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Building power shortest inter-Area TE LSPs using pre-computed paths
draft-mjsraman-rtgwg-intra-as-psp-te-leak-01

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This is an older version of an Internet-Draft whose latest revision state is "Expired".
Authors Shankar Raman , Balaji Venkat Venkataswami , Gaurav Raina
Last updated 2012-03-11
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draft-mjsraman-rtgwg-intra-as-psp-te-leak-01
RTGWG Working Group                                        Shankar Raman
Internet-Draft                                Balaji Venkat Venkataswami
Intended Status: Experimental RFC                           Gaurav Raina
Expires: September 2012                                    I.I.T, Madras
                                                          March 11, 2012

  Building power shortest inter-Area TE LSPs using pre-computed paths
              draft-mjsraman-rtgwg-intra-as-psp-te-leak-01

Abstract

   In this paper, we propose a framework to reduce the aggregate power
   consumption of an Autonomous System (AS) using a collaborative
   approach between areas within an AS. We identify the low-power paths
   within non-backbone areas and then use Traffic Engineering (TE)
   techniques to route the packets along the stitched paths from non-
   backbone areas / backbone area to other non-backbone areas. Such low-
   power paths can be identified by using the power-to-available-
   bandwidth (PWR) ratio as an additional constraint in the Constrained
   Shortest Path First (CSPF) algorithm. For routing the data traffic
   through these low-power paths, the Inter-Area Traffic Engineered
   Label Switched Path (TE-LSP) that spans multiple areas can be used.
   Extensions to the Interior Gateway Protocols like OSPF and IS-IS that
   support TE extensions can be used to disseminate information about
   low-power paths in the respective areas (backbone or non-backbone)
   that minimize the PWR ratio metric on the links within the areas and
   between the areas thereby creating a collaborative approach to reduce
   the power consumption. 

   The feasibility of our approaches is illustrated by applying our
   algorithm to an AS with a backbone area and several non-backbone
   areas. The techniques proposed in this paper for the Inter-Area power
   reduced paths require a few modifications to the existing features of
   the IGPs supporting TE extensions. The proposed techniques can be
   extended to other levels of Internet hierarchy, such as Inter-AS
   paths, through suitable modifications as in [11].

   When link state routing protocols like OSPF or ISIS are used to
   discover TE topology, there is the limitation that traffic engineered
   paths can be set up only when the head and tail end of the label
   switched path are in the same area. There are solutions to overcome
   this limitation either using offline Path Computation Engine (PCE)
   that attach to multiple areas and know the topology of all areas.
   This document proposes an alternative approach that does not require
   any centralized PCE and uses selective leaking of low-power TE path
   information from one area into other areas. 
 

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Status of this Memo

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Table of Contents

   1  Introduction  . . . . . . . . . . . . . . . . . . . . . . . . .  4
     1.1  Terminology . . . . . . . . . . . . . . . . . . . . . . . .  4
     1.1 Low-power routers and switches . . . . . . . . . . . . . . .  4
     1.2 Power reduction using routing and traffic engineering  . . .  4
   2.  Methodology of the proposal  . . . . . . . . . . . . . . . . .  6
     2.1 ABR Operation  . . . . . . . . . . . . . . . . . . . . . . .  6
     2.2 TE Path Head-end Operation . . . . . . . . . . . . . . . . . 10
 

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     2.3 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . 12
   3  Security Considerations . . . . . . . . . . . . . . . . . . . . 13
   4  IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 13
   5  References  . . . . . . . . . . . . . . . . . . . . . . . . . . 13
     5.1  Normative References  . . . . . . . . . . . . . . . . . . . 13
     5.2  Informative References  . . . . . . . . . . . . . . . . . . 13
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 14

 

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1  Introduction

   Estimates of power consumption for the Internet predict a 300%
   increase, as access speeds increase from 10 Mbps to 100 Mbps [3],
   [8]. Access speeds are likely to increase as new video, voice and
   gaming devices get added to the Internet. Various approaches have
   been proposed to reduce the power consumption of the Internet such as
   designing low-power routers and switches, and optimizing the network
   topology using traffic engineering methods [2].

1.1  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [RFC2119].

