Comparative analysis of path computation techniques for MPLS traffic engineering

Comparative analysis of path computation techniques forMPLS traffic engineering

Gargi Banerjee *, Deepinder Sidhu

Department of Computer Science and Electrical Engineering, Maryland Center for Telecommunications Research,

University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA

Abstract

We consider the problem of computing traffic engineered paths for requests having bandwidth and delay require-

ments, when these requests arrive in the network independent of one another. Providing bandwidth guarantees to

applications has been important in networks offering service differentiation. With the increase in the number of real-

time applications in the Internet, provision of delay guarantees is also receiving much attention. This necessitates the

development of sophisticated path selection algorithms which deviate from the shortest-path routing philosophy in

traditional IP networks. While these algorithms perform well from the perspective of satisfying application require-

ments, they often do not take into account long term effects on the network state. One of the major concerns of a service

provider is to run the network at maximum utilization while reducing network costs and preventing congestion in the

network. For this reason, providers are looking at traffic engineering (TE) to automate path selection procedures and to

maintain network loading at an optimal level. In this paper we propose two TE path selection algorithms that consider

the application’s delay–bandwidth requirements as well as the TE constraints on the network. We compare the pro-

posed algorithms to existing path computation solutions and present results that show that by considering these ad-

ditional constraints, improvement is achieved in terms of reduction in request blocking probability, reduction in

network costs and load distribution.

� 2002 Elsevier Science B.V. All rights reserved.

Keywords: Traffic engineering; Path computation; Multi-constrained path; QoS; MPLS

1. Introduction

The exponential growth of the Internet has ledto the increasing importance of network manage-ment and control functions. It is evident today

that adding more bandwidth to networks is notthe solution to all congestion problems. At thesame time, more and more providers are showinginterest in making revenues from offering differ-entiation of services in their networks. This re-quirement has increased the importance of gainingcontrol over networks via automated traffic engi-neering (TE). The most common TE objectives areto reduce congestion, improve network utilization,satisfy diversified requirements and thus lead to anincrease of revenue.

Computer Networks 40 (2002) 149–165

www.elsevier.com/locate/comnet

*Corresponding author. Tel.: +1-410-455-3063/2860.

E-mail addresses: [email protected] (G. Banerjee),

[email protected] (D. Sidhu).

1389-1286/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S1389-1286 (02 )00270-0

mail to: [email protected]

One of the most important applications ofMPLS networks will be in TE [2]. MPLS trafficengineering (MPLS-TE) enables a MPLS back-bone to expand upon TE capabilities by routingflows across the network based on the resourcesthe flow requires and those currently available.Since the essence of TE is mapping traffic flowsonto a physical topology, it implies that at theheart of MPLS-TE resides the problem of pathcomputation.

The Internet Protocol (IP), and the architectureof the Internet itself, is based on the simple con-cept of best-effort service and makes no guaranteesabout when data will arrive, or how much it candeliver. Though the simplicity and scalability of IPhas made it highly popular, it does not provide awide range of services. This has not been a prob-lem in the past with most of the applications beingof types Web, email and file transfer. However, asmore and more applications connect to the Inter-net, the nature of service required by them is be-coming increasingly varied. Applications nowrequire more predictability from the networks andin turn are potential sources of revenue to networkservice providers. Thus, in order to increase reve-nue earnings, the providers need to traffic engineertheir networks to help them run at maximum uti-lization. For this reason a number of QoS and TEmechanisms have evolved over the years to satisfythe variety of needs of applications as well as thatof service providers.

QoS based path computation has assumed a lotof importance over the last couple of years. In thesimplest terms, to offer QoS means to provideconsistent, predictable data delivery service. Cus-tomers or users of a network may need severaltypes of QoS guarantees from the network andthey specify these requirements in the form ofservice level agreements (SLA). QoS path compu-tation then translates to finding paths through thenetwork such that these requirements are satisfied.While previous path computation algorithms weremainly hop-by-hop distributed algorithms opti-mizing static metrics (e.g., link cost, length, etc.),the new generation of path algorithms is movingtowards source routing schemes that also take intoaccount dynamic metrics. A few examples of thesedynamic metrics are available bandwidth on links,

link reliability, link load, jitter, packet loss, etc. Inaddition, due to the varied QoS requirementsof today’s applications, path computation algo-rithms may need to work with multiple QoS met-rics. Path computation based on a single QoSmetric is studied in [1,6,13,16]. Bandwidth is themost common QoS metric considered in these al-gorithms. A more difficult task is to solve the prob-lem of computing paths when multiple constraintsneed to be satisfied. Path computation based onmultiple QoS constraints has been studied in [4,9,10,17,18]. In this case, applications express theirservice requirements not only in terms of the band-width required, but also in terms of maximumdelay tolerated, delay variation, reliability, etc.Among the multiple QoS metrics, the principalones are bandwidth and delay. Most applicationsexpress their requirements either in terms of theminimum/average bandwidth required or in termsof the minimum bandwidth and the maximumacceptable end-to-end delay. We refer to the aboveproblems as the bandwidth constrained and thedelay–bandwidth constrained path computationproblems, respectively.

