 Mbits/s of available bandwidth on the link. The encoding
of this available bandwidth of 1'600 Mbits/s is 6;400 * 8^5, which
corresponds to a granularity of 8^5 approx. 30 kBytes/s, and has a
binary representation of %(101) 1 1001 0000 0000% or decimal value
of 47,360. The advertised cost of the link with this load level, is
then %(010) 0 0110 1111 1111%, or (2^16-1) -47;360 = 18;175.
Note that the cost function behaves as it should, i.e., the less
bandwidth is available on a link, the higher the cost and the less
attractive the link becomes. Furthermore, the targeted property of
better granularity for links with less bandwidth available is also
achieved. It should, however, be pointed out that the numbers given
in the above examples match exactly the resolution of the proposed
encoding, which is of course not always the case in practice. This
leaves open the question of how to encode available bandwidth
values when they do not exactly match the encoding. The standard
practice is to round it to the closest number. Because we are
ultimately interested in the cost value for which it may be better
to be pessimistic than optimistic, we choose to round costs up and,
therefore, bandwidth down.
----------------------------
8. exponent in parenthesis
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4.2.2. Encoding Delay
Delay is encoded in microseconds using the same exponential method
as described for bandwidth except that the base is defined to be 4
instead of 8. Therefore the maximum delay that can be expressed is
(2^13-1) *4^7 approx.134 seconds.
4.3. Packet Formats
Given the extended TOS notation to account for QoS metrics, no
changes in packet formats are necessary except for the introduction
of Q-bit in the options field. Routers not understanding the Q-bit
should either not consider the QoS metrics distributed or consider
those as `unknown' TOS.
4.4. Calculating the Inter-area Routes
This document proposes a very limited use of OSPF areas, that is, it
is assumed that summary links advertisements exist for all networks
in the area. This document does not discuss the problem of providing
support for area address ranges and QoS metric aggregation. This is
left for further studies.
4.5. Open Issues
Support for AS External Links, Virtual Links, and incremental updates
for summary link advertisements are not addressed in this document
and are left for further study. For Virtual Links that do exist, it
is assumed for path selection that these links are non-QoS capable
even if the router advertises QoS capability. Also, as stated
earlier, this document does not address the issue of non-QoS routers
within a QoS domain.
Acknowledgments
We would like to thank the many people who have helped shape various
aspects of this document and the approaches it describes, either
through discussions or explicit suggestions. In particular, we would
like to acknowledge the help and inputs of John Moy, Dilip Kandlur,
George Apostolopoulos and Dimitrios Pendarakis.
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APPENDICES
A. Pseudocode for BF Algorithm
Note: The pseudocode below assumes a hop-by-hop forwarding approach in
updating the neighbor field. The modifications needed to support
explicit route construction are straightforward. The pseudocode
also does not handle equal cost multi-paths for simplicity, but the
modification needed to add this support are straightforward.
Input:
V = set of vertices, labeled by integers 1 to N.
L = set of edges, labeled by ordered pairs (n,m) of vertex labels.
s = source vertex (at which the algorithm is executed).
For all edges (n,m) in L:
* b(n,m) = available bandwidth (according to last received update)
on interface associated with the edge between vertices n and m.
* If(n,m) outgoing interface corresponding to edge (n,m) when n is
a router.
H = maximum hop-count (at most the graph diameter).
Type:
tab_entry: record
bw = integer,
neighbor = integer 1..N.
Variables:
TT[1..N, 1..H]: topology table, whose (n,h) entry is a tab_entry record, such
that:
TT[n,h].bw is the maximum available bandwidth (as known
thus far) on a path of at most h hops between
vertices s and n,
TT[n,h].neighbor is the first hop on that path (a neighbor
of s). It is either a router or the destination n.
S_prev: list of vertices that changed a bw value in the TT table
in the previous iteration.
S_new: list of vertices that changed a bw value (in the TT table
etc.) in the current iteration.
