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Design and performance analysis of an inductive QoS routing algorithm

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Design and performance analysis of an inductive QoS routing algorithm
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  Design and performance analysis of an inductive QoS routing algorithm Abdelhamid Mellouk a, * , Saïd Hoceïni a , Sherali Zeadally b a LISSI Laboratory, University of Paris 12-Val de Marne, Paris-Est University, 122 rue Paul Armangot, Vitry sur Seine 94400, France b Dept. of Comp. Sci. and Inf. Tech., University of The District of Columbia, Washington, DC 20008, USA a r t i c l e i n f o  Article history: Available online 15 May 2009 Keywords: Quality of service based routingShortest path routingReinforcement learningDynamic networkState dependent model a b s t r a c t Routing mechanism is key to the success of large-scale, distributed communication and heterogeneousnetworks. Consequently, computing constrained shortest paths is fundamental to some important net-work functions such as QoS routing and traffic engineering. The problem of QoS routing with multipleadditive constraints is known to be NP-complete but researchers have been designing heuristics andapproximation algorithms for multi-constrained paths algorithms to propose pseudo-polynomial timealgorithms. Thispaper introduces apolynomial timeapproximationqualityofservice(QoS) routingalgo-rithm and constructs dynamic state-dependent routing policies. The proposed algorithm uses an induc-tive approach based on trial/error paradigm combined with swarm adaptive approaches to optimizelexicographicallyvariousQoScriteria. Theoriginalityofourapproachisbasedonthefactthatoursystemis capable to take into account the dynamics of the network where no model of the network dynamics isassumed initially. Our approach samples, estimates, and builds the model of pertinent aspects of theenvironment which is very important in heterogeneous networks. The algorithmuses a model that com-binesbothastochasticplannedpre-navigationfortheexplorationphaseandadeterministicapproachforthe backward phase. Multiple paths are searched in parallel to find the  K   best qualified ones. To improvethe overall network performance, a load adaptive balancing policy is defined and depends on a dynamictraffic path probability distribution function. We conducted a performance analysis of the proposed QoSrouting algorithm using OPNET based on a platform simulated network. The obtained results demon-strate substantial performance improvements as well as the benefits of learning approaches over net-works with dynamically changing traffic.   2009 Elsevier B.V. All rights reserved. 1. Introduction Today, providing a good quality of service (QoS) in heteroge-neous networks for irregular traffic flows remains a significantchallenge. A general problem of large-scale distributed systemssuch as networks is the ever-increasing complexity of their opera-tion. This complexity is mainly driven by heterogeneity. The widevariety of the technologies deployed within a network and theirdifferent, if not proprietary, operational paradigms put a too com-plex equation for the network operators to solve. Moreover net-work operations are typically handled by one or more humanoperators. Manual control is time-consuming, expensive, and er-ror-prone. Nevertheless, both technologies and needs continue todevelop and to grow. The risk is thus that complexity and cost be-come limiting factors to the evolution of networks into the futureandtotheenrichedservicestheyareexpectedtodeliver.Moreovermanagement to network element interactions are mostly limitedto configuration functions and/or bulk data retrieval; intelligenceis most often outside the strict scope of such environments.The main directions of the research community are to providesolutionsenablingtobuildascalableandrobustenvironmentwithlow complexity for large-scale, dynamic networks. The objectivewill be met relying on the decentralization of functions, theirself-organisation but also the methods, techniques and tools fordata retrieval and analysis and learning participating to the globaldecision process simplifying human actions.Oneofthemostpromisingdirectionsunderlyingheterogeneousnetworks is routing mechanisms, that is, to guarantee new valueadded services by addressing the integration of dynamic criteriasupported