Hybrid Multipath Routing Algorithms for Load Balancing ... - IEEE Xplore

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Armand Toguyeni

Ahmed Rahmani

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,QWURGXFWLRQ Traffic engineering is concerned with the performance optimization of operational networks. Its main objective is to reduce the congested hot spots and improve resource utilization across the network through carefully managing the traffic distribution inside a network [1]. Multipath routing is the one of the mechanisms for load balancing in which the total load from a source to a destination is spatially distributed over several paths. When disseminating traffic into multiple paths, routers should adaptively allocate flows to each path in order to achieve load balancing among multiple paths. For the sake of more efficient traffic engineering in IP networks, network administrators must be able to control the paths of packets. MPLS (Multi Protocol Label Switching) [2] can provide the connections with LSPs (Label Switched Paths) that are explicit routes connecting pairs of ingress-egress edge routers in an MPLS network. We get the objective of traffic engineering to minimize the maximum link utilization in the network.

When the maximum link utilization minimizes, naturally the rejection rate for demand can be reduced. If we assume that traffic grows in proportion to the current traffic pattern, this objective will ensure that the extra traffic causes minimum congestion. This paper focuses on flow-based routing which is better than packet-based routing in the point of preventing the packet reordering overhead. The objective of this study is first to evaluate relevant propositions with regard to two steps that characterize multipath routing algorithm in section 2 [3]. In section 3, it describes some modular steps for hybrid combination and our new traffic splitting algorithm is also proposed. In section 4, we construct new hybrid algorithms by combining each modular steps. We simulate them using QV to analyse their results in section 5. The last section gives the conclusion and some perspectives of this study.

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0XOWLPRGHOVFKHPH>@ Multipath routing algorithm consists in two main steps as Figure1: FRPSXWDWLRQ RI PXOWLSOH SDWKV and WUDIILFVSOLWWLQJDPRQJWKHVHPXOWLSOHSDWKV In the first step, it computes the set of candidate paths which is a subset of all the paths between a pair of considered routers. According to the nature of a cost function, different algorithms can be applied to determine these candidate paths. The authors consider various static criteria such as bandwidth, hop count, delay, error ratio, and so on for a cost function. This problem of a cost function definition is typically a multi-criteria problem [4]. &RVW I EDQGZLGWKKRSFRXQWGHOD\HUURUUDWLR The second step is to split traffic among multiple candidate paths. These paths are qualified of candidate paths because all of them are not necessary to be used at a given time. The repartition rate of a demand on candidate paths depends on the evaluation of dynamic

Proceedings of the 20th International Conference on Advanced Information Networking and Applications (AINA’06) 1550-445X/06 $20.00 © 2006

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criteria such as the blockages, the packet loss ratio, the measured delay, the jitter, and so on. &RVW I EORFNDJH SDFNHW ORVV UDWH PHDVXUHGGHOD\MLWWHU

(MIP hereafter) for the bifurcation case is formulated as follows. 0LQLPL]H Subject to (1) 0, , ,

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0 d ; d1, 0 d J d1, 0 dD, 0 =, 0 d 0 d ¬1/ J¼ )LJXUH3ULQFLSDOVFKHPHRI0XOWLSDWK URXWLQJ. If multiple criteria must be optimized simultaneously, the complexity of the algorithms usually becomes very high [5]. A lot of heuristic algorithms are proposed to solve this problem.

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Let us consider Traffic Bifurcation (TB) problem as a formulation to give an optimal bound to determine whether our hybrid algorithms give satisfactory performance. This problem will be solved based on LPF (Linear Programming Formulation). The TB problem consists of finding multiple paths carrying a part of or all the traffic between ingress and egress node which minimizes the maximum of link utilization . When splitting a traffic demand onto multiple paths, the granularity of load splitting, J(J) is defined to represent how coarsely a traffic demand can be divided. The network is modelled as a directed graph, * (9(), where 9 is the set of nodes and ( represents the set of links. The capacity of a directional link (LM) ( is F Each traffic demand N . is given for a node pair between an ingress router V and an egress router W . The variable ; represents the fraction of the traffic demand N assigned to link (LM). The integer variable 0 represents how many units of basic discrete split demands for a traffic demand N are assigned to link (LM) Let G be a scaling factor to normalize total traffic demand from the source to become 1. The Mixed Integer Programming problem

Equations (1), (2) and (3) represent the flow constraints for intermediate, source, and sink nodes, respectively. Equation (4) is the link capacity constraint. Equation (5) states that the fraction of the demand N assigned to a link is proportional to the number of units of the demand that have been assigned to the link (LM). The TB(g) MIP problem can be solved by searching the branch-and-bound tree with an MIP solver such as MATLAB, and the solution gives the optimal flow values, ; . In a realistic environment, these equations are generally not satisfied. So, heuristics are needed to obtain a reasonably good solution close to the optimal one instead of solving the above optimization models directly. Our three hybrid algorithms and other routing algorithms will be compared with this TB(g) optimal value to decide how much close to optimal value.