The Algorithm:
begin;
for n:=1 to N do /* initialization */
begin;
TT[n,0].bw := 0;
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TT[n,0].neighbor := null
TT[n,1].bw := 0;
TT[n,1].neighbor := null
end;
TT[s,0].bw := infinity;
reset S_prev;
for all neighbors n of s do
begin;
TT[n,1].bw := max( TT[n,1].bw, b[s,n]);
if (TT[n,1].bw = b[s,n]) then TT[n,1].neighbor := If(s,n);
/* need to make sure we are picking the maximum */
/* bandwidth path for routers that can be reached */
/* through both networks and point-to-point links */
if (n is a router) then
S_prev := S_prev union {n}
/* only a router is added to S_prev, */
/* if it is not already included in S_prev */
else /* n is a network: */
/* proceed with network--router edges, without */
/* counting another hop */
for all (n,k) in L, k <> s, do
/* i.e., for all other neighboring routers of n */
begin;
TT[k,1].bw := max( min( TT[n,1].bw, b[n,k]), TT[k,1].bw );
/* In case k could be reached through another path */
/* (a point-to-point link or another network) with */
/* more bandwidth, we do not want to update TT[k,1].bw */
if (min( TT[n,1].bw, b[n,k]) = TT[k,1].bw )
/* If we have updated TT[k,1].bw by going through */
/* network n */
then TT[k,1].neighbor := If(s,n);
/* neighbor is interface to network n */
if ( {k} not in S_prev) then S_prev := S_prev union {k}
/* only routers are added to S_prev, but we again need */
/* to check they are not already included in S_prev */
end
end;
for h:=2 to H do /* consider all possible number of hops */
begin;
reset S_new;
for all vertices m in V do
begin;
TT[m,h].bw := TT[m,h-1].bw;
TT[m,h].neighbor := TT[m,h-1].neighbor
end;
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for all vertices n in S_prev do
/* as shall become evident, S_prev contains only routers */
begin;
for all edges (n,m) in L do
if min( TT[n,h-1].bw, b[n,m]) > TT[m,h].bw then
begin;
TT[m,h].bw := min( TT[n,h-1].bw, b[n,m]);
TT[m,h].neighbor := TT[n,h-1].neighbor;
if m is a router then S_new := S_new union {m}
/* only routers are added to S_new */
else /* m is a network: */
/* proceed with network--router edges, without counting them as */
/* another hop */
for all (m,k) in L, k <> n,
/* i.e., for all other neighboring routers of m */
if min( TT[m,h].bw, b[m,k]) > TT[k,h].bw then
begin;
/* Note: still counting it as the h-th hop, as (m,k) is a */
/* network--router edge */
TT[k,h].bw := min( TT[m,h].bw, b[m,k]);
TT[k,h].neighbor := TT[m,h].neighbor;
S_new := S_new union {k}
/* only routers are added to S_new */
end
end
end;
S_prev := S_new;
/* the two lists can be handled by a toggle bit */
if S_prev=null then h=H+1 /* if no changes then exit */
end;
end.
B. Pseudocode for On-Demand Dijkstra Algorithm
Note: The pseudocode below assumes a hop-by-hop forwarding approach in
updating the neighbor field. The modifications needed to support
explicit route construction are straightforward. The pseudocode
also does not handle equal cost multi-paths for simplicity, but the
modifications needed to add this support have been described in
section 2.3.2 and are straightforward.
Input:
V = set of vertices, labeled by integers 1 to N.
L = set of edges, labeled by ordered pairs (n,m) of vertex labels.
s = source vertex (at which the algorithm is executed).
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For all edges (n,m) in L:
* b(n,m) = available bandwidth (according to last received update)
on interface associated with the edge between vertices n and m.
* If(n,m) = outgoing interface corresponding to edge (n,m) when n is
a router.
d = destination vertex.
B = requested bandwidth for the flow served.
Type:
tab_entry: record
hops = integer,
neighbor = integer 1..N,
ontree = boolean.
