Load Balancing by MPLS in Differentiated Services Networks

Transcription

1 Load Baancing by MPLS in Differentiated Services Networks Riikka Susitaiva, Jorma Virtamo, and Samui Aato Networking Laboratory, Hesinki University of Technoogy P.O.Box 3000, FIN HUT, Finand {riikka.susitaiva, jorma.virtamo, Abstract. Muti Protoco Labe Switching (MPLS) assigns a short abe to each packet and packets are forwarded according to these abes. The capabiity of MPLS of expicit routing as we as of spitting of the traffic on severa paths aows oad baancing. The paper first concentrates on two previousy known approximations of the minimum-deay routing. Using these oad baancing agorithms from the iterature as a starting point, the main goa of this report is to deveop optimization agorithms that differentiate casses in terms of mean deay using of both routing and WFQ-scheduing. Both optima and approximative agorithms are deveoped for the joint optimization of the WFQ-weights and routing. As a resut it is found that the use of the approximations simpifies the optimization probem but sti provides resuts that are near to optima. 1 Introduction In the conventiona IP routing, forwarding decisions are made independenty in each router, based on the packet s header and precacuated routing tabes. MPLS (Muti Protoco Labe Switching) is a fexibe technoogy that enabes new services in IP networks and makes routing more effective [1, 2]. It combines two different approaches, datagram and virtua circuit, as a compact technoogy. MPLS is based on short fixed ength abes, which are assigned to each packet at the ingress node of the MPLS coud. These abes are used to make forwarding decisions at each node. The assignments of a particuar packet to a particuar FEC (Forwarding Equivaence Cass) are made ony once. This simpifies and improves forwarding. The architecture of MPLS is defined in [3]. One of the most significant appications of MPLS is Traffic Engineering. Traffic Engineering (TE) concerns performance optimization of operationa networks [4]. Traffic Engineering using MPLS provides mechanisms to route traffic that have equa starting point and destination aong severa paths. The most important benefit of traffic spitting is the abiity to baance oad. MPLS and its Traffic Engineering capabiities coud provide technica support to the impementation of Quaity of Service (QoS). The differentiation of services can be obtained by an aternative fow aocation that has the same principes as the oad baancing methods. In order to make differentiation more effective, scheduing mechanisms, ike WFQ-scheduing, can be utiized in the same context. Our goa is to adjust routing and scheduing parameters that optimize differentiation of experienced service of different casses in terms of their mean deays. We use oad

2 baancing methods as a starting point in the further deveopment. The routing and scheduing methods to be introduced are divided into two types. The first type tries to optimize ony fow aocation so that differentiation is achieved. The second type of methods makes use of WFQ-weights. In each node, each service cass has a WFQ-weight and the bandwidth is shared according to these weights using approximation of parae independent queues. More detais of these methods can be found in [5]. The rest of this paper is organized as foows: In the second section we concentrate on the three previousy known oad baancing agorithms. In section 3 we introduce fow aocation methods that differentiate traffic casses by routing ony. We present the fow aocation mode that makes use of WFQ-scheduing in section 4. We deveop both optima and approximative agorithms. In section 5 we present numerica resuts of a agorithms. Finay, section 6 makes some concusions. 2 Load baancing agorithms Load baancing methods make an attempt to baance oad in the network and therefore achieve better performance in terms of deay. The basic optimization probem minimizes the mean deay in the network. The use of the ink deays of M/M/1-queues eads to a non-inear optimization probem (NLP). Many exact agorithms have been introduced to this optimization, the most famous one being Gaager s agorithm from year 1977 [6]. 2.1 Minimum-deay routing First we formuate the oad baancing as an optimization probem, which minimizes the mean deay of the network. Consider a network consisting of N nodes. A pair of nodes (m, n) can be connected by a directed ink (m, n) with bandwidth equa to b. The number of inks is denoted by L and the topoogy is denoted by T, which is a set of node-pairs. Let A R N L be the matrix for which A(i, j) = 1 if ink j directs to node i, A(i, j) = 1 if ink j eaves from node i and A(i, j) = 0 otherwise. The traffic demands are given by the matrix [d (i,j) ], where i is the ingress and j is the egress node. R (i,j) R N is a vector for each ingress-egress pair (i, j) such that R (i,j),k = d (i,j), if k is the ingress node, R (i,j),k = d (i,j), if k is the egress node, and R (i,j),k = 0 otherwise. Demands and capacities are assumed to be constant (or average traffic rates). Let x (i,j), be the aocated traffic of ingress-egress pair (i, j) on ink (m, n). Then the tota traffic on the ink (m, n) is X = (i,j) x (i,j),. (1)