1.1 Low-power routers and switches

   Low-power router and switch design aim at reducing the power consumed
   by hardware architectural components such as transmission link,
   lookup tables and memory. In [4] it is shown that the router's link
   power consumption can vary by 20 Watts between idle and traffic
   scenarios. Hence the authors suggest having more line cards and
   running them to capacity: operating the router at full throughput
   will lead to less power per bit, and hence larger packet lengths will
   consume lower power. The two important components in routers that
   have received attention for high power consumption are buffers and
   TCAMs. Buffers are built using dynamic RAM (DRAM) or static RAM
   (SRAM). SRAMs are limited in size and consume more power, but have
   low access times. Guido [1] states that a 40Gb/s line card would
   require more than 300 SRAM chips and consume 2:5kW. DRAM access times
   prevent them from being used on high speed line cards. Sometimes the
   buffering of packets in DRAM is done at the back end, while SRAM is
   used at the front end for fast data access. But these schemes cannot
   scale with increasing line speeds. Some variants of TCAMs have been
   proposed for increasing line speeds and for reduced power consumption
   [7].

1.2 Power reduction using routing and traffic engineering

   At the Internet level, creating a topology that allows route
   adaptation, capacity scaling and power-aware service rate tuning,
   will reduce power consumption. In [8] the author has proposed a
   technique to traffic engineer the data packets in such a way that the
   link capacity between routers is optimized. Links which are not
   utilized are moved to the idle state. Power consumption can be
   reduced by trading off performance related measures like latency. For
 

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   example, power savings while switching from 1 Gbps to 100 Mbps is
   approximately 4 W and from 100 Mbps to 10 Mbps around 0:1 Watts.
   Hence instead of operating at 1 Gbps the link speed could be reduced
   to a lower bandwidth under certain conditions for reduced power
   consumption.

   Multi layer traffic engineering based methods make use of parameters
   such as resource usage, bandwidth, throughput and QoS measures, for
   power reduction. In [6] an approach for reducing Intra-AS power
   consumption for optical networks that uses Djikstra's shortest path
   algorithm is proposed. The input to this method assumes the existence
   of a network topology using which an auxiliary graph is constructed.
   Power optimization is done on the auxiliary graph and traffic is
   routed through the low-power links. However, the algorithm expects
   the topology to be available for getting the auxiliary graph. This
   topology is easy to obtain for Intra-AS scenario, but by using a
   centralized PCE (Path Computation Element) as in a hierarchical PCE
   approach. Here for each area a PCE is assigned and each such PCE
   calculates the path from a head-end router to a tail-end router, both
   falling within the same area. When TE paths have to be stitched
   across several areas then the hierarchical PCE which may be one level
   up from the respective area PCEs is contacted for such a stitching.

   In our approach, we propose a collaborative approach by the
   respective areas in calculating low-power paths that result in power
   reduction within an AS. This document proposes an alternative
   approach that does not require any centralized PCE and uses selective
   leaking of low-power TE path information from one area into other
   areas. The core of most ISP ASes use the Multi-Protocol Label
   Switching (MPLS) technology. MPLS label switched paths that traverse
   multiple areas carry traffic from a head-end to a tail-end that can
   be situated in different areas within the AS. The AS uses the
   Interior Gateway Protocol (IGP) for exchanging routing related
   information. The topology of one area is not revealed to the other in
   OSPF-TE and IS-IS-TE.

   The CSPF algorithm as proposed here is run on a specific area with
   the available power-to-bandwidth (PWR) ratio as a constraint, to
   determine "k" (where k is a suitable number) low-power-paths from the
   head-end to the tail-end within the same area. The low-cost power
   paths that minimize the PWR ratio can be exchanged among the
   collaborating areas using IGP-TE TLVs that we propose in this
   document. Explicit routing using RSVP-TE (for signalling) then can be
   achieved between the head-end and the tail-end routers traversing
   multiple areas through these low-power paths connecting the head-end
   and tail-end using the Inter-Area Traffic Engineered Label Switched
   Path (TE-LSP) that span multiple areas.

 

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2.  Methodology of the proposal

   There are three known solutions to inter-area TE 

   (a) hop expansion at area boundaries where the head end can only
   choose the path to area boundary rather than right to tail end, 

   (b) centralized PCE is attached to all areas and is aware of entire
   topology, and 

   (c) path stitching by designating ABRs acting as BGP route
   reflectors.