by each kind of network. The most popular formulationof the optimal distributed routing problem in a data network isbased on a multicommodity flow optimization whereby a separa-ble objective function is minimized with respect to the types of flow subject to multicommodity flow constraints. However, dueto their complexity, increased processing burden, a few proposedrouting schemes could be accepted for the Internet.Besides, the impressive emergence and the increasing de-mands of real-time, multiservice traffic (such as data, video, 0140-3664/$ - see front matter   2009 Elsevier B.V. All rights reserved.doi:10.1016/j.comcom.2009.05.002 *  Corresponding author. Tel.: +33 141807313; fax: +33 141807376. E-mail address:  mellouk@univ-paris12.fr (A. Mellouk).Computer Communications 32 (2009) 1371–1376 Contents lists available at ScienceDirect Computer Communications journal homepage: www.elsevier.com/locate/comcom  voice, etc.) over IP-based networks require continuous QoS aswell as scalability. To support the requirements of theseemerging multimedia applications several research efforts inrecent years have been exploring various QoS routing designsand approaches for heterogeneous networks and IP-basedbackbone architectures characterized by high and irregulartraffic [1].Thegoal of QoSroutingistofindanetworkpathwhichsatisfiesthe given constraints and to simultaneously optimize the resourceutilization. The integration of QoS parameters increases the com-plexity of current routingalgorithms. Infact, the problemof deter-mining a QoS route that satisfies two or more path constraints (forexample, delay and cost) is knownto be NP-complete[2]. One ma- jor difficulty is that the time required to solve the multi-con-strained optimal path problem exactly cannot be upper-boundedby a polynomial function. Hence much of the focus over the lastfewyearshasbeenonthedevelopmentofpseudo-polynomialtimealgorithms, heuristics, and approximation algorithms for multi-constrained QoS paths [3].Recently, several studies have been conducted on QoS routingalgorithmswhichconsiderQoSrequirementsintosuchalgorithms.In [4], the authors introduce heuristics to find a source-to-destina-tion path that satisfies two or more additive constraints based onedge weights. In [5], the authors proposed a polynomial timeapproximation algorithm for  k  multi-constrained path which usesa shortest path algorithmsuch as Dijkstra algorithm[6]. In [7], the authors propose a randomized heuristic that employs two phases.Inthe first phase, a shortest pathis computedfor eachof the k  QoSconstraints as well as for a linear combination of all  k  constraints.In the second phase a randomized breadth-first search is per-formed for a  k  multi-constrained problem. In [3], the authors sug-gest that QoS routing in realistic networks could not be NP-complete with respect to a particular class of networks (topologyand link weight structure).Given such complexity, QoS routing problems are dividedinto several classes according to their characteristics. For exam-ple, we distinguish the single path routing problem and themulti-path routing problem, where routers maintain multipledistinct paths of arbitrary costs between a source and a desti-nation. The multi-path routing approach offers several advanta-ges such as good bandwidth, bounded delay variation,minimum delay, and improved fault tolerance. In addition, mul-ti-path routing makes effective use of the graph structure of anetwork compared to single path routing which superimposesa logical routing tree over the network topology. On the otherhand, as Internet is a large collection of more than 25,000 inde-pendent domains called  autonomous systems  (ASs), the coopera-tion between ASs is not optimized at the network level, but israther based on business relationships between organizations.The fully-independent management actions in each AS are ex-pressed in terms of a policy-based routing strategy which pri-marily controls the outbound traffic of the AS and caninclude conflicting policies. A global solution for QoS routingover all the ASs must be able to handle both different QoS pro-visioning mechanisms and service specifications. Such a solutionof building models of large ISP’s is too complex to achieve [8].In this case, routing is divided into two classes: interior gate-way protocol (IGP) (such as OSPF or IS-IS) computes the inte-rior paths in one AS while exterior gateway protocols (EGP)(such as BGP) is responsible for the selection of interdomainpaths. To fulfil application QoS requirements, many ISPs havedeployed mechanisms to provide differentiated services in theirnetworks. In fact, in the last decade, none of QoS routing pro-posals has been deployed in practice. This is because ISPs preferoverprovisioning of their networks over the delivery and man-agement of QoS [9]. 