3 The formuation of the optimization probem that minimizes the mean deay in the whoe network is as foows: Minimize E[D] = 1 Λ X b X, subject to the constraints X < b, Ax (i,j) = R (i,j), for each (m, n), for each (i, j), where Λ is the tota offered traffic of the network. The ast equation in (2) states that, at every node n, incoming traffic of each ingress-egress pair must be equa to outgoing traffic [7]. 2.2 Fow aocation using two-step agorithm The agorithm that cacuates an optima fow aocation in terms of mean deay may be approximated by using the approach presented in [8]. The approximative agorithm soves first the paths to be used by LP-optimization and, after that, aocates the traffic to these paths using NLP-optimization. The pair-based fow formuation that minimize the maximum ink oad is as foows: [ Minimize ɛz + ] w x (i,j), subject to the constraints (i,j) x (i,j), 0; Z 0, x (i,j), + b Z b, for each (m, n) with b > 0, (i,j) Ax (i,j) = R (i,j), for each (i, j) at each node n. Free parameter Z in (3) describes the minimum vaue of the proportiona unused capacity. When the LP-probem (3) is soved and variabes x (i,j), found, we have to find paths for each ingress-egress pair. The agorithm to define paths to ingress-egress pair (i, j) is as foows: We have the origina topoogy T, which consists of the set of directed inks. Because one ingress-egress pair uses ony part of the whoe topoogy, we define a new topoogy T (i,j), which consists of the inks for which x (i,j), differs from zero. Topoogy T (i,j) is oop-free, because if there were oops, the origina aocation woud not be optima. We search a paths to one ingress-egress pair (i, j) by a breadth-firstsearch agorithm. As a resut of the breadth-first-search agorithm, we have a set of possibe paths P (i,j) for one ingress-egress pair. Let K (i,j) be the number of paths and Q (i,j) R L (i,j) K (i,j) be the matrix, where (2) (3) { 1, if path k uses ink of topoogy T Q (i,j),(,k) = (i,j), 0, otherwise, (4)

4 for each ingress-egress pair (i, j). Let y (i,j),k be the traffic aocation in path k. Unknown y (i,j),k s can be soved from matrix equation Q (i,j) y (i,j) = x (i,j), for each (i, j), (5) where x (i,j) RL (i,j) is the fow vector for each ingress-egress pair (i, j). Finay, if eement k of the soution vector y (i,j) differs from zero, ingress-egress pair (i, j) uses path k, ese not. So reducing the unused paths from path set P (i,j) we get the actua path set. The objective is to find an optima fow aocation to these paths. Let K = (i,j) K (i,j) be the tota number of paths in the network, P (i,j),k be the k:th path of node-pair (i, j), and φ (i,j),k be the fraction of d (i,j) aocated to path P (i,j),k. The structure of path k is defined by δ,(i,j),k as foows: { 1, if path p(i,j),k uses ink (m, n), δ,(i,j),k = 0, otherwise. (6) Note that the traffic aocation y (i,j),k above is a specia case of traffic aocation d (i,j) φ (i,j),k. Our objective is to minimize the mean deay of the tota network. So the optimization probem is as foows: Minimize 1 Λ (i,j),k b δ,(i,j),k d (i,j) φ (i,j),k (i,j),k δ,(i,j),k d (i,j) φ (i,j),k, subject to the conditions δ,(i,j),k d (i,j) φ (i,j),k < b, (i,j),k for each (m, n), φ (i,j),k 0, for each (i, j), k, (7) K (i,j) k=1 φ (i,j),k = 1, for each (i, j). 2.3 Heuristic approach The heuristics presented in [9] to aocate traffic into the network using a particuar eve of granuarity is very simpe. The traffic granuarity refers to the eve of traffic aggregation [9]. The finer the eve of the granuarity the finer the traffic partitioning to different paths. In this agorithm, depending on the eve of granuarity, traffic demands from ingress to egress node are divided into streams (e.g. using some hashing function). The streams are sorted in descending order in terms of their traffic demand. After that each stream is routed sequentiay one at a time to the shortest path defined by Dijkstra s agorithm using the mean deay of an M/M/1-queue as a ink cost.