   It is of course possible to build out low-power paths through the
   above techniques but they suffer limitations such as not knowing for
   certain whether the path exists a-priori. This document proposes a
   technique where a-priori low-power paths are pre-computed in the
   various areas and are leaked into other areas so that provisioning
   these paths is done much more quicker than is otherwise possible. 

   Assume {N} as the set of nodes in a network running link state
   routing protocol and {N' } be the set of nodes that are known to be
   the endpoints of the traffic engineered paths. The topology {N, E}
   has been divided into hierarchical areas with backbone area as the
   second level that connects first level of all non-backbone areas. We
   assume the network runs either OSPF-TE or ISIS-TE for establishing TE
   paths. The set of nodes {N'} can be situated in any non-backbone area
   or the backbone area. Nodes in {N'} may become aware of being
   potential endpoints through offline configuration.

   Once the nodes in {N'} become aware of being TE endpoints, they
   advertise themselves in a special TLV in TE link state information.
   We would term this "TE Endpoint TLV". In OSPF, they would advertise a
   newly defined TLV in TE LSA and in ISIS, they would advertise a newly
   defined TLV in TE LSP. Apart from nodes in {N'} the area border
   routers or ABRs advertise another newly defined TLV that we would
   term as "Area Border TLV".

2.1 ABR Operation

   Apart from standard OSPF/ISIS ABR functions, each ABR should discover
   the TE endpoints in every area attached to it. Assume for an ABR, let
   the set discovered be {Ai, Nj}. The ABR should compute k-power-
   shortest-paths to every element in {Ai, Nj} based on the constraints
   applicable to the network. The constraint applied here is the
   minimization of the PWR ratio which is defined as follows.

 

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   For a given router that is either an ABR or a core router within an
   area (be it backbone or non-backbone), all egress links that can be
   potentially be used as a link towards a TE endpoint are identified.
   The link / links that have the maximum of the available bandwidth at
   that instant in time are identified. The maximum available bandwidth
   so identified is used in the following equation to determine the PWR
   ratio.

   PWR = (Power Consumed by the router) DIVIDED BY (Maximum bandwidth of
   all links that are potentially leading to a TE endpoint).

   In other words PWR = POWER-CONSUMED / MAX BANDWIDTH OF EGRESS LINKS

   The power consumed by each router may fluctuate over short time
   intervals. In order to dampen these fluctuations which can cause
   unnecessary updates, power can be measured when falling within
   intervals of suitable size (say a range of values). This is as
   opposed to measuring power as a discrete quantity. This method of
   power measurement reduces the frequency of triggered updates from the
   routers due to power change.

   This PWR metric is then assigned to the links that are ingress links
   in the path leading towards the TE endpoint. Potentially for all TE
   endpoints west of the non-backbone area core router the PWR metric is
   usually the same. For TE endpoints east of the router the reverse
   directional traffic TE-LSP computation would take into account the
   PWR metric to be taken into consideration. 

   For a Area Border Router having part of its links in Area 1 and the
   rest in Area 0 (backbone area) the PWR metric would be assigned to
   the incoming links I(1) and I(2) of the ABR router as follows.

                                 .__________________
                                (   Area 1 ....>
                               (      E(1)
                \ I(1)        (     +--------->(Area 1 router)
                 \        +-------+ /  1Gb
                  +------>|       |/         E(2)
    200KW / (60*60*1.5Gb) |  ABR  |------------>(Area 1 router)
                  +------>|  of   |\  1Gb
                 /  I(2)  | Area 1| \      
                /         +-------+  \       E(3)
                              (      +-------->(Area 1 router)
                               (      1.5Gb
                                .__________________

 

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   For a Area 1 core router the following would be the PWR metric
   assigned to the incoming links I(1) and I(2) respectively of the said
   Core Area 1 router as follows.

   In an Area core router the maximum condition is modified. The "X"
   most highest bandwidths of all the egress links towards the TE
   endpoint are taken where "X" is <= "k" and the appropriate
   calculations done for PWR derivation.

   PWR = (Power Consumed by the router) DIVIDED BY ("X" highest
   bandwidth of all links that are potentially leading to a TE
   endpoint).