QoS schemes essentially provide differentiationof services. They also provide different degrada-tion of performance for different traffic whentraffic load is heavy. Under low-load conditionshowever best-effort schemes work just as well.Thus the question arises as to whether we canmaintain the network always in a state of opti-mized load and avoid congestion. This is the mo-tivation for TE. TE helps in maintaining networksin a well-balanced state. This in turn makes iteasier to satisfy the QoS requirements of flowsrouted across it. Thus TE in ISP networks, andproviding quality of service guarantees to cus-tomers that use the network, are closely related toeach other. Some of the common TE objectives areto reduce the blocking probability in a network,reduce congestion on links, reduce network costs,etc. These objectives translate into new restrictionson the path selected and TE path computationalgorithms should satisfy these objectives in orderto maintain consistently high network utilization.For example, if the QoS metrics considered aredelay and bandwidth and the TE objective in aprovider’s network is to minimize network costs,

150 G. Banerjee, D. Sidhu / Computer Networks 40 (2002) 149–165

then the problem translates to finding the mini-mum cost delay–bandwidth constrained path. Wedenote the QoS requirements specified by appli-cations by the general term Q-metrics. Withoutloss of generality, we call the problem of findingpaths that satisfy the Q-metric constraints and aswell maintain the additional TE objectives, theTE-Q-metrics constrained path computation prob-lem. If the application specified Q-metrics includeonly bandwidth, then we call it the TE-bandwidthconstrained problem. Otherwise, if the applica-tion specified Q-metrics are delay and bandwidththen we call it the TE-delay–bandwidth constrainedproblem.

In this paper, we present two TE path compu-tation heuristics, which solve the TE-bandwidth(TE-B) and the TE-delay–bandwidth (TE-DB)constrained problems respectively. Both these al-gorithms attempt to maintain the three TE objec-tives of (1) increasing network revenue, (2) limitingnetwork costs and (3) distributing network load.We compare the performance of these two algo-rithms with other existing competitive algorithmsthat use the same application specified constraints.We show that by considering the additional TEconstraints, both algorithms achieve considerableperformance benefits and provide more completeTE solutions. The rest of the paper is organized asfollows. Section 2 introduces concepts in TE basedpath computation and presents the proposed pathcomputation algorithms. Section 3 reports simu-lation results and performance analysis of theproposed algorithms and Section 4 concludes thepaper.

2. TE-Q-metrics constrained path computation

Routing models can be broadly classified asonline routing (i.e., requests arrive one by one andfuture requests are not known) or offline routing(i.e., all demands are known a priori and requestscan be routed accordingly). There also exists anintermediate model in which (some statisticalknowledge about the requests may be available,e.g., the average arrival rate for a node pair. Theadvantage of offline routing, is that pre-provi-sioning of resources can be done so that the maxi-

mum number of requests can be routed. However,with the advent of services that permit dynamicand frequent requests for capacity change, onlinerouting of requests has assumed a great impor-tance.

Online routing algorithms need to be prettyfast since they compute route(s) for every requestarrival in the system. The time complexity ofa routing algorithm is often determined by thenature and the number of path metrics consid-ered. Commonly path metrics can be divided intothree classes: additive, multiplicative and concave.Bandwidth is an example of a concave metric,whereas delay, cost, etc. are additive metrics. Morebackground on path metrics can be found in[19]. Problems dealing with one or more concavemetrics and one additive/multiplicative problemcan be solved in polynomial time. However, theproblem of computing optimal routes subject toconstraints of two or more additive and/or multi-plicative metrics is known as the multiple con-strained path selection (MCP) [14]. The MCPdecision problem is known to be NP-complete [7].Related to MCP, but with a slightly different ob-jective is the restricted shortest-path (RSP) prob-lem. In RSP, the path is required to satisfy oneconstraint while being optimal with respect toanother parameter. Any solution to RSP applies tothe MCP problem. RSP is also known to be NP-complete [14]. The difference between the MCPand the RSP problem is that MCP does not opti-mize the values of any parameter. Instead, itsearches for a feasible path that satisfies bothconstraints.

In this paper, we assume requests arrive onlineand no assumption is made about future requests.We assume that all applications specify their ser-vice requirements in terms of two QoS metrics:bandwidth and delay. Two forms of QoS requestsare considered entering the network:

1. (A, B, Bw) where A: source node, B: destinationnode and Bw: minimum bandwidth the applica-tion requires.

2. (A, B, Bw, D) where A: source node, B: destina-tion node, Bw: minimum bandwidth the appli-cation requires and D: maximum end-to-enddelay the application can tolerate.

G. Banerjee, D. Sidhu / Computer Networks 40 (2002) 149–165 151

We assume that the requested bandwidth units arereserved along path PA–B by some TE signalingmechanism like RSVP or CR-LDP [3,11] and areavailable for the application. We also assume thatthe available QoS information is accurate.

2.1. TE objectives

The TE objectives considered in this paper areto minimize blocking of future requests (andthereby earn more revenue), minimize the overallcost of paths and distribute the loading on paths.We now take a closer look at these TE objectives.