5 3 Methods to achieve differentiation by routing In this section we present such fow aocation methods that try to differentiate traffic casses by routing ony. The traffic casses with a higher priority are routed aong the paths that are not congested, for exampe. We differentiate casses by minimizing the sum of weighted mean deays, by fixing the ratio of mean deays, and using a heuristic approach. 3.1 Optimization using cost weights We consider the situation where the tota traffic is divided into traffic casses, into the god, siver and bronze casses, for exampe. The god cass has the highest priority and the bronze cass the owest priority. Each traffic cass has its own traffic matrix [d,(i,j) ], where i is the ingress node and j is the egress node. R,(i,j) R N is an array for each cass and ingress-egress pair (i, j), where R,(i,j),k = d,(i,j), if k is the ingress node, R,(i,j),k = d,(i,j), if k is the egress node and R,(i,j),k = 0 otherwise. The tota traffic offered by cass is denoted by Λ. Let x,(i,j), be the aocated traffic of ingress-egress pair (i, j) of cass on ink (m, n). So the tota traffic of cass on ink (m, n) is X, = (i,j) x,(i,j),, for each, (m, n). (8) Let w be the cost weight associated to traffic cass. Additiona notation used is the same as in section 2.2. The purpose is to divide traffic into paths so that casses with higher priority achieve smaer mean deay than other casses. So the cost of deay is highest in the god cass and so on. The optimization probem, where we minimize the sum of the weighted mean deays of the casses, is as foows: Minimize w E[D ] = subject to the constraints X, < b, Ax,(i,j) = R,(i,j), w X, Λ b, X, for each (m, n), for each, (i, j), (9) where traffic aocations x,(i,j), are decision variabes. When the cost weights of different casses differ sufficienty, the optimization function tries to minimize the mean deays of high priority casses at the expense of ower priority casses. The high priority cass can be routed through the shortest path and the other casses through some other path in order to provide enough capacity to the high priority cass. As a resut, the routing obtained by the optimization function above differs from

6 the routing obtained by the oad baancing, because in the oad baancing approach the deays in the nodes are baanced to be amost equa and the differentiation coud occur ony if the paths are of different ength. 3.2 Optimization with a fixed mean deay ratio Now we fix the ratio of the mean deays of various casses to some vaue in order to differentiate casses. For exampe, in the case of two casses (god and siver), the ratio of the mean deays between the siver and the god cass coud be fixed to parameter q: 1 X 2, E[D 2 ] E[D 1 ] = Λ 2 1 b X 1, X, = q. (10) Λ 1 b X, After that the optimization can be done by minimizing the mean deay of either cass. Compared to the optimization in the previous section, this approach does not incude cost weights and the actua ratio of the mean deays is known before the optimization. In order to make the optimization procedure easier it is usefu to constraint the ratio of the mean deays to some sma interva rather than to the exact vaue. 3.3 Heuristics There exists a demand to provide aso simpe routing methods that can be impemented without heavy optimization. The approach that routes traffic to the network near optimay but sti obtains the differentiation in terms of mean deay tries to adapt the heuristic approach presented in section 2.3. The heuristic approach in the case of two casses (god and siver) is as foows: The god cass is routed using heuristics introduced in 2.3. Then the aocated traffic of the god cass is mutipied by 1 +. The siver cass is then routed using heuristics in 2.3. The idea of the heuristics is that the inks that are used by the god cass ook more congested than they actuay are. So the routing scheme tries to baance oad by routing the siver cass by some other way. That is, the artificia congestion forces the siver cass to avoid inks used by the god cass and therefore the god cass shoud achieve more bandwidth. The choice of the parameter depends on how much there is traffic offered compared to the capacity of the network. 4 Methods to achieve differentiation in mean deay using routing and WFQ-scheduing The possibiities to provide differentiated services using routing ony are imited. To achieve certain ratio of mean deays may ead up to disadvantageous routing because the