   Here "X" is decremented step by step to derive at least "k" shortest
   paths from the calculating router.

   In other words PWR = POWER-CONSUMED / MAX BANDWIDTH OF EGRESS LINKS
   is calculated at each step after excluding the link whose bandwidth
   was included in the previous step till "X" becomes 0. If there exist
   no such link after excluding one link after another then the
   algorithm stops. The intention is to calculate as many disjoint paths
   as possible initially. It is possible to compute partially disjoint
   paths as well with suitable modifications to the above steps.

                                    Area 1 ....>
                                      E(1)
                \ I(1)              +--------->(Area 1 router)
                 \        +-------+ /  1Gb
      PWR metric  +------>|       |/         E(2)
    300KW / (60*60*1.5Gb) | Core  |------------>(Area 1 router)
                  +------>| Router|\  1Gb
                 / I(2)   | Area 1| \      
                /         +-------+  \       E(3)
                                     +-------->(Area 1 router)
                                      1.5Gb

   After computing the ingress link PWR metrices in a given step there
   is a flooding done within the area of the assigned metrices of given
   Ingress links of a router with a new TLV that we will call "PWR
   metric TLV". This TLV contains details of the calculating router and
   the link metric for the assigned Ingress links of the said router.
   This TLV is taken into account to produce various PWR metric assigned
   topologies such as the one seen in the next page. Dampening is done
   to avoid frequent flooding based on the bandwidth and PWR
   fluctuations (which are produced as intervals of power rather than a
   discrete quantity). This is implementation dependent and its study is
 

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   out of scope of this document.

   Assume the following topology in a non-backbone area after
   calculating the PWR ratio in a given stage of the algorithm.

                    0.5
          (C)  +----------------+
        0.5|  /                 |
           | /                  |
      0.05 V/ 0.1   0.03   0.2  V
   (A)--->(B)--->(D)--->(G)--->(H)
           |             |      |
           |          0.5|      | 0.1
           |             V      V
           +----------->(E)--->(X)
              0.5           0.3

   Here (B) is a Area Border Router and has to ingress links into it
   from (C) and (A) which are in the backbone area. Connectivity within
   the backbone area are not shown here. Assume (C) and (A) are
   connected in some way with other routers in the backbone area.
   Routers (D), (G), (E), (H), (X) are routers in the non-backbone area.
   Routers (H), (E) and (X) are potential TE endpoints. The PWR metrics
   shown here on the edges within the area represent metrics for a
   specific TE endpoint. The metrics on edges (C)->(B) and (A)->(B) are
   for any traffic ingressing through (B) into the non-backbone area
   heading towards any TE endpoint (H), (E) or (X).

   The number of constraints is likely to be few and the most widely
   used constraints are TE metric, link groups and bandwidth. But no
   restriction is assumed on use of other constraints. Thus here we add
   the PWR metric of a link as an additional constraint. Once the ABR
   computes k-power-shortest-paths to every {Ai, Nj} it has topology
   information about, it advertises the k-power-shortest-paths as a
   reachability vector in a newly defined "TE Reachability Vector TLV". 

   Consider an example network show below. TEh is head-end and TEt is
   tail-end of a TE path, ABR1 and ABR2 are area border routers.

           TEh2---R2                               R4-----TEt2
                   \                               /
                    \                             /
        TEh1---R1----ABR1-----Rb1-----Rb2-----ABR2----R3----TEt1
             Area 1             Backbone          Area2

   In this example, ABR1's TE Reachability vector TLV for area 1 and
   area 0 are given below.
 

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   { ABR1, [<TEh1, <Path info 1>>, <TEh2, <Path info 2>>]}
   { ABR1, ABR2, [<TEt1, <Path info 3>>, <TEt2, <Path info 4>>]}

   Here the vector TLVs are arranged as per increasing PWR metric
   associated with each path. That is the summation of all PWR metrics
   of the links in the path is done and the vector TLVs are ordered in
   increasing order of PWR metric sums. So the lowest-cost-power path is
   listed first and so on. If the least cost power path is to be chosen
   then the path in the first TLV is chosen.

   Similarly ABR2's TE Reachability vector TLV for area 2 and area 0 are
   given below.