Variables:
TT[1..N]: topology table, whose (n) entry is a tab_entry
record, such that:
TT[n].bw is the available bandwidth (as known
thus far) on a shortest-path between
vertices s and n,
TT[n].neighbor is the first hop on that path (a neighbor
of s). It is either a router or the destination n.
S: list of candidate vertices;
v: vertex under consideration;
The Algorithm:
begin;
for n:=1 to N do /* initialization */
begin;
TT[n].hops := infinity;
TT[n].neighbor := null;
TT[n].ontree := FALSE;
end;
TT[s].hops := 0;
reset S;
v:= s;
while v <> d do
begin;
TT[v].ontree := TRUE;
for all edges (v,m) in L and b(v,m) >= B do
begin;
if m is a router
begin;
if not TT[m].ontree then
begin;
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/* bandwidth must be fulfilled since all links >= B */
if TT[m].hops > TT[v].hops + 1 then
begin
S := S union { m };
TT[m].hops := TT[v].hops + 1;
TT[m].neighbor := v;
end;
end;
end;
else /* must be a network, iterate over all attached routers */
begin; /* each network -- router edge treated as zero hop edge */
for all (m,k) in L, k <> v,
/* i.e., for all other neighboring routers of m */
if not TT[k].ontree and b(m,k) >= B then
begin;
if TT[k].hops > TT[v].hops then
begin;
S := S union { k };
TT[k].hops := TT[v].hops;
TT[k].neighbor := v;
end;
end;
end;
end; /* of all edges from the vertex under consideration */
if S is empty then
begin;
v=d; /* which will end the algorithm */
end;
else
begin;
v := first element of S;
S := S - {v}; /* remove and store the candidate to consider */
end;
end; /* from processing of the candidate list */
end.
C. Pseudocode for Precomputed Dijkstra Algorithm
Note: The pseudocode below assumes a hop-by-hop forwarding approach in
updating the neighbor field. The modifications needed to support
explicit route construction are straightforward. The pseudocode
also does not handle equal cost multi-paths for simplicity, but
the modification needed to add this support have been described in
section 2.3.2 and are straightforward.
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Input:
V = set of vertices, labeled by integers 1 to N.
L = set of edges, labeled by ordered pairs (n,m) of vertex labels.
s = source vertex (at which the algorithm is executed).
bw[1..Q] = array of bandwidth values to ``quantize'' flow requests to.
For all edges (n,m) in L:
* b(n,m) = available bandwidth (according to last received update)
on interface associated with the edge between vertices n and m.
* If(n,m) = outgoing interface corresponding to edge (n,m) when n is
a router.
Type:
tab_entry: record
hops = integer,
neighbor = integer 1..N,
ontree = boolean.
Variables:
TT[1..N, 1..Q]: topology table, whose (n,q) entry is a tab_entry
record, such that:
TT[n,q].bw is the available bandwidth (as known
thus far) on a shortest-path between
vertices s and n accommodating bandwidth b(q),
TT[n,q].neighbor is the first hop on that path (a neighbor
of s). It is either a router or the destination n.
S: list of candidate vertices;
v: vertex under consideration;
q: ``quantize'' step
The Algorithm:
begin;
for r:=1 to Q do
begin;
for n:=1 to N do /* initialization */
begin;
TT[n,r].hops := infinity;
TT[n,r].neighbor := null;
TT[n,r].ontree := FALSE;
end;
TT[s,r].hops := 0;
end;
for r:=1 to Q do
begin;
S = {s};
while S not empty do
begin;
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v := first element of S;
S := S - {v}; /* remove and store the candidate to consider */
TT[v,r].ontree := TRUE;
for all edges (v,m) in L and b(v,m) >= bw[r] do
begin;
if m is a router
begin;
if not TT[m,r].ontree then
begin;
/* bandwidth must be fulfilled since all links >= bw[r] */
if TT[m,r].hops > TT[v,r].hops + 1 then
begin
S := S union { m };
TT[m,r].hops := TT[v,r].hops + 1;
TT[m,r].neighbor := v;
end;
end;
end;
else /* must be a network, iterate over all attached
routers */
begin;
for all (m,k) in L, k <> v,
/* i.e., for all other neighboring routers of m */
if not TT[k,r].ontree and b(m,k) >= bw[r] then
begin;
if TT[k,r].hops > TT[v,r].hops + 2 then
begin;
S := S union { k };
TT[k,r].hops := TT[v,r].hops + 2;
TT[k,r].neighbor := v;
end;
end;
end;
end; /* of all edges from the vertex under consideration */
end; /* from processing of the candidate list */
end; /* of ``quantize'' steps */
end.