7 ow priority cass is routed aong ong and congested paths in order to artificiay obtain the desired ratio of the mean deay. Weighted Fair Queueing as a packet scheduing mechanism divides bandwidth among the parae queues. Each queue achieves a guaranteed bandwidth, which depends on the WFQ-weight of that queue and the ink capacity. We try to find optima routing that differentiates the quaity of service by incuding the WFQ-weighs to the optimization function as free parameters. Because WFQ-scheduing is a work-conserving discipine, the bandwidth that is guaranteed for a cass in our mode can be viewed as the ower bound. Actuay, the bandwidth avaiabe to a cass can be much greater as the other casses may not aways use the bandwidth reserved for them. The bandwidth of each ink is shared according to WFQ-weights. We approximate the behavior of WFQ-scheduing as foows: Let γ,(i,j) be the WFQ-weight that determines the proportion of tota bandwidth that is given to cass. The bandwidth b, of cass on ink (m, n) is thus b, = γ, b, for each, (m, n). (11) The sum of the WFQ-weights of the casses must equa to one. As a resut, we have changed over from the WFQ-scheduing system to the system of parae independent queues with ink capacities described above. 4.1 Optimization using cost weights In this section we obtain the differentiation between casses by using the cost weights as in (9). The god cass gets the greatest cost weight and so on. The joint optimization of fow aocation and WFQ-weights where the sum of weighted mean deays is minimized is as foows: Minimize w E[D ] = w Λ subject to the constraints X, < γ, b, Ax,(i,j) = R,(i,j), X, γ, b X,, for each, (m, n), for each, (i, j), 0 < γ, < 1, for each, (m, n), γ,(i,j) = 1, for each (i, j), where traffic aocations x,(i,j), and WFQ-weights γ, are decision variabes. This straightforward optimization is referred to as Str. The optimization probem presented in (12) is quite heavy and time-consuming. We introduce near optima agorithms that make the size of the probem smaer and the cacuation easier. The first two agorithms first aocate the traffic into the network and after that optimize WFQ-weights. The structure of both agorithms is as foows: (12)

8 1. Aocate the traffic into the network without WFQ-weights so that the weighted sum of mean deays is minimized. The formuation of the optimization agorithm is presented in section Fix the traffic aocation obtained in the first step. 3. Determine WFQ-weights using optimization probem (12). Now the number of free variabes equas the number of WFQ-weights, the number of inks in the network mutipied by the number of casses minus one. The cost weights of the optimization function are seected twice, in steps 1 and 3. In the first two-step agorithm (referred to as 2StepV1 ) we seect the cost weights in the first step to be w = Λ k Λ. (13) k Now the fow aocation is optima and differences in mean deays do not appear in the first step. This agorithm makes ony use of WFQ-scheduing when trying to differentiate casses. In the second two-step agorithm (referred to as 2StepV2 ) the cost weights in the first and third steps are equa. So this agorithm utiizes both routing and WFQscheduing when differentiating casses and can therefore be coser to the optima. The third approximative agorithm makes use of the two-step agorithm presented in section 2.2 and is referred to as QoS-LP-NLP. The paths are first cacuated using the inear optimization that minimizes the maximum ink oad. Then the traffic is aocated to these paths and WFQ-weights are determined using the non-inear optimization (12) appied to the fixed paths. 4.2 Fixing the ink deay ratio In the routing with WFQ-weights, if the ratio of mean deays is fixed ike in the agorithm presented in section 3.2, the optimization probem is demanding. One possibiity is to fix the mean deay ratios at the ink eve. If the engths of paths of different casses do not differ significanty, this approach shoud resut approximatey in the same mean deay ratio in the whoe network. We consider the case with two casses, god and siver. We fix the ratio of ink deays to parameter q and sove WFQ-weights γ 1, s as a function of the traffic of both casses, that is γ 1,(X 1,, X 2,) = qb + X 1, qx 2,, for each (m, n). (14) b (q + 1) The optimization probem of the fow aocation with the fixed ratio of mean deays is amost simiar to optimization probem (12). The difference is that the WFQ-weights are not free parameters in the approach with fixed ink deays. If we want to differentiate the casses by fixing the ink deays ony, the cost weights of the optimization function are equa to one (referred to as FLD ). We can aso optimize the sum of the weighted mean deays (referred to as FLDW ). The probem is now how to determine the cost weights in reation to the ratio of ink deays.