2.1.1. Reducing blocking of requestsReducing the blocking probability of requests

in a network is a crucial TE objective. In [13], theauthors present the intuition that the blockingprobability of requests can be reduced, if the totalavailable flow in the network is maximized. Theassumption is that the set of transmitting source–destination (src–dest) node pairs is known. Thetotal amount of available flow between a src–destpair is known as the maximum flow (max-fiow) [5]between the pair of nodes. Associated with eachmax-flow is a set of minimum cut links (min-cut)[5]. The max-flow of a particular src–dest pairdecreases whenever the capacity of any of the linksin its min-cut for that pair decreases infinitesi-mally. When a request R is routed over a path Pbetween a particular src–dest pair s–d, the max-flow between s–d always decreases. However therequest may also go over links that belong to themin-cut set of other src–dest pairs. Thus routingthis request R over P may also decrease the max-flow between other src–dest pairs. The approachattempts to route R over a path, which maximizesthe available flow between other src–dest pairs.The problem is NP-hard and the authors proposea heuristic algorithm that gives reasonably goodsolutions. For every request of Bw units of band-width between a pair of src–dest nodes s–d, theheuristic algorithm assigns a weight to each linkin the network. This weight, which we call themax-flow reduction weight, is proportional to theamount of flow it will reduce between all othersrc–dest pairs, if the flow of Bw units is routedacross it. The larger amount of flow that a link

reduces, the higher its assigned weight is. Ashortest-path algorithm based on the new weightsthen returns the minimum flow-blocking path. Inthis paper, we achieve the TE objective of reducingthe number of blocked requests by adopting theabove approach of routing requests along the leastflow-blocking paths. If f ði; jÞ denotes the max-flowreduction weight of a link lði; jÞ, and P is a path,then we define the max-flow reduction weight ofpath P as

path flow reductionðP Þ ¼X

f ði; jÞ; 8lði; jÞ 2 P :

Note that if the bandwidth demands in the re-quests are much smaller compared to the capacityof the links in the network, the max-flow valuesand the min-cut links do not change much. In thatrespect max-flow and min-cut are quasi-staticmetrics in such a network.

2.1.2. Minimizing network costIn this paper, we assume that network usage

costs are solely dependent on the cost of the pathsbeing used. Thus, the TE objective of minimizingnetwork costs directly translates to the problemof minimizing the path cost. Path cost is a staticmetric and is expressed as the sum of its componentlink costs. If uði; jÞ denotes link cost for link lði; jÞand P is a path, then we define cost of P as

path costðP Þ ¼X

uði; jÞ; 8lði; jÞ 2 P :

Static TE metrics help in maintaining networkstability under high-load conditions. Path cost isoften directly related to path length. Motivationfor using the static path length as a TE constraintis derived from the findings reported in [16] thatshow that algorithms that optimize path lengthperform better under high-load conditions thanalgorithms that do not.

2.1.3. Distributing network loadThe TE objective of distribution of network

load is a difficult objective to meet since it does notdirectly translate to optimizing a path metric.However, we note that distribution of networkload is a dynamic function and hence depends onsome dynamic path metric [16] shows that bal-ancing network load by using a dynamic link


metric works well, especially under low-load con-ditions.

2.1.3.1. Path criticality. We now define a TEmetric, path criticality, which we propose to usefor load distribution. The idea behind our metricis that if there exists highly loaded links in a net-work then these links should be avoided duringselection of paths for requests. These heavilyloaded links are called critical links. All criticallinks in a path contribute towards the criticality ofthe path.

We can rely on existing TE infrastructure toprovide the loading information on links. Thebasic assumption is that most networks run linkstate Interior Gateway Protocols (IGP) for routingpurposes. [12] suggests simple extensions to IGPsby which dynamic TE information like reservedlink bandwidth can be periodically fed-back to thesource nodes. This information is used for identi-fication of heavily loaded links. We define linkloading of a link lði; jÞ aslink loadðlÞ ¼ ðReserved Bw on l=Total reservable

Bw on lÞ � 100:

A critical link is now defined as a link which has itsload running above a threshold percentage U.Criticality of link l is defined as

link criticalðlÞ ¼ 0; if link loadðlÞ 6U ;

¼ f ðlink loadðlÞÞ; otherwise;

where f: monotonically increasing function oflink loadðlÞ.

A critical path is one which has critical com-ponent links. The more heavily a path is loaded,the more critical it is. Also the higher the numberof critical component links on a path, the morecritical it is. From these ideas, we now definecriticality of a path P as

path criticalðP Þ ¼X

link criticalðlÞ; 8l 2 P :

Intuitively, thus to distribute path loading onewould select the least critical paths. Criticality isan additive metric.

Consider the example network in Fig. 1. Thenumbers beside the links represent the loading onthe corresponding links. Let the threshold U be

fixed at 28. The dark lines then represent thecritical links. By our definition, the three pathsranked in ascending order of path criticality areA–B–D–E, A–D–E and A–C–D–E. Note that bydefinition, path criticality differs from path load.Path load is a concave metric and is defined as themaximum link load on its component links. In thissense, criticality is a more fine-tuned metric ascompared to load since it depends on the loadingon all component links. The difference between thetwo metrics can be seen in Fig. 1, where all thethree paths have the same path load but differ inpath criticality. We later show through our ex-periments that the overall distribution of load at-tained by using the path criticality metric is muchbetter than using the path load metric.