2. Related work  A reviewof the literature revealed that various approaches [10]have been proposed to take into account QoS requirements. Con-straints (such as bandwidth, delay, loss) imposed by QoS require-ments are often referred to as QoS constraints, and the associatedrouting is referred to as QoS routing which is a part of Con-strained-Based Routing (CBR). Interest in constrained-based rout-ing has been attracting a lot of attention in recent years. Toreduce complexity, most of these approaches are based on heuris-tics. We can classify three main categories of CBR below:   Label switching/Reservation approaches:  spurred by approachessuch as ATM PNNI, MPLS or GMPLS. With MPLS, fixed lengthlabels are attached to packets at an ingress router, and forward-ing decisions are based on these labels in the interior routers of the label-switched path. MPLS Traffic Engineering allows over-riding the default routing protocol, thus forwarding over pathsnot normally considered. A resource reservation protocol suchas RSVP must be employed to reserve the required resources.Another architecture proposed to provide Internet QoS is theDifferentiated Services (DiffServ) architecture. DiffServ scaleswell by pushing complexity to network domain boundaries.   Multi-constrained path approaches (MCP):  the goal of all of suchapproaches is to retrieve the shortest path among the set of fea-sible paths between two nodes. Considerable work in the litera-turehas focusedon a special case of the MCPproblemknownasthe Restricted Shortest Path (RSP) problem. The goal is to findthe least-cost path among those that satisfyonlyone constraint.An overview of these approaches can be found in [10].   Inductive approaches:  tobeabletomakeanoptimalroutingdeci-sion according to relevant performance criteria, a network nodeneeds to have a completeknowledgeof the entirenetworkstateand an accurate prediction of the evolution of the network andits dynamics. This, however, is impossible unless the routingalgorithm is capable of adapting to the network state changesalmost in real-time. Thus, it is necessary to design intelligentand adaptive optimizing routing algorithms which take intoaccount the networkstate and its evolution. We need to exploreQoS- based state-dependent routing algorithm.In this paper, we focus our attention on developing a systembased on inductive approaches with continuous learning dynamicnetwork parameters. Basically, these approaches select routesbasedonQoSflowrequirementsandnetworkresourceavailability.Theoriginalityofourapproachisbasedonthefact thatoursystemis capable to take into account the dynamics of the network whereno model of the network dynamics is assumed initially. Our ap-proach samples, estimates, and builds the model of pertinent as-pects of the environment which is very important inheterogeneous networks. In Section 3, we discuss the family of inductive approaches. Next, we present our algorithm which per-forms the following three steps: (1) select  K   best candidate pathsbased on the cost cumulative path from the source and the desti-nation nodes; (2) traffic is distributed among the  K   best Pathsaccording the end-to-end delay criteria optimized by reinforce-mentlearningfeedbackand(3)thedistributionisbasedonaprob-abilistic module which take into account the packet delivery timecomputed by the  Q  -learning process and the latency router’s wait-ingqueues.Atrafficmodelthatenablesthecreationofbenchmarksfor real cases will be proposed and presented in Section 5. AllexperimentsareconductedusingtheOPNETsimulatorfordifferenttraffic loads and compared to an early version of our system. InSection 6, we make some concluding remarks and highlight somefuture areas of work. 1372  A. Mellouk et al./Computer Communications 32 (2009) 1371–1376   3. Inductive approaches The modern Internet has become a large complex distributedsystem composed of interoperating complex sub-systems basedon several dynamic parameters. The drivers of this growth