   { ABR2, [<TEt1, <Path info 3>>, <TEt2, <Path info 4>>]}
   { ABR2, ABR1, [<TEh1, <Path info 1>>, <TEh2, <Path info 2>>]}

   The first thing to be noted is that head-ends are also considered as
   TE-endpoints. Essentially this means any head-end or tail-end of a
   inter-area TE-LSP can be considered as tail-end or head-end
   respectively.

   Note that the reachability vector advertised by ABR1 also contains
   the reachability vector of ABR2. For example, if ABR2 is brought up
   first, then it is likely that ABR1 would only have the following as
   TE Reachability vector TLV for area 0 before ABR2 computes path to
   the TE endpoints in area 2. { ABR1, ABR2 }

   Note that <Path info> TLV would only contain the aggregate of link
   attributes namely cost, bandwidth etc and most importantly the PWR
   metric as well but not the complete path of intermediate nodes. For
   example, <Path info 1> may be a set of <2, admin-group-1|admin-group-
   2, 1Gbps> (where the 1Gbps could be the minimum bw available along
   the path). The above example topology has only one path from ABRs to
   TE endpoints. The number of path info "k" may have a default value or
   can be configured by the operator on all nodes.

2.2 TE Path Head-end Operation

   When any TE application requests TE path to be setup to an endpoint
   that is not present in the same area, the head-end scans the TE
   Reachability vector TLVs advertised by ABRs and selects the path
   using the <Path info> contained in the vector TLVs.

   Here is an example with multiple paths in area 1, backbone and area 2
   called Figure 2.0

 

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        TEh3----R5---ABR3----Rb3-----Rb4------ABR4----R6--TEt4
             \         /          ___/          \  ___/
              \       /          /               \/
        TEh2---R2---ABR5------Rb5--------ABR6---R4-----TEt2
              /       \          \____           /\___
             /         \              \         /     \
        TEh1---R1----ABR1-----Rb1-----Rb2-----ABR2----R3----TEt1
             Area 1             Backbone          Area2

   In this topology in figure 2.0 taking the tail-ends represented in
   the diagram, it is noted that TEt4 is reachable via ABR4, ABR6 and
   ABR2 as well. The TE reachability TLVs advertised by ABR6 for area 2
   would be multiple to each tail-end since there exist multiple paths
   to reach at least most of them in area 2 once a packet reaches any of
   the ABRs in area 2.

   Here again the least cost power shortest path is listed first and so
   on.

   { ABR6, [<TEt4, <Path info 1>>, <TEt4, <Path info 2>>, <TEt2, <Path
   Info 3>>, etc.. }

   For area 0 the TE reachability TLV would be 

   { ABR6, ABR1, [<TEh1, <Path info 4>>, <TEh1, <Path info 5>>...]}
   { ABR6, ABR5, [<TEh1, <Path info 6>>, <TEh1, <Path info 7>>...]}
   { ABR6, ABR3, [<TEh1, <Path info 8>>, <TEh1, <Path info 9>>...]}

   For the sake of brevity we do not enumerate all path information
   possible as it would be quite extensive.

   It is possible that there may be already setup LSPs which are being
   used for transit traffic on the backbone or in other non-backbone
   areas. It is also feasible to advertize already set up LSPs in the
   path info; no additional TLV is required for that purpose. The case
   where this may be useful would be if such transport LSPs exist in the
   backbone area and there is a willingness to provide higher preference
   to these LSPs to carry transit LSPs over backbone.

   There can be selective suppression of advertisements to other areas
   (backbone or non-backbone)  of LSPs if these are existing LSPs setup
   along a path which are utilized to a greater degree. If underutilized
   with respect to the PWR metric a more favourable metric could be
   advertized to other areas.

   For example, backbone area transport LSPs will be advertized as
   transit LSPs which would provide connectivity to LSP sections lying
 

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   in non-backbone areas and would be updated more frequently since they
   facilitate inter-Area TE.

   Once a path in the TLV has been used for reserving bandwidth for
   traffic over that path, then it is withdrawn from the advertisements
   so that it becomes unusable. Another path may be computed over the
   same path but with possibly a different PWR metric sum since it is
   possible that the traffic over that path could have changed the PWR
   metrices in the edges along that path.