2.2. TE-Q-metrics problem statement

We now formally define our TE-Q-metricsconstrained path computation problem. Given adirected network G of N nodes and L links, eachlink l 2 L has a pre-assigned non-negative linkdelay parameter dðlÞ and a non-negative link costparameter cðlÞ. The constraints placed on a pathP, are derived from the application specified Q-metrics. In this paper, the Q-metrics considered arethe minimum bandwidth requirement (Bw) and themaximum end-to-end delay (D) between a givensource s and destination d. Let us denote theavailable bandwidth and the delay on path P asbandwidth(P) and delay(P) respectively. Addi-tionally, the path has to satisfy the modified TEobjectives of minimizing flow reduction, minimiz-ing cost and minimizing path criticality in thenetwork. Thus, for any path P, the problemstatement can be written as

Fig. 1. Example network showing critical links.


(a) minimize path_flow_reduction(P),(b) minimize path_cost(P),(c) minimize path_critical(P),

subject to the constraints:

1. delayðPÞ6D,2. bandwidthðPÞPBw.

The above formulation of the TE-Q-metric con-strained problem has multiple objective functionsand constraints, of which only one of them (i.e.,bandwidth) is a concave path metric and the otherfour, are additive metrics. Thus, it is a variation ofthe RSP problem and is NP-complete. We nowattempt to investigate suitable heuristics that findgood solutions to the above problem.

2.3. Single QoS constraint

When application’s QoS requirements arespecified only in terms of bandwidth, the TE-Q-metric problem reduces to the TE-B constrainedproblem. Before we present our heuristic to solvethis problem, we discuss some existing QoS pathcomputation algorithms that take into account thebandwidth constraint. We also highlight some ofthe reasons why these existing solutions fail toqualify as an overall TE solution.

The minimum interference routing algorithm(MIRA) [13] heuristic was proposed to find a pathbetween a pair of nodes that blocks the smallestavailable max-flow between all other src–destnodes. MIRA’s basic intuition is to avoid routingrequests on links that reduce the max-flow betweenother src–dest pairs. The interested reader is ref-erenced to [13] for details. Note that none of thestatic constraints (e.g., path length, path cost) isconsidered in MIRA. While at low to moderatenetwork load this might be acceptable, longerpaths selected at high-load conditions may causeinstability by occupying more resources in an al-ready overloaded network. In addition, with thistype of algorithm, the path lengths can becomelong enough to make the path practically unus-able. MIRA also does not take into account thecurrent load condition on the paths. In an n-nodenetwork with m links and integral link capacities in

range [1;U ], the time complexity of the algorithmis Oðnmþ n2 logUÞ [13] and its space complexity isOðnÞ.

The widest shortest (WID-SHORT) path algo-rithm [16] makes use of the possible existence ofmore than one shortest path in the network. Ifseveral such shortest paths exist, then the widestone (i.e., one with the maximum available band-width) is selected. The effectiveness of this algo-rithm depends on the presence of multiple shortestpaths in the network. If there is always only asingle shortest path, then its performance becomesidentical to that of any minimum distance routingalgorithm. From the TE perspective, WID-SHORT considers the path cost and path loadbut does not take into account the blocking offuture requests. The time complexity is Oðn log nÞand its space complexity is OðnÞ. A similar algo-rithm, the shortest-widest path selects the shortestpath among paths with equal amount of availablebandwidth. However [16] shows that at high-loadconditions the performance of the shortest-widestpath algorithm deteriorates severely.

Least-critical-K-shortest (LCKS) path algo-rithm is proposed in this paper as an improvementto the WID-SHORT algorithm. Since the occur-rence of multiple shortest paths may be rare inmany networks, we propose to find the k-shortestpaths between a pair of nodes. LCKS uses theproposed path criticality metric to distributeloading, rather than the path load metric. Fromthe set of k candidate paths, it selects the leastcritical path. The time complexity of the algorithmis Oðn log nþ kÞ and space complexity is OðknÞ. Allthe algorithms described above perform well eitherin terms of reducing blocking or in terms of re-ducing path cost/load. The objective is to look fora more complete solution that succeeds in main-taining all TE objectives. We propose the TE-Bconstrained algorithm as a complete solution tothe TE path computation problem.

2.3.1. TE-bandwidth constrained path computationThis section presents our path computation

heuristic, the TE-B constrained algorithm. TE-Buses the quasi-static, static and dynamic TE met-rics of max-flow reduction, path cost and pathload respectively, in addition to the application


specified QoS constraint of bandwidth. Let theminimum bandwidth requirement of the applica-tion be Bw units. We assume the bandwidth de-mands are much smaller compared to the capacityof the network. The set of constraints and objec-tive functions for the system are same as presentedin Section 2.2, with only the delay constraint re-moved. As mentioned before, this is a version ofthe RSP problem. [9] suggests that the MCPproblem is easier to solve than the RSP problem.Thus, in order to simplify the problem, we trans-form some of the objective functions into con-straints. By our assumption, cost and max-flow arestatic and quasi-static metrics respectively. Sincestatic optimization metrics can be transformedinto constraints, we introduce a new path costconstraint (C) and a new max-flow reductionconstraint (F). Since path criticality is a dynamicmetric we retain the minimization criterion on it.Thus, we re-write the problem statement as

(a) minimize path_critical(P), subject to con-straints:

1. bandwidthðP ÞPBw,2. path flow reductionðP Þ6 F ,3. path costðP Þ6C.