includechanges in technology and changes in regulation. In this context,the methodology approach that allows us to address the QoS rout-ing problem is dynamic programming which, however, is verycomplex to solve precisely. To design adaptive algorithms for dy-namic networks routing problems, we focused on the use of Rein-forcement Learning (RL) approaches [11]. The salient feature of RL algorithms is the nature of their routing table entries which areprobabilistic. With such algorithms, to improve the routing deci-sion quality, a router tries out different links to see if they producegood routes – a mode of operation called  exploration . Informationlearntduringthisexplorationphaseisusedtotakefuturedecisions– a mode referredto as  exploitation . Bothexplorationand exploita-tionphases inRLparadigmsarenecessaryfor effectiveroutingandthechoiceoftheoutgoinginterfacedependsontheactiontakenbythe router. With RL algorithms, the learning and evaluation modestakeplacecontinuously(asshowninFig. 1). Notethat, theRLalgo-rithm assigns credit to actions based on reinforcement from theenvironment. In the case where such credit assignment is con-ducted systematically over a large number of routing decisions(such that all actions have been sufficiently explored), RL algo-rithms converge to solve stochastic shortest path routing prob-lems. Finally, algorithms for RL are distributed algorithms thattake into account the dynamics of the network where no modelof the network dynamics is assumed initially. The RL algorithmsamples, estimates, and builds the model of pertinent aspects of the environment.Most efforts have investigated the use of these inductive ap-proaches based on artificial neuronal intelligence together withbiologically inspired techniques to control network behavior inreal-timesoas toprovideusers withtheQoStheyneed, andtoim-prove network robustness and resilience. We note the followingapproaches that have been recently proposed:   Q-Routing approach:  in this technique [12], each node makes itsrouting decision based on the local routing information, repre-sented as a table of   Q   values which estimate the quality of thealternative routes. These values are updated each time the nodesends a packet to one of its neighbors. However, when a  Q   valueis not updated for a long time, it does not necessarily reflect thecurrent state of the network and hence a routing decision basedon such an unreliable  Q   value will not be accurate. The updaterule in  Q  -Routing does not take into account the reliability of theestimatedorupdated Q   valuebecauseitdependsonthetraf-fic pattern, and load levels. In fact, most of the  Q   values in thenetwork are unreliable. For this purpose, other algorithms havebeen proposed such as Confidence based  Q  -Routing (CQ-Rout-ing) or Confidence based Dual Reinforcement  Q  -Routing (DRQ-Routing).   Cognitive Packet Networks (CPNs.):  CPNs [13] are based on ran-dom neural networks. These are store-and-forward packet net-works in which intelligence is constructed into the packetsrather than at the routers or in the high-level protocols. CPN isa reliable packet network infrastructure, which incorporatespacket loss and delays directly into user QoS criteria and usethese criteria to do routing. Cognitive packet networks carrythree major types of packets: smart packets, dumb packets,and acknowledgments (ACK). Smart or cognitive packets routethemselves, they learn to avoid link, node failures and conges-tion to avoid being lost. They learn from their own observationsabout the network and/or from the experience of other packets.They rely minimally on routers. The major drawback of algo-rithms based on cognitive packet networks is the convergencetime, which is very important when the network is heavilyloaded.   