A MIXED-METRIC ROUTING WITH OPTIMAL FLOW DISTRIBUTION FOR MPLS NETWORKS

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5 MIXED-METRIC ROUTING, OPTIMAL FLOW DISTRIBUTION 163 N 1 N where f ij is the total flow at the network input. The optimum distribution i1 j2 of network flows, i, i=1, 2,..., L, can be found by finding the set of flows that minimizes T n, subject to the constrain L T i, where T is the total link i1 flows. Certainly, T is not yet known. However, if we set a given "average number, k," of hops as a target in our optimization. Then, a good estimate of T would be T k. Now, finding the optimum distribution of the network flows can be found using the Lagrangean technique, and the following Kuhn-Tucker conditions [13], for i=1,... L L L i X - ( i - T ) 0 (8) i 1( - X i) i i i1 where, is the lagrange multiplier. Solving the following set of Kuhn-Tucker conditions for i, gives, Xi 2 ( i - Xi ) - 0 In order to check that i obtained from equation (9) will result in a minimum of T n, we differentiate (8) once more. This gives, 2X ( i - Xi ) (10) As we know, for a stable network i X i for all links, otherwise the delay will be infinite. This makes equation (10) positive, thus insuring a minimum network delay performance. Equation (9), gives us the optimum link flows but in terms of. So we should find first. Rewriting equation (9) gives, X L X L i 2 X i i1( i - X i ) i1 = T n from which is obtained. Note that, to be achieved. Tn L X L X i i1 X i (9) T n here is the mean network delay performance (11)

6 164 o finally, the set of optimum link flows, i, i=1,2, L, are obtained from equation (9), o i i i. (12) X X As mentioned earlier, constraining the routing algorithm such that no link flow should o exceed its pre-computed level, i, would enforces a lower bound on overall network delay performance. IV. PERFORMANCE EVALUATION The mixed-metric routing technique, and the optimum flow distribution system are both implemented as a traffic engineering tool for setting up LSPs between ingress-egress routers in an MPLS cloud. In this section, we study the effectiveness of applying this, analytical, tool. Two network graphs with arbitrary topologies are chosen. The first one is comprised of 15-MPLS-router (node), interconnected using 27-link. The second consists of 20-MPLS-router, with 40-links interconnecting them. In all scenarios, we have assumed equal traffic demands between any ingress-egress router pairs as well as equal link capacities. This would help us gaining a better understanding of the behavior of our algorithms. Short (LSPs) paths between MPLSrouters are obtained using the well known Dijkestra algorithm. The network topologies chosen are shown in figures 1, and 2 below. As shown, each router is identified by an alphabetic letter, while links are identified using numeric "titles". Phase I: Validation of the mixed-metric routing 4 e 11 i 19 l e 10 i 20 p b b n 34 t a d 9 f j 22 o a 3 d 8 f 12 j 29 q g n 2 g l s c c r k h k m h m 31 o Figure 1: 15-router MPLS cloud. Figure 2: 20-router MPLS cloud. Figures 3, and 4, show the number of LSPs sharing the capacity of each link in the two networks. The light-shaded histogram is obtained after running the OSPF algorithm, and the heavily-shaded one results after running the mixed-metric routing technique (equation (5)). As can be seen, the OSPF algorithm tends to over load some

8 166 high network delay performance (see equation (6)). This should not leads us to a wrong conclusion. As we know the routing process is a fairly network-topology depended process, that is, it depends largely on route availability in the physical network. Moreover, this very observation have encouraged us towards finding the optimal flow bounds. Per Link Traffic Utilization Router, 27-Directed Link Network Link Title (k), k=1, 2,..., 27 Fig.(5), Per Link Traffic Utilization OSPF Mixed Metric Per Link Traffic Utilization Router, 40-Directed Link Network Link Title (k), k=1, 2,..., 27 Fig.(6), Per Link Traffic Utilization OSPF Mixed Metric

9 MIXED-METRIC ROUTING, OPTIMAL FLOW DISTRIBUTION 167 Figures 7, and 8, completes our discussion by showing the LSP-lengths in terms of the number of hops (links) traversed. As can be seen, under the mixed-metric routing, some LSPs had to traverse longer paths which are found to be less congested. This might indicate that LSPs under the mixed-metric system would result in a longer network delay. This, in fact, is not true. Simply because traversing a relatively longer paths comprised of less congested links would not necessarily results in a longer path delays. In order to validate this argument, Table I, gives a sample delay performance results for the per link, and the end-to-end (ETE) delays (measured m. Sec.). Of importance here to note that the numbers given in Table I, presents a set of figures we have used for comparison sake apart from the implications of their actual values. Number of LSPs Router, 27-Directed Link Network LSP Lengths (Number of Hops) Fig.(7),LSP Length in Hops OSPF Mixed Metric Number of LSPs Router, 40-Directed Link Network LSP Lengths (Number of Hops) Fig.(8),LSP Length in Hops OSPF Mixed Metric

11 MIXED-METRIC ROUTING, OPTIMAL FLOW DISTRIBUTION 169 Number of LSPs Router, 40-Directed Link Network LSP Lengths (Number of Hops) Fig.(10),LSP Length in Hops No Constrains Constrained Another results are shown in Figures 11, and 12, but for a heavily loaded, randomized network traffic matrix. As can be seen, the optimal flow constrains results in a semi equalized link loadings. This would in turn, leads to a better, and bounded mean network delay performance. Table II quantifies the network delay performance. Per Link Traffic Utilization Router, 40-Directed Link Net., Randomized Traffic Matrix No Constrains Constrained Link Title (k), k=1, 2,..., 40 Fig.(11), Optimum Link Utilization, Randomized Traffic Matrix.