D. Zero-Hop Edges
The need to handle zero-hop edges is due to the potential presence
of multiple access networks, e.g., T/R, E/N, or ATM, to interconnect
routers. Such entities are also represented by means of a vertex
in the current OSPF operation. Clearly, in such cases a network
connecting two routers should be considered as a single hop path
rather than a two hop path. For example, consider three routers
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A, B, and C connected over an Ethernet network N, which the OSPF
topology represents as:
In the above example, although there are directed edges in both
directions, an edge from the network to any of the three routers
must have zero ``cost'', so that it is not counted twice. It should
be noted that when considering such environments in the context
of QoS routing, it is assumed that some entity is responsible
for determining the ``available bandwidth'' on the network. The
specification of the operation of such an entity is beyond the scope
of this document.
E. Explicit Routing Support
As mentioned before, the scope of the path selection process can
range from simply returning the next hop on the QoS path selected for
the flow, to specifying the complete path that was computed, i.e.,
an explicit route. Obviously, the information being returned by the
path selection algorithm differs in these two cases, and constructing
it imposes different requirements on the path computation algorithm
and the data structures it relies on. While the presentation of
the path computation algorithms focused on the hop-by-hop routing
approach, the same algorithms can be applied to generate explicit
routes with minor modifications. These modifications and how they
facilitate constructing explicit routes are discussed next.
The general approach to facilitate construction of explicit routes
is to update the neighbor field differently from the way it is done
for hop-by-hop routing as described in Section 2. Recall that in the
path computation algorithms the neighbor field is updated to reflect
the identity of the node adjacent to the source node on the partial
path computed. This facilitates returning the next hop at the
source for the specific path. In the context of explicit routing,
the neighbor information is updated to reflect the identity of the
previous router on the path.
In general, there can be multiple equivalent paths for a given hop
count. Thus, the neighbor information is stored as a list rather
than single value. Associated with each neighbor, additional
A----N----B
|
|
C
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information is stored to facilitate load balancing among these
multiple paths at the time of path selection. Specifically, we store
the advertised available bandwidth on the link from the neighbor to
the destination in the entry.
With this change, the basic approach used to extract the complete
list of vertices on a path from the neighbor information in the QoS
routing table is to proceed `recursively' from the destination to
the origin vertex. The path is extracted by stepping through the
precomputed QoS routing table from vertex to vertex, and identifying
at each step the corresponding neighbor (precursor) information. The
process is described as recursive since the neighbor node identified
in one step becomes the destination node for table look up in the
next step. Once the source router is reached, the concatenation of
all the neighbor fields that have been extracted forms the desired
explicit route. This applies to algorithms of Sections 2.3.1 and
2.3.3. If at a particular stage there are multiple neighbor choices
(due to equal cost multi-paths), one of them can be chosen at random
with a probability that is weighted by the associated bandwidth on
the link from the neighbor to the (current) destination.
Specifically, assume a new request to destination, say, d, and with
bandwidth requirements B. The index of the destination vertex
identifies the row in the QoS routing table that needs to be checked
to generate a path. How the row is searched to identify a suitable
path depends on which algorithm was used to construct the QoS routing
table. If the Bellman-Ford algorithm of Section 2.3.1 is used, the
search proceeds by increasing index (hop) count until an entry is
found, say at hop count or column index of h, with a value of the bw
field that is equal to or greater than B. This entry points to the
initial information identifying the selected path. If the Dijkstra
algorithm of Section 2.3.3 is used, the first quantized value bB
such that bB B is first identified, and the associated column then
determines the first entry in the QoS routing table that identifies
the selected path.