Swarm Ant Colony Optimization (AntNet): Antsroutingalgorithms[14] are inspired by dynamics of how ant colonies learn theshortest route to food source using very little state and compu-tation. Instead of having fixed next-hop value, the routing tablewill have multiple next-hop choices for a destination, with eachcandidate associated with a possibility, which indicates thegoodness of choosing this hop as the next hop in favour to formthe shortest path. Given a specified source node and destinationnode, the source node sends out some kind of ant packets basedonthepossibilityentriesinitsownroutingtable.Thoseantswillexplore the routes in the network. They record the hops theyhave passed. When an ant packet reaches the destination node,the ant packet will return to the source node along the sameroute. Along the way back to the destination node, the antpacket will change the routing table for every node it passesby. The rules of updating the routing tables are: increase thepossibility of the hop it comes fromwhile decrease the possibil-ities of other candidates. The Ants approach is immune to thesub-optimal route problem since it explores, at all times, allpathsofthenetwork.However,thetrafficgeneratedbyantalgo-rithms is higher than the traffic generated by concurrentapproaches. 4. System model In [15], we have presented an adaptive routing algorithmbasedon the  Q  -learning approach. The  Q   function is approximated by areinforcement learning based neural network (NN). In this ap-proach, NN ensures the prediction of parameters depending ontraffic variations. Compared to approaches based on a  Q   table,the  Q   value is approximated by a reinforcement learning basedonaneuralnetworkofafixedsize,allowingthelearnertoincorpo-rate various parameters such as local router’s queue size and thepacket delivery time into its routing cost estimation function. In-deed, a neural network allows the modelling of complex functionswithagoodprecisionalongwithadiscriminatingtrainingandtak-ing into account the context of the network. Moreover, it can beusedto predict non-stationary or irregular traffic. In this approach,theobjectiveis tominimizetheaveragepacket deliverytime. Con-sequently,thereinforcementsignalchosencorrespondstotheesti-mated time to transfer a packet to its destination. Typically, thepacketdeliverytimeincludesthreevariables: thepacket transmis-sion time, the packet treatment time in the router and the latencyin the waiting queue. Fig. 1.  Reinforcement learning paradigm.  A. Mellouk et al./Computer Communications 32 (2009) 1371–1376   1373  Unfortunately, this first version of our routing algorithm ex-ploreall thenetworkenvironment,doesnottakeintoaccountloopproblems and takes a long time to converge. To address this draw-backandreducethecomputationaltime,wehavemodifiedandex-tended our earlier  Q  -neural routing algorithm. The resultingsystem,called‘‘KBestOptimal Q  -routingAlgorithm( KOQRA )”,con-tains three stages. The objective of the first stage is to select the  K  best candidate paths according to the cumulative cost path fromthe source and the destination nodes (for simplicity, we considerhere all link costs equal to 1). The second stage is used to integratetraffic dynamics. During this stage, a continuous end-to-end delayamong the  K   best selected paths is computed using a reinforce-ment  Q  -learning function. To force the router to take alternativeroutes during this second stage, we add a probability distributionmodule for all the obtained  K   best paths based on packet deliverytime obtained from the second stage and the router’s queue la-tency associated with each path. 4.1. First stage: constructing k best paths based on static criteria Firstof all, inspiteof exploringtheentirenetworkenvironmentwhich needs large computational time and space memory, our ap-proach reduces this environment to  K   Best no loop paths in termsof cumulative cost links. Thus, each router maintains a link statedatabase of the network topology map. We used a label settingalgorithm based on the optimality principle and a generalizationof Dijkstra’s algorithm.To find these  K   best paths, a variant of the Dijkstra’s algorithmwas proposed in [16], which does not stop when the destination isreached, but continues until the destination has been reached  K  times. The  K   best path is applied to the intermediate nodes onthe path from source node to destination node, establishing a listof multiple sub-paths from the source to intermediate nodes. Thespace complexity is  O ð Kmn Þ , where  K   is the number of paths,  n (resp.  m ) is the number of nodes (resp. the number of links). Byusing a pertinent data structure [5], and the principle of Paretonon-dominated paths [17] to reduce the search-space withoutcompromising the solution, the time complexity can be kept at O ð Knlog  ð Kn Þ þ  K  2 m Þ .When a network link changes its state (i.e., goes up or down, orits utilization is increased or decreased), the network is floodedwith a link state advertisement (LSA) message. This message canbeissuedperiodicallyorwhentheactuallinkstatechangeexceedsacertainrelativeorabsolutethreshold. Obviously, thereistradeoff between the frequency of state updates (the accuracy of the linkstate database) and the cost of performing those updates. In ourapproach, the link state information is updated when the actuallink state changes. Once the link state database at each router isupdated, the router updates the set of the  K   best paths. 