The next step is to define the constraints C andF, which could either be statically specified by an

administrator or selected dynamically. In our de-sign, they are defined as dynamic constraints, withC being the cost of the path with least max-flowreduction weight, and F being the max-flow re-duction weight of the least cost path. This serves asloose upper bounds and the aim is to find pathswhose cost and max-flow reduction weight metricsare far from the bounds C and F respectively. Wenow try to design a heuristic which give near-optimal solutions to the above problem. We usethe definitions shown in Fig. 2 for our algorithm.

We propose a heuristic, TE-B (shown in Fig.3a), that firsts finds a candidate set of paths thatsatisfy constraints 1–3 simultaneously. From thisset, it then selects the least critical path. To satisfyconstraint 1, links that have less than Bw units ofresidual bandwidth are removed. We now need tofind a candidate set of paths that satisfy bothconstraints 2 and 3 simultaneously. Ref. [15] de-scribes the A*Prune algorithm for finding kshortest-paths subject to multiple constraints.However the worst case running complexity canbecome exponential. Ref. [17] describes a heuristicfor solving the MCP problem by finding a candi-date set of k paths whose metrics are far from theconstraint bounds. We adopt this approach forsolving the TE-B constrained problem. The stepsfor computing the set CA;B and the candidate pathset A are the most computationally expensive stepsin the algorithm and governs the time complexity

Fig. 2. Definitions and terminology.


of the TE-B algorithm. In an n-node networkwith m links and integral link capacities in range[1;U ], the fastest known max-flow algorithm hasa running time of Oðminðn2=3;m1=2Þm logðn2=mÞlogUÞ [8]. A set of paths subject to two simulta-neous constraints can be computed in timeOðkn logðknÞ þ k32mÞ [17]. The space complexity ofthe algorithm is OðknÞ. On an average, to computea TE-B route takes 0.15–0.2 ms on a Sun SPARCUltraWorkstation (n ¼ 18,m ¼ 62, k ¼ 4),whereasnormal Dijkstra-based routing takes about 0.05–0.09 ms.

The performance of the algorithm also dependson the appropriate definition of the constraints Cand F. The quality of a solution may deteriorate incase the bounds are too loose. A tighter boundimproves the probability of the algorithm findingthe optimal solution. We can use an iterativemethod detailed in [9] that starts with the looseupper bound and progressively searches for atighter cost bound. When this method is run as apre-cursor to the algorithm, the search space re-duces resulting in better quality solutions.

2.4. Multiple QoS constraints

When application’s QoS requirements arespecified in terms of bandwidth and delay, the TE-Q-metric problem reduces to the TE-DB con-strained problem. Before we present our solutionto this problem we discuss some existing QoS pathcomputation algorithms that take into accountthe multiple constraints of delay and bandwidth.We also highlight some of the reasons why these

existing solutions fail to qualify as an overall TEsolution.

Minimum delay (MIN-DELAY) algorithm [18]is a bandwidth–delay based routing algorithm thatprunes links that do not satisfy the bandwidthrequirement, and then finds the shortest path w.r.t.delay in the reduced graph. In an n-node networkwith m links, time complexity of MIN-DELAYis the same as that of Dijkstra’s algorithm, i.e.,Oðn log nÞ and its space complexity is OðnÞ. Thisalgorithm considers none of the TE constraints.

Tunable accurate multiple constrained routingalgorithm (TAMCRA) [17] is an efficient multipleQoS routing algorithm, for solving the MCP al-gorithm with K constraints. Using a non-linearweight function, it finds a candidate set of k pathswhose metrics are far from the constraint bounds.In an n-node network with m links, time com-plexity of TAMCRA is Oðkn logðknÞ þ k3KmÞ [17]where K is the number of constraints and k is thesize of the candidate set. Space requirement ofTAMCRA is OðknÞ. This algorithm does notconsider the TE constraints of reducing blockingof requests or that of distributing load.

2.4.1. TE-delay–bandwidth constrained path com-putation

This section presents our path computationheuristic, the TE-DB constrained algorithm. It isvery similar to TE-B constrained problem formu-lation, except that we now have an additional de-lay constraint. We use the same set of definitionsas in Fig. 2. Let the minimum bandwidth re-quirement of the application be Bw units and the

Fig. 3. (a) TE-B and (b) TE-DB.


maximum acceptable delay be D units. As ex-plained in Section 2.3.1, let C and F represent thecost and the max-flow reduction constraints re-spectively. The problem statement becomes:

(a) minimize path_critical(P), subject to con-straints:

1. bandwidthðP ÞPBw,2. delayðP Þ6D,3. path flow reductionðP Þ6 F ,4. path costðP Þ6C.