Once this first entry has been identified, reconstruction of the
complete list of vertices on the path proceeds similarly, whether
the table was built using the algorithm of Sections 2.3.1 or 2.3.3.
Specifically, in both cases, the neighbor field in each entry points
to the previous node on the path from the source node and with the
same bandwidth capabilities as those associated with the current
entry. The complete path is, therefore, reconstructed by following
the pointers provided by the neighbor field of successive entries.
In the case of the Bellman-Ford algorithm of Section 2.3.1, this
means moving backwards in the table from column to column, using at
each step the row index pointed to by the neighbor field of the entry
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in the previous column. Each time, the corresponding vertex index
specified in the neighbor field is pre-pended to the list of vertices
constructed so far. Since we start at column h, the process ends
when first column is reached, i.e., after h steps, at which point
the list of vertices making up the path has been reconstructed.
In the case of the Dijkstra algorithm of Section 2.3.3, the
backtracking process is similar although slightly different because
of the different relation between paths and columns in the routing
table, i.e., a column now corresponds to a quantized bandwidth value
instead of a hop count. The backtracking now proceeds along the
column corresponding to the quantized bandwidth value needed to
satisfy the bandwidth requirements of the flow. At each step, the
vertex index specified in the neighbor field is pre-pended to the
list of vertices constructed so far, and is used to identify the next
row index to move to. The process ends when an entry is reached
whose neighbor field specifies the origin vertex of the flow. Note
that since there are as many rows in the table as there are vertices
in the graph, i.e., N, it could take up to N steps before the
process terminates.
Note that the identification of the first entry in the routing table
is identical to what was described for the hop-by-hop routing case.
However, as described in this section, the update of the neighbor
fields while constructing the QoS routing tables, is being performed
differently in the explicit and hop-by-hop routing cases. Clearly,
two different neighbor fields can be kept in each entry and updates
to both could certainly be performed jointly, if support for both
explicit routing and hop-by-hop routing is needed.
F. Computational Complexity
One generic aspect of the algorithmic complexity of computing
QoS paths is the efficiency of the shortest path algorithm used.
Specifically, in this document, we have described approaches based on
both Bellman-Ford and Dijkstra shortest paths algorithms. Dijkstra's
algorithm has traditionally been considered more efficient for
standard shortest path computations because of its lower worst case
complexity. However, the answer is not as simple as may appear, and
in this section we briefly review a number of considerations, in
particular in the context of multi-criteria QoS paths, which indicate
that a BF approach may often provide a lower complexity solution.
The asymptotic worst-case complexity of the Dijkstra algorithm is
O(NlogN + M), where N is the number of vertices in the graph,
and M the number of edges. However, this bound is obtained
under the assumption of a Fibonnaci heap implementation of the
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Dijkstra algorithm, which is impractical due to the large constants
involved [CLR90]. In practice, the Dijkstra algorithm is typically
implemented using binary heaps, for which the asymptotic worst-case
bound is O(MlogN).
The asymptotic worst-case bound for the BF algorithm is O(H . M),
where M is again the number of edges in the graph, and H, which is
the maximum number of iterations of the algorithm, is an upper-bound
on the number of hops in a shortest path. Although, theoretically,
H can be as large as N - 1, in practice it is usually considerably
smaller than N. Moreover, in some network scenarios an upper-bound
U of small size (i.e., U << N) is imposed on the allowed number
of hops; for example, it might be decided to exclude paths that
have more than, say, 16 hops, as part of a call admission scheme.