9 5 Numerica resuts The formuations of the optimization probems were written using a Genera Agebraic Modeing System (GAMS), which is a high-eve modeing anguage for mathematica programming probems [10]. We have used sover modue Minos 5 in our optimizations. The agorithms are tested in a known test-network, which consists of 10 nodes, 58 inks and 72 ingress-egress pairs. The ink capacities and the traffic demands are avaiabe at web-page In order to make optimizations simper, we study ony the case of two casses, god and siver. The traffic matrices of both casses are equa, the haf of the origina demands, so that the comparison between the traffic casses is easier. 5.1 Load baancing routing The mean deay and the reative deviation of the mean deay from the optima as a function of the traffic oad of the three routing methods of section 2 is presented in Figure 1. With the heuristic approach, we use the granuarity eve 32, except in the cases of heavy oad (the traffic oad is over 95%) when the used granuarity eve is 128. We can see that the mean deays of different methods do not differ significanty. Ony when the traffic oad is near to the tota capacity of the network is the performance of the minimum-deay routing notabe. The mean deay minimum-deay LP-NLP heuristics The difference % LP-NLP heuristics % % Fig. 1. The mean deay and the reative deviation of the mean deay from the optima as a function of the traffic oad 5.2 Methods to achieve differentiation using routing ony The three approaches in section 3 make an attempt to differentiate the casses by routing ony. The first optimization probem minimizes the sum of weighted mean deays. As a resut, the ratio of the mean deay of the siver cass to the mean deay of the god cass and the growth of the tota mean deay as a function of the cost weight of the god cass is presented Figure 2. We take the tota mean deay of the network as a function of the ratio of mean deay as a performance indicator. The increase in mean deay describes the cost of achieving a

10 The ratio of mean deays The weight of the god cass The mean deay The weight of the god cass Fig. 2. The ratio of mean deays and the tota mean deay as a function of the weight of the god cass certain eve of differentiation. A three methods are compared in Figure 3. The figure shows that the first and second optimizations generate the same resut. However, the benefit of optimization function (10) is that the ratio of mean deays is known a priori, whie the cost weights of optimization function (9) must be determined The mean deay weights fixed heuristics The ratio of mean deays Fig. 3. The tota mean deay as a function of the ratio of mean deays 5.3 Methods to achieve differentiation by routing and WFQ-scheduing First we have impemented the optimization method that minimizes the weighted sum of mean deays straightforwardy and the optimization methods that divide the probem into two steps (introduced in section 4.1). A near optima routing can aso be achieved using an iterative approach (referred to as 2StepIt ). The fow aocation and the WFQ-weights are optimized aternatingy. The number of iterations is ten, which means that ten fow aocations and ten WFQ-weight determinations are done in the optimization. The ratio of the mean deay of the siver cass to the mean deay of the god cass and the tota mean deay of a five agorithms are presented in Figure 4. Note that aso the tota mean deay is cacuated using the approximation of parae queues. Thus the figures in this subsection are not comparabe with the figures in subsection 5.2. The irreguarities in the curve of the straightforward routing are perhaps a consequence of numerica errors in the optimization procedure. In order to simpify optimization and to provide differentiation aso at the ingressegress pair eve, we have impemented optimizations that fix the ratio of ink deays

