Abstract
We consider the problem of optimal routing in a multi-stage network of queues with constraints on queue lengths. We develop three algorithms for probabilistic routing for this problem using only the total end-to-end delays. These algorithms use the smoothed functional (SF) approach to optimize the routing probabilities. In our model all the queues are assumed to have constraints on the average queue length. We also propose a novel quasi-Newton based SF algorithm. Policies like Join Shortest Queue or Least Work Left work only for unconstrained routing. Besides assuming knowledge of the queue length at all the queues. If the only information available is the expected end-to-end delay as with our case such policies cannot be used. We also give simulation results showing the performance of the SF algorithms for this problem.
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References
Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: A survey. Comp. Netw. 38, 393–422 (2002)
Bhatnagar, S.: Adaptive newton-based smoothed functional algorithms for simulation optimization. ACM Trans. on Model. Comput. Simul. 18(1), 27–62 (2007)
Bhatnagar, S., Hemachandra, N., Mishra, V.: Stochastic approximation algorithms for constrained optimization via simulation (2009) (preprint)
Bonnans, J.F., Gilbert, J.C., Lemaréchal, C., Sagastizábal, C.A.: Numerical Optimization: Theoretical and Practical Aspects. Springer, Heidelberg (2006)
Borkar, V., Das, D.: A novel aco scheme for emergent optimization via reinforcement and initial bias. Swarm Intell. 3, 3–34 (2009)
Cohen, J.E., Kelly, F.P.: A paradox of congestion in a queueing network. J. Appl. Prob. 27, 730–734 (1990)
Dennis, J.E., More, J.J.: Quasi-newton methods, motivation and theory. SIAM Review 19(1), 46–89 (1977)
Dorigo, M., Blum, C.: Ant colony optimization theory: A survey. Theor. Comp. Sci. 344, 243–278 (2005)
Gupta, V., Harchol-Balter, M., Sigman, K., Whitt, W.: Analysis of join-the-shortest-queue routing for web server farms. Perf. Eval. 64, 1062–1081 (2007)
Harchol-Balter, M., Crovella, M., Murta, C.: On choosing a task assignment policy for a distributed server system. J. Parll. Dist. Comput. 59(2), 204–228 (1999)
Harrison, P.G., Patel, N.M.: The representation of multistage interconnection networks in queuing models of parallel systems. J. of ACM 37(4), 863–898 (1990)
Katkovnik, V.Y., Kulchitsky, Y.: Convergence of a class of random search algorithms. Automat. Remote Contr. 8, 1321–1326 (1972)
Kolavali, S., Bhatnagar, S.: Ant colony optimization algorithms for shortest path problems. In: Altman, E., Chaintreau, A. (eds.) NET-COOP 2008. LNCS, vol. 5425, pp. 37–44. Springer, Heidelberg (2009)
Spall, J.C.: Adaptive stochastic approximation by the simultaneous peturbation method. IEEE Trans. on Automat. Contr. 45, 1839–1853 (1992)
Xiao, X., Ni, L.M.: Internet qos: A big picture. IEEE Netw. 13, 8–18 (1999)
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Lakshmanan, K., Bhatnagar, S. (2011). Smoothed Functional and Quasi-Newton Algorithms for Routing in Multi-stage Queueing Network with Constraints. In: Natarajan, R., Ojo, A. (eds) Distributed Computing and Internet Technology. ICDCIT 2011. Lecture Notes in Computer Science, vol 6536. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19056-8_12
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DOI: https://doi.org/10.1007/978-3-642-19056-8_12
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