In such cases, the number of iterations of the BF algorithm can be
limited to U, thus bounding the number of operations to O(U . M),
i.e., effectively to O(M). As a consequence, as noted in [BG92],
in practical networking scenarios, the BF algorithm can offer an
efficient solution to the shortest path problem, one that often
outperforms the Dijkstra algorithm. (9)
In the context of QoS path selection, the potential benefits of the
BF algorithm are even stronger. As mentioned before, efficient
selection of a suitable path for flows with QoS requirements cannot
usually be handled using a single-objective optimization criterion.
While multi-objective path selection is known to be an intractable
problem [GJ79], the BF algorithm allows us to handle a second
objective, namely the hop-count, which is reflective of network
resources, at no additional cost in terms of complexity. The
Dijkstra algorithm requires some modifications (or approximations,
e.g., bandwidth quantization) in order to be able to deal with hop
count as a second objective.
Therefore, in the context of a QoS path selection algorithm,
where one objective is some QoS-oriented metric, such as available
bandwidth, whereas the second is a hop-count metric, a BF-based
algorithm provides an efficient scheme for pre-computing paths,
i.e., one with a worst case asymptotic complexity of O(H . M).
Alternatively, if QoS paths are pre-computed using a Dijkstra
----------------------------
9. For example, in the experimental comparison reported in [CGR94], the
BF algorithm outperformed the Dijkstra algorithm in about one third
of the studied types of topology, and in several of the other
topologies it outperformed the Dijkstra algorithm for networks of up
to about 16,000 nodes. It should be noted that in those experiments
no upper bound on the number of hops in a shortest path was set.
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algorithm with Q quantized bandwidth values, the corresponding worst
case asymptotic complexity is O(Q . (M logN)). Both approaches
provide solutions of comparable orders of complexity, whose exact
merits depend on the respective values of H, Q and N. If on-demand
computations of QoS paths are practical, then a standard Dijkstra
algorithm provides a solution of complexity O(MlogN).
G. Extension: Handling Propagation Delays
In general, the framework proposed for path selection does not allow
us to explicitly account for link propagation delays. As mentioned,
this aspect is dealt with through a policy mechanism, which for
delay-sensitive connections deletes from the topology database links
with high propagation delays, such as satellite links. However, it
is worth pointing out that a simple extension to the proposed path
selection algorithm allows us to directly account for delay in a
number of special cases. We proceed to describe next this extension
and the case where it applies.
A common way to map delay guarantees into bandwidth guarantees
(e.g., consistent with the schedulers and corresponding delay
bounds presented in [GGPS96, PG94]) is according to the following
expression:
D(p) =A(h(p))=b +sum(l in p) d(l) (1)
where p is the path traversed, D(p) is the guaranteed (upper-bound)
end to end delay, h(p) is the number of hops, b is the reserved
bandwidth, d(l) is the (fixed) propagation delay of a link l, and A(h)
is a parameter that grows with h (a typical value is A(h)= B +h . c,
where B is the burst size and c is the maximum packet size).
Since we deal with intra-domain routing, and since links with
prohibitively high propagation delays are assumed to be filtered out
by means of policy, it can be assumed that typically there is some
value d which is a reasonable upper bound on the propagation delays
d(l) of all links. Expression (1) then implies that an end to end
delay requirement D can be translated into a bandwidth requirement
b(h) by the following expression:
b(h) =A(h)=(D -h. d) (2)
where h is the number of hops on the path established for the
connection.
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H. Accounting for Link Metric Inaccuracy in Path Selection
Suppose that each node sends a Link State Advertisement (LSA) only
when the ratio between the current value bw of a link and the last
reported value is above (or below) some threshold, say 2. (10).
This implies that, when a path with some b units of bandwidth is
sought, links with advertised bandwidth values above 2 . b are ``safe
bets'', those with values below b_2should be excluded, and all the
rest may supply the required bandwidth with various degrees of
certainty. This means that a third objective is added to our two
standard objectives of bandwidth and hop count, namely certainty.