4.2. Second stage: optimizing the end-to-end delay with the Q-learning algorithm After finding the  K   best optimal paths based on link costs, thesecond step is to distribute the traffic on these  K   candidate paths.For this, we use a dynamic criterion another criteria based onend-to-end delays. The selected reinforcement signal correspondsto the estimated time to transfer a packet to its destination. Thisvalue is computed by a variant of the  Q  -Routing algorithm whichis considered as an asynchronous relaxation of the Bellman–Fordalgorithm. Typically, the packet delivery time includes three vari-ables: the packet transmission time, the packet treatment time inthe router and the latency in the waiting queue. In our case, thepacket transmission time is not taken into account. In fact, thisparameter can be neglected in comparison to the other latenciesand has negligible effect on the routing process.In this approach, each router  x  maintains in a  Q  -table a collec-tion of values of   Q  ð  x ;  y ; d Þ  for every destination  d  and for everyinterface  y .Thisvaluereflectsadelayofdeliveringapacketfordes-tination  d  via interface s. Then, the router  x  forwards the packet tothe next best router  y  determined from the  Q  -table. Just afterreceivingthispacket, the router  y  provides  x  anestimateof itsbest Q   value to reach the destination. This new information is thenadded in the  Q   values of the router  x .The reinforcement signal  T   employed in the  Q  -learningalgorithm can be defined as the minimum of the sum of the estimated  Q  ð  x ;  y ; d Þ  sent by the router  y  neighbor of router  x  and the latency in the waiting queue  q  x  corresponding torouter  x . T   ¼  min  y 2 neighbor of x f q  x  þ  Q  ð  x ;  y ; d Þg ð 1 Þ where  Q  ð  x ;  y ; d Þ , denote the estimated time by the router  x  so thatthe packet  p  reaches its destination  d  through the router  y . Thisparameterdoesnotincludethelatencyinthewaitingqueueof rou-ter  x . The packet is sent to the router  y  which determines the opti-mal path to send this packet.Oncethechoiceofthenextrouterismade, therouter  y  putsthepacket in the waiting queue, and sends back the value  T   as a rein-forcement signal to the router  x . It can therefore update its rein-forcement function as: D Q  ð  x ;  y ; d Þ ¼  g ð c þ  T     Q  ð  x ;  y ; d ÞÞ ð 2 Þ c  and  g  are the packet transmission time between  x  and  y  and thelearning rate, respectively.So, the new estimation  Q  0 ð  x ;  y ; d Þ  can be written as follows: Q  0 ð  x ;  y ; d Þ ¼  Q  ð  x ;  y ; d Þð 1  g Þ þ g ð T   þ c Þ ð 3 Þ The system based on these two first stages is called  KSPQR  in therest of the paper. 4.3. Third stage: traffic adaptive path distribution The goal of this stage is to distribute the traffic on  K   best pathsina probabilistic manner. Inorder totakeintoaccountthe dynam-icsofirregulartraffic,andtoforcetheroutertotakethealternativeroutes found in the second stage and not only the best path, weautomatically compute a load balancing distribution on the ob-tained  K   paths. In this way packets reach their destinations withtimes close to optimal, while ensuring a good exploration of theremaining paths. The process is based on the packet delivery timecomputed by our  Q   reinforcement learning and the latency inqueue associated for each path.Let  D i ð t  Þ  be the packet delivery time for path  i  at time  t  .Let  T  n 0 i  ð t  Þ  be the latency in the queue associated with the clos-est router  n 0 in the direction of the path  i  at time  t   (that is,the neighbour of router  n Þ . The following formula allows us tocompute the probability  P  ni  ð t  Þ  for the  i th path in router  n  attime  t  : P  ni  ¼  1 D i  a   1 T  n 0 i ! b 2435X K i ¼ 1 "  1 D i  a   1 T  n 0 i ! b ,35  ð 4 Þ where  a  and  b  are two tuneable parameters that determine theinfluence of delay time and waited queue time respectively. Theyhaveequivalent influencefor the case of   a  ¼  b . This formulaassoci-atesasmallprobabilityforpathswithhighrouterprocessingdelaysand/or high queueing time. This is due to the fact that when delaytimeincreasesthevalueof  ½ 1 = D i ð t  Þ a ,queuingdelaycauses ½ 1 = T  i ð t  Þ b to decrease.Tostudytheimpactofthismoduleonthewholesystem,weusethe name  KOQRA  of the entire system with all the stages. 