Abstract
In this paper, we consider the routing problem described in Mohanty and Cassandras (Ref. 1). As in Ref. 1, we show that the optimal Bernoulli split to minimize mean time in the system is asymptotically independent of the variance of the service time. We give simple proofs of the results in that paper. We exploit the fact that the optimal split to minimize the mean queueing time is variance independent and the special structure of the Karush–Kuhn–Tucker optimality conditions to derive the optimal solution. Apart from being very straightforward, the proofs also give insight into the reason for the existence of the variance-independent asymptotically optimal routing policy.
Similar content being viewed by others
References
Mohanty, B., and Cassandras, C. G., Effect of Model Uncertainty on Some Optimal Routing Problems, Journal of Optimization Theory and Applications, Vol. 27, pp. 257–290, 1993.
Bonomi, F., Doshi, B. T., Kaufman, J. S., and Lee, T. P., A Case Study of an Adaptive Load Balancing Algorithm, Queueing Systems, Vol. 7, pp. 23–49, 1990.
Bonomi, F., and Kumar, A., Adaptive Optimal Load Balancing in a Nonhomogeneous Multiserver System with a Central Job Scheduler, IEEE Transactions on Computers, Vol. 39, pp. 1232–1250, 1990.
Chang, F., and Wu, L., An Optimal Adaptive Routing Algorithm, IEEE Transactions on Automatic Control, Vol. 31, pp. 690–700, 1986.
Chow, Y. C., and Kohler, W. H., Models for Dynamic Load Balancing in a Heterogeneous Multiple Processor System, IEEE Transactions on Computers, Vol. 28, pp. 354–361, 1979.
Ibaraki, T., and Katoh, N., Resource Allocation Problems: Algorithmic Approaches, MIT Press, Cambridge, Massachusetts, 1988.
Mohanty, B., and Cassandras, C. G., Asymptotic Analysis of the Effect of Model Uncertainties in Some Optimal Routing Problems, Journal of Optimization Theory and Applications, Vol. 86, pp. 199–222, 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kodialam, M.S. Effect of Modeling Uncertainty on Some Routing Problems. Journal of Optimization Theory and Applications 101, 203–211 (1999). https://doi.org/10.1023/A:1021731329866
Issue Date:
DOI: https://doi.org/10.1023/A:1021731329866