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LDM and WDP algorithms are selected to be used as the modular part of the hybrid algorithms. In addition, our new traffic splitting algorithm is used also as one modular part for the second step. These modular parts are combined to give three new hybrid algorithms. This section describes these modular parts.

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with regard to bottleneck links. The width of path U(Z is a way to detect bottlenecks in the network and to avoid them if possible. It is computed as follows, where F is the average residual bandwidth on link (LM). Z PLQF with (LM) r (6) And path distance of path U (G ) is defined as follows. 1 (7) G ¦F A path is added to the subset of good paths if its inclusion increases the width of this subset. At the opposite, a path is deleted if its suppression does not reduce the width of the subset of good paths. This is a heavy computation to perform on every path, and the algorithm is very time-consuming: computing a set of Q paths will take 2Q cycles because the path selection procedure is clearly in 2Q and allows selecting one path at each iteration considering all potential paths between the pair of ingress-egress routers. The procedure to compute a width of path set 5 is as follows: PROCEDURE :,'7+5 : While 5 Þ Z = PD[Z U 5 5 ^UU 5Z Z ` G PLQG U 5 U ^UU 5 G G ` : :Z For ea c h O in U FO FO±Z 11. 5 5?U Return : END PROCEDURE 1. 2. 3. 4.

In line 8 of this procedure, WDP paper does not consider the element number of path set U . Let us called FU this number. To improve this procedure we propose to modify this line as it follows.

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. 3DWK VHOHFWLRQ SDUW RI /'0 >@ The LDM algorithm tries to find a minimal set of good paths. The set is built on two criteria: the metric hop-count and the utilization rate limit ( fixed by the administrator. A good path must have its utilization rate inferior to The candidate path set could either be pre-computed when there are some significant changes in the dynamic network status or can also be computed on demand for a new arriving of a user flow request. LDM decides

whether to expand the candidate path set based on the congestion level of candidate path set. A longer LSP is added to the candidate path set if the minimum utilization of the current candidate LSP set is higher than and the utilization of this longer LSP is relatively lower than the LSPs with the maximum link utilization among the LSPs in the current candidate path set. It is done in a 2Qð time in the worst case, the number of iterations growing with the utilization of the network. Here Q refers to the number of paths available for the considered ingressegress pair of nodes.

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7UDIILF6SOLWWLQJSDUWRI/'0>@The traffic splitting is done using a heuristic to determine a repartition policy for incoming flows at an ingress edge router. Each path is adjoined a probability of selection 3(O) using the formula (8). Once probabilities are defined, each incoming flow is directed to one route selected randomly. The K(O) and G(O) functions refer to the length and the remaining capacity of /63 O, while & and & are constants computed to make 3(O) a probability. The D and D factors are defined by the administrator to fit its needs. ( )

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The complexity of the whole procedure is clearly 2Q Here Q refers to the number of candidate paths. 3URSRVLWLRQRIDQHZWUDIILFVSOLWWLQJPHWKRG Our proposition of traffic splitting is an improvement of LDM splitting step. It calculates each probability on candidate paths like LDM but it is different from LDM in the point of how it selects one path for sending the current flow. The assignment of an incoming flow is based on the selection probability of candidate path O 6O . D&DOFXODWLQJDGLVWULEXWLRQSUREDELOLW\ Since we cannot split individual flows, consecutive packets from the same flow can be viewed as a single logical packet train that cannot be further divided by the traffic splitter. Thus a large number of long packet trains will have negative effects on the traffic splitting performance. Traffic splitting is significantly harder when there is small number of large flows. The traffic splitting is done using a heuristic to determine a


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repartition policy for incoming flows. Each path is adjoined a splitting probability using the following formula (9) and (10). The calculation of the probability uses the traffic matrix which is made in the precedent link state update period. For each incoming traffic flow, an ingress router selects one LSP among the candidate paths according to two probabilities: calculated repartition ratio U and effective distributed ratio between two update periods H Using these two values, we calculate the probability 6 for selecting the considered LSP to assign among candidate paths. We define several notations to calculate U H and 6 Suppose that candidate path set by WDP algorithm is &3 {O O « O } where N is the number of the selected paths. + is the constant to make the sum of the probabilities that are inversely proportionate to the hop count of an LSPi, KF(O ) Let E(O ) is the bottleneck’s residual bandwidth of /63 in &3. % is the sum of E(O ). (9) 1

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U is the function of both the length and the residual capacity of the /63 and it represents its splitting probability. U is given by equation (10), with S and S factors defined by the administrator to fit its needs.