We propose a heuristic TE-DB (shown in Fig.3b) to solve the above problem. The algorithm issimilar to the algorithm described in Section 2.3.1except that we now have constraints 2–4 that weneed to satisfy simultaneously. As before, the al-gorithm works by first pruning off links whichhave less than Bw units of residual bandwidth. Itthen runs the k-shortest-path algorithm on thereduced graph to find a candidate set of pathsthat satisfy constraints 2–4. From among thecandidate set the algorithm selects the least criti-cal path. As before, max-flow computations takeOðminðn2=3;m1=2Þm logðn2=mÞ logUÞ, and comput-ing a set of paths subject to three simultaneousconstraints takes Oðkn logðknÞ þ k33mÞ. TE-DB’sspace complexity is OðknÞ. On an average, tocompute a TE-DB route takes 0.2–0.25 ms on aSun SPARC Ultra Workstation (n ¼ 18, m ¼ 62,k ¼ 4).

3. Performance studies

We evaluate the performance of TE-B and TE-DB with other algorithms that consider similarQoS constraints. We compare TE-B with WID-SHORT, MIRA and LCKS. We also compare theperformance of TE-DB with that of MIN-DELAYand TAMCRA. Performance comparison is doneon the basis of stochastic simulations, where con-nection requests randomly arrive in the network.Each algorithm attempts to route these connec-tions and the network performance (in terms ofmetrics discussed in Section 3.3) is measured.

3.1. Simulation model

The network model used for our experiments isshown in Fig. 4. It represents a typical ISP net-work and is based on the ATT backbone networkwith a few additional links. The dark shaded nodesrepresent the gateway nodes, which serve as entryand exit points for the network traffic. The re-maining nodes are the backbone nodes, whichcarry transit traffic only. Link capacities are eithermoderate (OC3 links) or high (OC12 links). Alllinks are symmetric and link weights are assignedrandomly. The link delays, also assigned ran-domly, are of the order of a few milliseconds. Inreality, link delays and weights vary largely fromone provider’s network to another. However, thereexists a range of acceptable values for these

Fig. 4. ISP network.


parameters that are used in most studies (e.g.,link delays for OC3 links are usually in the rangeof 10–100 ms). In the absence of real values, wesimulate the link parameters by generating themrandomly from the acceptable range of values.Experiments are repeated several times to averageout the effect of randomness. In order to corrob-orate the results, experiments are also performedon random networks consisting of 10–40 nodeswith average node degrees varying in the range of4–6. Similar results are obtained for these randomnetworks and hence are not shown. The parameterk determines the size of the candidate set of paths.The more candidate paths we have, better qualitysolutions we can attain. However the complexityof the algorithm also increases with k. Ref. [17]suggests 4–6 as a possible range of k values. Weuse k ¼ 4 for all our experiments.

3.2. Request generation

Requests are generated by an offline utility andare of the form (Src, Dest, Bw, D, Hold-Time).The bandwidth requirement of requests variesuniformly between 1 and 200 kbits/s. The delayrequirement varies uniformly between 50 and 100ms. We assume that requests arriving in the systemcan either have a finite lifetime, i.e., the flows aretorn down after certain holding time, or they canhave infinite lifetime, i.e., flows are never torndown. Finite flows arrive in the system accordingto a Poisson process and the holding time is ex-ponentially distributed.

The request generation follows two models,uniform and non-uniform. For each network, Srepresents the set of possible src–dest pairs be-tween which there is traffic flow. We assume thatthis set S is known a priori. In the uniform model,requests are uniformly distributed between all src–dest pairs in S. This model represents networkswhere there is an equal proportion of trafficflowing between all end-points. In the non-uni-form model, src–dest pairs could be categorized ashot or cold pairs, where hot pairs receive the ma-jority of the routing requests. This model repre-sents networks where a heavy portion of trafficflows between some (hot) end-points, while there isrelatively less flow of traffic between other (cold)

end-points. The ratio of traffic distribution be-tween a hot pair and a cold pair and the ratio ofnumber of hot pairs to number of cold pairs areimportant parameters in this model. We considerthree scenarios for the non-uniform model: (a) hotand cold pairs are evenly distributed, (b) hot pairsare very high in number compared to cold pairsand (c) hot pairs are very low in number comparedto cold pairs. The traffic distribution ratio betweenhot and cold pairs is fixed at 9:1.

3.3. Performance metrics

The evaluation of all algorithms is done from aTE perspective with the purpose of analyzing howthese algorithms compare with each other in termsof blocking requests, reducing network costs anddistributing network load. We define the followingparameters:

• Available max-flow: Request blocking can beclosely related to the available max-flow be-tween src–dest pairs. More available max-flowbetween ingress–egress pairs indicates that morerequests can be routed between them in the fu-ture, while less available max-flow indicates po-tential increase in blocked requests. Thus, wedefine the max-flow factor metric as

Max-flow factor ¼ Current available

max-flow between all

src–dest pairs=Initial

available max-flow

between all src–dest pairs:

• Reducing network cost: In order to minimizenetwork costs the path costs should be mini-mized. In our experiments, the path length so-lely determines path cost. An algorithm thaton the average returns less costly paths will bemore successful in lowering network costs thanalgorithms, which select more expensive paths.