Its incorporation in the path selection process can be handled with
various degrees of complexity and sophistication, of which we outline
a few. For further enhancements of these schemes the reader is
referred to [GOW97].
(1) A probabilistic approach: The bandwidth value of a link l is, for
the decision maker, a random variable that takes values in (bl_2;2 . bl),
where blis the last advertised value. Making some assumptions
on the probability distribution of these values, e.g. uniform
distributions, one can compute for each bandwidth requirement b
the success probability of a link l, say pl(b), and then run a BF
algorithm on the metric {wl}, where wl = -log(pl(b)) (see [GO97] for
details). However, the problem here is that a different path should
be computed for each bandwidth value b, hence rendering this approach
too complex in the case of pre-computed routes. We are thus behooved
to consider a simpler approach.
(2) A simple approach:
Here we run the standard BF algorithm, described in Section
2.3.1, obtaining as an output an N . H QoS routing table. Let ff,
0:5 ff 1, be a parameter that indicates the ``risk proneness''
of the decision maker (the lower the value, the higher the risk
proneness is). Also, let HR be a parameter that indicates how
many hops the decision maker is willing to trade for safety. Then,
upon accommodating a connection request with b values of bandwidth,
perform the following:
1. From the routing table, get hmin, the minimal number of hops of a
path with bandwidth of at least ff.b units.
----------------------------
10. To keep the discussion simple, we do not bother here about potential
oscillations when the values become very small, an issue that can be
addressed by switching to an additive rule for such values.
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2. From the routing table, get hmax, the minimal number of hops of a
safe path, i.e., with bandwidth of at least 2.b.
3. If hmin+ HR hmax: choose the safe path.
4. Otherwise: from the table, choose the path that has the maximal
bandwidth among those having at most hmin+ HR hops.
References
[Alm92] P. Almquist. Type of Service in the Internet Protocol
Suite. INTERNET-RFC, July 1992.
[BG92] D. Bertsekas and R. G. Gallager. Data Networks. Prentice
Hall, Englewood Cliffs, NJ, 2nd edition, 1992.
[Car79] B. Carre. Graphs and Networks. Oxford University Press,
ISBN 0-19-859622-7, Oxford, GB, 1979.
[CGR94] B. V. Cherkassky, A. V. Goldberg, and T. Radzik. Shortest
Paths Algorithms: Theory and Experimental Evaluation.
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[CLR90] T. H. Cormen, C. E. Leiserson, and R. L. Rivest.
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[GGPS96] L. Georgiadis, R. Guerin, V. Peris, and K. N. Sivarajan.
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[GLG+97] Der-Hwa Gan, T. Li, R. Guerin, E. Rosen, and S. Kamat.
Setting up reservations on explicit paths using rsvp.
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Inaccurate Information: Theory and Algorithms. In IEEE
INFOCOM'97, pages 75--83, Kobe, Japan, April 1997.
[GOW97] R. Guerin, A. Orda, and D. Williams. QoS Routing
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Authors' Address
Roch Guerin
IBM T.J. Watson Research Center
P.O. Box 704
Yorktown Heights, NY 10598
guerin@watson.ibm.com
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VOICE +1 914 784-7038
FAX +1 914 784-6205
Sanjay Kamat
IBM T.J. Watson Research Center
P.O. Box 704
Yorktown Heights, NY 10598
sanjay@watson.ibm.com
VOICE +1 914 784-7402
FAX +1 914 784-6205
Ariel Orda
Dept. Electrical Engineering
Technion - I.I.T
Haifa, 32000 - ISRAEL
ariel@ee.technion.ac.il
VOICE +011 972-4-8294646
FAX +011 972-4-8323041
Tony Przygienda
Bell Labs, Lucent Technologies
prz@dnrc.bell-labs.com
VOICE +1 732 949-5936
Doug Williams
IBM T.J. Watson Research Center
P.O. Box 704
Yorktown Heights, NY 10598
dougw@watson.ibm.com
VOICE +1 914 784-5047
FAX +1 914 784-6318
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