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H is the effective repartition ratio on /63 in &3and is calculated as its effective distributed traffic over total demands from the last link state update period until now. HIIHFWLYH WUDIILF RQ /63 (11) H WRWDO GHPDQG IRU D SHULRG E6HOHFWLQJRQH/63WRDVVLJQWKHWUDIILF 6 is the value to estimate how much of U is satisfied with its repartition probability in real. Ingress router calculates the differences between its pre-computed probability U and the effective repartition ratio H . Then the probability of selection 6 for each candidate path is calculated as follows.

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If 6 is greater than 0, it means that the quantity of assigned flow to the /63 is inferior of what has been planned. At the opposite, if 6 is less than 0, it means

that too much flow has already been assigned to this path. So we must keep out of sending current traffic on it because there are risks to provoke congestion on this path. Consequently, the assignment rule consists in selecting the element of CP with the greatest value of 6 . However, if all paths in the candidate path set have a negative 6 , the algorithm must restart to calculate a new candidate path set. The assignment rule is improved by taking into account the quantity of bandwidth requested by the incoming flow. Indeed, even if an LSP has a positive 6 , it is not selected when its residual bandwidth capacity is inferior to the demand.

3URSRVLWLRQRI+\EULGDOJRULWKPV In this section, we define three hybrid algorithms by combining the selection algorithm WDP with the splitting of algorithm of LDM and our new proposition of splitting. Let us recall that the objective is to minimize the maximum link utilization over the network

:'3IRUVWHSDQG/'0IRUVWHS +\EULG !:'3/'0 6WHS. Source-destination pair, demand size and flow duration time are randomly generated. 6WHS. Ingress router calculates the candidate path set by WDP algorithm using last updated link state information. 6WHSFor each candidate path, its probability value is calculated using path’s hop-count and utilization rate by LDM algorithm. 6WHSIt sends the traffic onto one LSP with the certain probability value randomly. 6WHS Every 3 seconds, link state information is updated. Link state information is conserved the same one till the next update time so there could be congestion because of this inaccurate link state information. By using WDP for candidate paths, this hybrid algorithm can reduce the congestion probability by comparison to the original LDM. Indeed, it takes benefit from the path independence technique of WDP.

/'0IRUVWHSDQG1HZ0HWKRGIRUVWHS +\EULG !/'01HZ0HWKRG 6WHS. Source-destination pair, demand size and flow duration time are randomly generated.


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6WHS. Candidate paths are selected starting with the shortest path. 6WHS. If minimum path utilization rate among candidates is more than 60 %, goto Step2 with smoothen criteria (5% less utilization rate and 1 more hop count).Else, goto Step4 6WHS. It calculates their Si value for every candidate paths and selects one path with the greatest one and sends the traffic. 6WHS. Every 3 seconds, link state information is updated. The advantage of gradient method is to reduce the probability of congestion by taking into account the residual bandwidth capacity of a path before it assigns an incoming flow.

2 gives more details of the flowchart of this hybrid, specially called LBWDP (Load Balancing over WDP).

6LPXODWLRQUHVXOWV We simulate our hybrids and other existing algorithms using QV Network Simulator [10] and 016 the ns extension for MPLS [11].

6LPXODWLRQWRSRORJ\ The simulation topology is MPLS-based IP network. The bandwidth between two routers is marked on the link between them.

:'3IRUVWHSDQG1HZ0HWKRGIRUVWHS +\EULG !:'31HZ0HWKRG 6WHS Source-destination pair, demand size and flow duration time are randomly generated. 6WHS. It calculates the candidate path set using last updated link state information by WDP algorithm. 6WHS. It calculates their 6 for every candidate paths and selects one path with the greatest one and sends the traffic. 6WHS. Every 3 seconds, link state information is updated.

)LJXUH/%:'3SULQFLSOH The best algorithm in the point of efficiency and reducing the congestion is third hybrid one. For candidate path selection, WDP is better owing to path disjointedness, and our new proposition of traffic splitting is better owing to repartition prospect. Figure

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7UDIILFVFHQDULRDQG6LPXODWLRQUHVXOWV Traffic Scenario for multiusers is as follows. The volume of each individual demand is 300kb per second. The source and destination pairs are Src0-Dst0, Src1-Dst1 and Src2-Dst2. These pairs are selected randomly among them every demand generation interval. One flow generated in certain time is stopped in a random time. We adapt a time based triggering as a triggering policy and update link state every 3 seconds. We compare our proposed hybrids’ simulation results using QV with the traffic bifurcation solution TB(1) using MATLAB. Let us notice that in our simulation TB(1) does not split an incoming demand to several LSPs. We also simulate other existing routing algorithms, Shortest Path algorithm and Shortest Widest Path [7] algorithm, and compare their results with our hybrid algorithms such as LBWDP’s. Shortest Path: selects the minimum hop path.