• Distributing load: To measure the distribution ofload characteristics of an algorithm we examinethe loading on paths. The maximum link loadon the component links of a path measures pathload. An algorithm, which on the average selectspaths with a lower path loading, will be more


successful in distributing network load than al-gorithms, which select highly loaded paths.

3.4. Results

We now present results of comparisons of thepath computation algorithms. Figs. 5–10 show theperformance of the algorithms with respect toparameters discussed in Section 3.3. Results are

shown for the network in Fig. 4. Hot and coldpairs of src–dest nodes are randomly selected andrequests are generated for the uniform and thethree non-uniform scenarios (a)–(c) (discussed inSection 3.2). Each algorithm tries to route theserequests through the network. If a route is found,resources are reserved along it and are held aslong as the request is active. Resources are freedonce a request’s holding time expires. A request is

Fig. 5. Max-flow reduction in uniform/non-uniform models (1 QoS constraint).

Fig. 6. Path length increase in uniform/non-uniform models (1 QoS constraint).


blocked if no route can be found for it. Experi-ments are repeated with different src–dest pairsand different request sets and the results report theaverage values of the measured metrics over all theexperiments. We refer to the region below 8k re-quests as low load, the region of 8k–14k as me-dium load and the region of 14k–20k requests andupwards as high load.

Figs. 5–7 present the results of experimentswhen only one QoS constraint, i.e., bandwidth,needs to be satisfied. All requests have infinitelifetime. The algorithms compared are MIRA,

LCKS, WID-SHORT and TE-B. Results areshown for the uniform model and one or morerepresentative scenarios of the non-uniform model.Fig. 5(I) and (II) shows the reduction in max-flowfactor of the four algorithms. We see that MIRAand TE-B do consistently better than the WID-SHORT and LCKS methods (by about 10–16%).The performance of TE-B is almost always asgood as that of MIRA. At low-load conditionsMIRA does a little better, but with increasingloads TE-B achieves performance comparable toMIRA.

Fig. 7. Average path load in uniform/non-uniform models (1 QoS constraint).


Fig. 6(I) and (II) shows the average lengthof paths returned by the four algorithms. Sincethe widest-shortest-path approach gives maxi-mum priority to finding shortest path(s), WID-SHORT succeeds in having the lowest path costsunder low-load conditions. LCKS paths areslightly longer under the same condition becauseit relaxes the shortest-path constraint and in-stead finds a set of k-shortest paths. MIRA re-

turns the longest paths. At low-load conditions,both LCKS and WID-SHORT outperform TE-Band MIRA. However as the load increases onthe network, TE-B returns lower cost paths thanLCKS, while achieving performance close tothat of WID-SHORT. At high-load conditions,on average, TE-B attains about 10–15% lowercost paths than the LCKS and MIRA algo-rithms.

Fig. 8. Max-flow reduction in uniform/non-uniform models (2 QoS constraints).

Fig. 9. Path length increase in uniform/non-uniform models (2 QoS constraints).


Fig. 7(I)–(III) shows the average path load forthe four algorithms. We note that the total net-work load being the same for all algorithms,LCKS paths have the least average load. TE-Bcomes a close second and has lower path loadingthan either WID-SHORT or MIRA. The perfor-mance gains of TE-B in terms of reduction in loadis about 10–20% when compared to MIRA orWID-SHORT. However, in scenario (c) of thenon-uniform model, we observe that since themajority of traffic is concentrated between few hotpairs, most of the paths between them run at very

high loads. In this case, since there are not manynon-critical paths to off-load the traffic, load dis-tributing does not help much in lowering the av-erage load on paths. Thus the benefit of using aload distributing mechanism like LCKS or TE-B ismuch more pronounced in the uniform model andscenarios (a) and (b) of the non-uniform model.Note that though WID-SHORT and LCKS aresimilar algorithms, the latter achieves about 40%more reduction in average path load by using theproposed criticality metric. Thus, TE-B has anoverall superior performance compared to the

Fig. 10. Average path load in uniform/non-uniform models (2 QoS constraints).


competitive algorithms in terms of reducingblocking, reducing network costs and distributingnetwork load.

Figs. 8–10 present the results of experimentswhen both QoS constraints of bandwidth and de-lay have to be satisfied. The algorithms comparedare MIN-DELAY, TAMCRA and TE-DB. Re-sults are shown for the uniform model and one ormore representative scenarios of the non-uniformmodel. All requests have infinite lifetime. Fig. 8 (I)and (II) shows the reduction in max-flow factorobtained from the three algorithms. We note thateven as more requests are admitted into the sys-tem, TE-DB succeeds in maintaining the maxi-mum available flow between transmitting src–destpairs in the network. We note that on an averageTE-DB out-performs MIN-DELAY and TAM-CRA by about 15–20%.