1374  A. Mellouk et al./Computer Communications 32 (2009) 1371–1376   5. Simulation results 5.1. Topology and traffic model To investigate the performance of our proposed algorithm, wefocus on IP datagram transmissions. The simulated network called NTTnet  , is presented in Fig. 2. It is not a well balanced network andincludes57interconnectedroutersand162bidirectional links.Thetraffic is sent/received by six end nodes (marked in the Fig. 2, P i ).We model traffic in terms of requests characterized by itssource and destination. For each node, an independent Poissonprocess regulates the arrival of new sessions where the sessions’inter-arrival times are negative exponentially distributed.Although we use arrival and departure of flows, we do not modelthe data traffic of the flows. We also chose not to implement aproper management of error, flow and congestion control. In fact,each additional control component has a considerable impact onthe network performance, making it very difficult to evaluate andto study properties of each control algorithm without taking inconsideration the complex way it interacts with all the other con-trol components. Therefore, we chose to test the behavior of ouralgorithm such that the routing component can be evaluated inisolation. For our simulation results, we studied the performanceof the algorithms with increasing packet traffic load, examiningthe evolution of the network status toward a saturation condition,and for temporary saturation conditions. We defined two kinds of traffic: lowtraffic loadandheavy traffic loadconditions of the net-work’s traffic. Moreover, some nodes act like temporary hot spots(i.e., they generate a heavy load of traffic but only for a short timeinterval). 5.2. Performance evaluation To validate our results, we compare our system with two kindsof algorithms [10]:– Those based on Shortest Path First (SPF) technique where rout-ing in this family used the only best path based on delayconstraint.– Those based on Standard Optimal QoS Multi-Path Routing(SOMR) where routing is based on finding  K   Best Optimal Pathsandusedacompositenonlinearfunctiontooptimizesimultane-oulsy delay and cost criteria.All algorithms have been implemented with OPNET and usedthe same data structure. Results given in all the figures are evalu-ated in terms of average packet end-to-end delivery time on thesame conditions. Time simulation is represented on the other axisof the figures.In the case of low load traffic (Fig. 3), one can note that after aperiod of initialization, performances of classical approaches arebetter than our algorithm. The conditions of the traffic are verysimple, our algorithm generates more useless messages than theclassical ones which increase the end-to-end delay. Fig. 4 illus-trates the case of continuous heavy load traffic generated by creat-ingperiodicallyconditionsofcongestiononthenetwork.Asshownin Fig. 4, our approach gives better results than the classical algo- rithms. This is due to the fact that in our new approach, routersare able to take into account not only the average of delivery delaybut also the waiting queue time. Thus, they are able to adapt theirdecisions swiftly and in close concordance with the networkdynamics. In spite of the many packages taking secondary ways,Shortest Path Routing does not present better performances be-cause it rests on a probabilistic method to distribute the load of thenetworkover onlytheclosest cost paths, andnot onthedegra-dation of the times of routing. Thus, mean of average packet deliv-ery time obtained by our approach is reduced by 39% compared totraditional Shortest Path Routing algorithms. The exploration of potential good paths, a priori no best, allow us to generate betterresults.Theintroductionofaprobabilisticmodulein KOQRA permit Fig. 2.  Simulated networks, NTTnet. Fig. 3.  End-to-end Delay with a low load of traffic. Fig. 4.  End-to-end Delay with a high load of traffic.  A. Mellouk et al./Computer Communications 32 (2009) 1371–1376   1375
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