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Shortest Widest Path: selects the paths that have largest bottleneck bandwidth. If multiple, the one with minimum hops is chosen. Simulations with different number of demands are executed for 150 seconds. Table1 represents the simulation results: the maximum link utilization of TB, SP, SWP and LBWDP as the number of demands grows. We can observe that Shortest Widest Path algorithm is relatively efficient when there is enough capacity but it degrades remarkably when demands are too much while LBWDP make a balance with the same volume of traffic. And we observe that even though performance of LBWDP is not much efficient with enough capacity, but it is evident that it does not degrade as the number of demands grows. As a result, LBWDP is more efficient than others in load balancing of the network when the demands are frequents. Demands TB LBWDP SP SWP one/20sec 0.0883 0.3250 0.2890 0.3610 one/10sec 0.1060 0.4160 0.3600 0.3010 one/5sec 0.2158 0.5955 0.8471 0.4984 one /3sec 0.2681 0.4898 1.0329 0.5632 one/2sec 0.2229 0.5866 1.2832 0.7822 one/1sec 0.5405 0.6352 3.5604 1.5040 7DEOH/%:'3DQGH[LVWLQJDOJRULWKPV

)LJXUH0D[LPXPOLQNXWLOL]DWLRQ As depicted in Figure4, even when there is saturation with SP and SWP algorithms, LBWDP achieves well load-balanced network. Table2 shows that our hybrids’ performances are efficient in load balancing in order LBWDP, Hybrid1, Hybrid2. Demands LBWDP WDP+LDM LDM+new one/20sec 0.3250 0.3360 0.2890 one/10sec 0.4160 0.3590 0.3560 one/5sec 0.5955 0.5986 0.5879 one/3sec 0.4898 0.6275 0.7300

one/2sec 0.5866 0.8170 0.9384 7DEOH7KUHHK\EULGDOJRULWKPV

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In this paper, we have modelled multipath routing scheme with two steps. We have suggested a new traffic splitting method. Among existing multipath routing algorithms, we have selected LDM and WDP and divided them into modular part of algorithms. With these modular parts and with our new splitting method, we propose three hybrid load balancing algorithms for multipath QoS. We have solved TB formulation using MATLAB as an optimal bound for comparison. By simulation using QV, LBWDP got better results for load balancing than other hybrid algorithms when the demands are frequents. The proposed three hybrid traffic engineering schemes will be useful for reducing the probability of congestion by minimizing the utilization of the most heavily used link in the network. Our hybrid algorithms have high load balancing effect but high complexity for achieving that. We have to study more scalable approach for large network.

5HIHUHQFHV [1] Z. Wang, Internet QoS: Architectures and Mechanisms for Quality of Service, Morgan Kaufmann Publishers, Lucent Technology (2001). [2] E. Rosen, A. Viswanathan, R. Callon, Multiprotocol Label Switching Architecture, Internet RFC 3031, Jan. 2001. [3] K. Lee, A. Toguyeni, A. Rahmani, Comparison of multipath algorithms for load balancing in a MPLS Network, ICOIN2005. [4] V. T’kindt, J. C. Billaut, Multicriteria Scheduling: Theory, Models and Algorithms. Springer, 300 pages (2002). [5] S. Chen, Routing Support for Providing Guaranteed End-to-End Quality-of-Service, Ph.D. thesis, UIUC, 207 pages (1999). [6] E. Crawley et al. A Framework for QoS-based Routing in the Internet, Internet RFC 2386 (1998). [7] Z. Wang, and J. Crowcroft, Quality-of-Service Routing for Supporting Multimedia Applications. IEEE Journal of Selected Areas in Communications 14 (1996) 1228-1234. [8] J. Song, S. Kim, M. Lee, Dynamic Load Distribution in MPLS Networks, Lecture Notes in Computer Science, Vol. 2662 (2003) 989-999. [9] S. Nelakuditi, Z. Zhang, On Selection of Paths for Multipath Routing, In Proc. IWQoS'01, Karlsruhe, Germany (2001). [10] The Network Simulator ns-2, http://www.isi.edu/nsnam / ns/. [11] MPLS Network Simulator MNS 2.0, http://flower. ce.cnu.ac.kr/ ~fog1.


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