12 170 Number of LSPs No Constrains Constrained 20-Router, 40-Directed Link Network LSP Lengths (Number of Hops) Fig.(12),LSP Length in Hops Table II: Mean Delay Performance. Performance, Deterministic-Traffic Matrix Randomized-Traffic Matrix No Constrains Constrained No Constrains Constrained Per Link Delay ETE Delay Mean Hops As can be seen, even under heavily loaded network scenarios, the traffic engineering tool proposed in this paper, still capable of optimally distributing the traffic load among all "possible" network links as long as there is a "feasible" physical path in the directed topology which we have chosen. On the other hand, it is not difficult to see that some links (e.g., #3, and #25 in all results obtained for the 20-router network) have inherently a low utilization profile. This is due to the physical structure of the network topology which constrains the availability of a given route. V. SUMMARY AND CONCLUSIONS This paper have presented a mixed-metric routing system with optimal LSPflow distribution for traffic engineering in MPLS networks. The mixed-metric system routes LSPs over links having maximum residual bandwidth, and minimum number of flows. This have led to a significant improvement in the overall network resource (link) utilization as seen from the results presented in previous section. Moreover, an

13 MIXED-METRIC ROUTING, OPTIMAL FLOW DISTRIBUTION 171 optimal LSP-flow distribution among network links is found, and its effectiveness is tested in the validation phase. Results have indicated that, when optimal flow distribution is imposed on the routing process. It results in a lower bounded network delay performance. Such a feature is considered mandatory for a variety of applications especially those with a real time relationships among contiguous parts of their traffic streams. Typically, voice, and video traffic streams are a good examples of such an applications. For future work, we will investigate a range of representative network topologies, and traffic models as well as other algorithms for optimizing the MPLS tunnel placement to allow for the placement of backup tunnels in case of network's link failures. VI. REFERENCES [1] D. Awduche, A. Chin, A. Elwalid, I Widjaja, and Xiao, "Overview, and principles of Internet traffic engineering," IETF RFC 3272, [2] D. O. Awduche, J. Malcolm, J. Agogbua, M. O'Dell, and J. McManus, "Requirements for traffic engineering over MPLS," Internet Draft, June [3] A. Apostolopoulos, R. Guerin, S. Kamat, Orda, T.Przygienda, and D. Williams, "QoS routing mechanisms and OSPF extensions," Internet Draft, April [4] Z. Zhang, C. Sanchez, B. Salkewicz, and E. Crawley, "Quality of Service Extensions to OSPF or Quality of service path first routing," Internet Draft, September [5] D. Awduche et al, "Requirements for traffic engineering over MPLS," IETF RFC [6] E. Rosen et al, "Multiprotocol Label Switching architecture," IETF RFC3031, [7] X. Xiao, A. Hannan, B. Baily, and L. M. Ni, "Traffic engineering with MPLS in the Internet," IEEE Network magazine, March/April [8] G. Swallow, "MPLS advantages for traffic engineering," IEEE Communication magazine, December [9] J. Boyle et al, "Application statement for traffic engineering with MPLS,' IETF RFC 3346, [10] C. Casetti, G. Favalessa, M. Mellia, and M. Munafo, "An adaptive routing algorithm for best-effort in integrated-services networks," presented at the 16 th Int. Teletraffic Congress (ITC-16), Edinburgh, UK, June [11] W. E. Leland, and D. V. Wilson, "High time-resolution measurements, and analysis of LAN traffic: Implementations for LAN interconnection," Proc. IEEE INFOCOM, 1991, pp [12] D. Gross, and C. M. Harris, "Fundamentals of Queuing Theory", 2 nd edition. New York: Wiley, [13] F. S. Hillier, and G. J. Lieberman, "Introduction to Operations Research", 4 th Ed. New York: Holden-Day, [14] A. Mameli, E. Manconi, and F. Ubaldi, "Edge distributed admission control in MPLS networks," IEEE Communi. Letters, Vol. 7, No. 2, Febr

14 172 تحديد المسارا باستخدا القي المتعددة مع التزيع اأعظ لحرك فى شبكا MPLS يقد هذا البحث نظا ديناميكي جديد لتحديد المسارا في شبكا MPLS يعتمد عى استخدا القي المتعددة مع التزيع اأعظ لحرك. يدف هذا البحث إلى ضع حد أدنى لمستى اأداء في هذا النع من الشبكا. قد أظر النتائج قدرة النظا المقترح عى تزيع أحمال الشبك بطريق مثالي حتى عند اأحمال العالي.

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