11 The ratio of mean deays Str 2StepV1 2StepV2 2StepIt QoS-LP-NL The weight of the god cass The mean deay Str 2StepV1 2StepV2 2StepIt QoS-LP-NL The weight of the god cass Fig. 4. The ratio of mean deays and the tota mean deay as a function of the weight of the god cass to some parameter q (probems FLD and FLDW ). In the atter probem we have impemented ony one case, where the cost weight is three times greater than ink deay ratio q. On the eft side of Figure 5 we present the reation between the ratio of ink deays and the ratio of mean deays of different casses. In the probem, where we fix ony q ( FLD ), the ratio of mean deays seems to be smaer than the ratio of ink deays. The expanation is that the routing agorithm tries to baance traffic oad by routing casses that achieve more bandwidth through ong routes. Finay, we compare a the methods. The performance metric is the same as in section 5.2, the tota mean deay of the network as a function of the ratio of mean deays. The resuts are presented on the right side of Figure 5. The straightforward optimization The ratio of mean deay FLD FLDW q The mean deay Str 2StepV1 2StepV2 2StepIt QoS-LP-NL FLD FLDW The ratio of mean deays Fig. 5. The ratio of mean deays as a function of q in the eft part and the tota mean deay as a function of the ratio of mean deays in the right side of the figure seems to have the smaest mean deay. The difference to other agorithms is significant when the ratio of mean deays is sma. When the ratio is greater, the performance of the two-step agorithm that utiizes both routing and WFQ-weights ( 2StepV2 ) is near to optima. As a concusion, the differentiation methods that make use of both routing and WFQ-scheduing ( Str, 2StepV2, 2StepIt, FLDW ) perform better than the differentiation methods that make use of ony WFQ-scheduing ( 2StepV1, QoS-LP- NLP and FLD ).

12 6 Concusions We have used oad baancing agorithms as a starting point when deveoping methods that try to differentiate traffic casses in terms of the mean deay. In the first mode differentiation is achieved by using routing ony. The mean deay using the agorithm that uses cost weights and the agorithm that fixes the ratio of mean deays are equa. The advantage of the atter agorithm is that the cost weights need not be known in advance. The mean deay using the heuristic approach is a itte greater than using the other two agorithms. We have aso presented a mode where the bandwidth of each ink is shared among the traffic casses according to the WFQ-weights. The optimization probem is to minimize the weighted mean deay. In addition, near-optima heuristic agorithms have been introduced. We notice that the use of the agorithm that makes use of both routing and WFQ-scheduing gives the best resut. The bandwidth guaranteed by WFQ-scheduing to each cass is the theoretica minimum. As a resut, the actua ratio of mean deays may differ from the resut obtained by the optimizations. It woud be interesting to know whether the actua ratio of mean deays is greater or smaer. A simuation study of WFQ-scheduing may provide some answers. That woud aso hep the comparison between differentiation with routing ony and differentiation with scheduing and routing. Adaptive agorithms used in the situation where the traffic matrices of the casses are unknown woud be usefu. References 1. A. Viswanathan, N. Fedman, Z. Wang and R. Caon, Evoution of Muti-Protoco Labe Swithing, IEEE Communication Magazine, Vo 36, Issue 5, pp , May G. Armitage, MPLS: The Magic Behind the Myths, IEEE Communications Magazine, Vo 38, Issue 1, pp , January E. Rosen, A. Viswanathan and R. Caon, Mutiprotoco Labe Switching Architecture, IETF RFC3031, January D. Awduche, J. Macom, J. Agogbua, M. O De and J. McManus, Requirements for Traffic Engineering over MPLS, IETF RFC 2702, September R. Susitaiva, Load Baancing by MPLS in Differentiated Services Networks, Master s Thesis, Hesinki University of Technoogy, R.G. Gaager, A Minimum Deay Routing Agorithm Using Distributed Computation, IEEE Transactions on Communication, Vo COM-25, Nr 1, pp , January J. Castro and N. Nabona, Computationa tests of a noninear muticommodity network fow code with inear side contraints through prima partitioning, DR 94/05, Statistics ans Operations Research Dept., Universitat Poitéctica de Cataunya, Barceona. 8. T. Ott, T. Bogovic, T. Carpenter, K. R. Krishnan and D. Shacross, Agorithms for Fow Aocation for Muti Protoco Labe Switching, Tecordia Technica Memorandum TM-26027, A. Sridharan, S. Bhattacharyya, R. Guérin, J. Jetcheva and N. Taft, On The Impact of Aggregation on The Performance of Traffic Aware Routing, Technica report, University of Pennsyvania, Juy