2.3 Advantages

   1) The TE Reachability vector TLV contains the aggregate of all link
   attributes along with TE constraints and so the head-end of the TE
   path can explicitly select the ABR that connects the destination area
   even though it does not know the complete topology of the backbone
   area.

   2) As the TE reachability vector contains only the aggregate
   attributes of k-power-shortest-paths, the flooding overhead to
   suppose the mechanism is limited.

   3) Centralized path computation element is not required for
   supporting inter-area power-shortest-path TE. The additional overhead
   of computing k-power-shortest-paths on ABR can be solved by
   offloading the computation overhead to additional processor in multi-
   core platforms.

 

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3  Security Considerations

   None.

4  IANA Considerations

   New TLV types for OSPF and IS-IS for the new TLVs that have been
   introduced need to be assigned. Their format needs to be arrived at
   in future versions of the document.

5  References

5.1  Normative References

   [KEYWORDS] Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC1776]  Crocker, S., "The Address is the Message", RFC 1776, April
              1 1995.

   [TRUTHS]   Callon, R., "The Twelve Networking Truths", RFC 1925,
              April 1 1996.

5.2  Informative References

              REFERENCES

              [1] G. Appenzeller, Sizing router buffers, Doctoral
              Thesis, Department of Electrical Engineering, Stanford
              University, 2005.

              [2] A. P. Bianzino, C. Chaudet, D. Rossi and J. L.
              Rougier, A survey of green networking research, IEEE
              Communications and Surveys Tutorials, preprint.

              [3] J. Baliga, K. Hinton and R. S. Tucker, Energy
              consumption of the internet, Proc. of joint international
              conference on optical internet, June 2007, pp. 1-3.

              [4] J. Chabarek, J. Sommers, P. Barford, C. Estan, D.
              Tsiang and S. Wright, Power awareness in network design
              and routing, Proc. of the IEEE INFOCOM 2008, April 2008,
              pp. 457-465.

              [5] B. Venkat et.al, Constructing disjoint and partially
              disjoint InterAS TE-LSPs, USPTO Patent 7751318, Cisco
 

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INTERNET DRAFT Building power shortest inter-Area TE-LSPs     March 2012

              Systems, 2010.

              [6] M. Xia et. al., Greening the optical backbone network:
              A traffic engineering approach, IEEE ICC Proceedings, May
              2010, pp. 1-5.

              [7] W. Lu and S. Sahni, Low-power TCAMs for very large
              forwarding tables, IEEE/ACM Transactions on Computer
              Networks, June 2010, vol. 18, no. 3, pp. 948-959.

              [8] B. Zhang, Routing Area Open Meeting, Proceedings of
              the IETF 81, Quebec, Canada, July 2011.

              [9] M.J.S Raman, V.Balaji Venkat, G.Raina, Reducing Power
              consumption using the Border Gateway Protocol, IARIA
              conferences ENERGY 2012.

              [10] A.Cianfrani et al., An OSPF enhancement for energy
              saving in IP Networks, IEEE INFOCOM 2011 Workshop on Green
              Communications and Networking

              [11] Shankar Raman et al., draft-mjsraman-rtgwg-inter-as-
              psp-01.txt, Work in Progress, February 2012.

   [EVILBIT]  Bellovin, S., "The Security Flag in the IPv4 Header",
              RFC 3514, April 1 2003.

   [RFC5513]  Farrel, A., "IANA Considerations for Three Letter
              Acronyms", RFC 5513, April 1 2009.

   [RFC5514]  Vyncke, E., "IPv6 over Social Networks", RFC 5514, April 1
              2009.

Authors' Addresses

   Shankar Raman
   Department of Computer Science and Engineering
   I.I.T Madras,
   Chennai - 600036
   TamilNadu,
   India.

   EMail: mjsraman@cse.iitm.ac.in

 

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INTERNET DRAFT Building power shortest inter-Area TE-LSPs     March 2012

   Balaji Venkat Venkataswami
   Department of Electrical Engineering,
   I.I.T Madras,
   Chennai - 600036,
   TamilNadu,
   India.

   EMail: balajivenkat299@gmail.com

   Prof.Gaurav Raina
   Department of Electrical Engineering,
   I.I.T Madras,
   Chennai - 600036,
   TamilNadu,
   India.

   EMail: gaurav@ee.iitm.ac.in

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