Fig. 9(I)–(II) shows the increase in length ofpaths returned by the three algorithms, with in-creasing network load. We assume that the lengthof the paths serves as an adequate measure of theircost. We note that TAMCRA paths are the short-est at low-load conditions. However as the loadincreases, TE-DB path costs closely catch up withthat of TAMCRA paths, and at highest load con-ditions TE-DB succeeds in maintaining the leastnetwork costs. MIN-DELAY paths are alwaysabout 40–50% more expensive than either TAM-CRA or TE-DB paths.

Fig. 10(I)–(III) shows the average load on pathsreturned by the three algorithms. On average, theTE-DB paths have the least load under all loadconditions. TE-DB attains a significant reductionin average path load, when compared to MIN-DELAY. This reduction is 60–70% at low load,30–40% at medium load and 10–20% at high load.TE-DB paths consistently attains 5–15% lowerpath load than TAMCRA paths. The total net-work load being the same for all three algorithms,we show that TE-DB is uniformly more effectivein terms of distribution of network load. However,this improvement is reduced in scenario (c) of thenon-uniform model. This can be attributed to thefact that in this model majority of the requests aredistributed between very few hot pairs. Thus allpaths between the hot pairs are congested and thereare none non-critical paths to off-load the traffic.

We now investigate a more dynamic environ-ment, where flows are setup and torn down fre-quently. This environment is closer to real lifescenarios, where an application requests networkresources only for a limited amount of time. In thisexperiment, 30% of the flows are assumed to beinfinitely long and the rest of them have a meanholding time of 250 s. Results are shown only forthe uniform case. Figs. 11 and 12 show that asbefore, TE-B and TE-DB maintain a high amountof available flow in the network.

Fig. 11. Max-flow reduction in uniform model (1 QoS con-

straint).

Fig. 12. Max-flow reduction uniform model (2 QoS con-

straints).


In the next experiment we show that the in-creased available flow translates to better perfor-mance. We load the network with finite-durationrequests and observe the number of requests re-jected by each of the algorithms. The blockingprobability is measured as the ratio of the rejectedrequests to the total requests in the system. Weconduct 10 trials and the results are shown in Figs.13 and 14. We observe that the TE algorithmsattain lower blocking probabilities, which corrob-orates the intuition that more requests can be

admitted by maintaining a higher amount ofavailable flow in the network.

4. Conclusion

In this paper, we propose two TE path compu-tation algorithms, TE-B and TE-DB. The former isused when applications specify their QoS require-ments only in terms of bandwidth, while the latteris used when both bandwidth and delay require-ments are specified. Both these algorithms try tomaintain the three TE objectives of (1) increasingnetwork revenue, (2) limiting network costs, and(3) distributing network load. We compare theperformance of these two algorithms with otherexisting competitive algorithms that use the sameapplication specified constraints. We show that byconsidering the additional TE constraints, bothTE-B and TE-DB achieve considerable perfor-mance enhancements. The other existing algo-rithms while performing well with respect to somemetric, suffer from poor performance with respectto other metrics. However, for the TE algorithmsour results show that their performance is alwayseither the most favorable or very close to the mostfavorable solution with respect to all the measuredmetrics. We believe that the TE algorithms can besuitably deployed in provider networks since theysucceed in maintaining high amount of availableflow between network end-points, reducing net-work costs and distributing network load. TE-Band TE-DB, thus, qualify as superior TE pathcomputation algorithms.

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Gargi Banerjee received the B.S. degreein Computer Science from Jadav-pur University, India in 1997. She re-ceived M.S. in Computer Science fromUniversity of Maryland, BaltimoreCounty in 2000 and is currently pur-suing her Doctoral studies at thesame University under the advise-ment of Dr. Deepinder Sidhu. Her re-search interests include computer andcommunication networks, networkingprotocols, routing and switching tech-nologies, optical networking, QoS andtraffic engineering solutions.

Deepinder P. Sidhu (SM’84/ACM’84)received the B.S. degree in ElectricalEngineering from University of Kan-sas, Lawrence, and the M.S. and Ph.D.degrees in Computer Sciences andTheoretical Physics respectively fromthe State University of New York,Stony Brook, NY.He is a Professor of Computer

Science with the Computer ScienceDepartment of the University of Mary-land, Baltimore County (UMBC) andthe University of Maryland Institutefor Advanced Computer Studies

(UMIACS) at College Park. He is the director of MarylandCenter for Telecommunications Research (MCTR) at UMBC.His current research interests are in the areas of computernetworks and distributed systems. He has published over 100papers in theoretical physics and computer science. His contri-butions to the determination of weak neutral current couplingsof quarks, in gauge theories of fundamental particles, were citedby Steve Weinberg in his 1979 Nobel Prize acceptance speech.Dr. Sidhu is the Editor-in-Chief of Journal of High Speed

Networks. He was ACM/SIGCOMM National Lecturer for1992–95. He is a co-founder of Protocol Development Corp.(acquired by Phoenix Techn. Ltd.) and Telenix Corp. He man-aged the Secure and Distributed Systems Department within theR&D Division of SDC-Burroughs (now Unisys). He is theauthor of a graduate level text, OSI Conformance Testing,(Englewood Cliffs, NJ: Prentice Hall, 1994).


Documents

Comparative analysis of path computation techniques for MPLS traffic engineering