Abstract
The sample path perturbation analysis technique developed earlier for the analysis of throughput sensitivities (Refs. 1–3) is extended to the performance measures involving mean sojourn times of customers. The major features of the sojourn time sensitivity problem are twofold. Firstly, it is a performance associated with servers, and not with customers. Secondly, the average sojourn time in any finite observation period can be a discontinuous function of mean service times when blocking is involved in a system. This discontinuity causes errors which must be accounted for in the estimation of sensitivities. Numerical experiments and analysis validate this method of computation of the sensitivities.
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Ho, Y. C.,Editor,speeds—A New Technique of the Analysis and Optimization of Queueing Networks, Harvard University, Division of Applied Sciences, Technical Report No. 675, 1983.
Ho, Y. C., andCao, X. R.,Perturbation Analysis and Optimization of Queueing Networks, Journal of Optimization Theory and Applications, Vol. 40, pp. 559–582, 1983.
Ho, Y. C., Cao, X. R., andCassandras, C.,Infinitesimal and Finite Perturbation Analysis for Queueing Networks, Automatica, Vol. 19, pp. 439–445, 1983.
Suri, R.,Implementation of Sensitivity Calculation on a Monte Carlo Experiment, Journal of Optimization Theory and Applications, Vol. 40, pp. 625–630, 1983.
Suri, R., andZazanis, M. A.,Perturbation Analysis Gives Strongly Consistent Estimates for the M/G/1 Queue, Management Science (to appear).
Cao, X. R.,On the Sample Performance Functions of Jackson Queueing Networks, Operations Research (to appear).
Cassandras, C., andHo, Y. C.,An Event Domain Formalism for Sample Path Perturbation Analysis of Discrete Event Dynamic Systems, IEEE Transactions on Automatic Control, Vol. 30, pp. 1217–1221, 1986.
Suri, R.,Infinitesimal Perturbation Analysis of Discrete Event Dynamic Systems: A General Theory, Proceedings of 22nd IEEE Conference on Automatic Control, ACM Performance Evaluation Review (to appear).
Suri, R., andCao, X. R.,The Phantom Customer and Marked Customer Methods for Optimization of Closed Queueing Networks with Blocking and General Service Times, ACM Performance Evaluation Review, pp. 243–256, 1983.
Disney, R. L.,Sojourn Times in Queueing Networks—An Unsolved Problem, Proceedings of 1982 International Large-Scale Systems Symposium, 1982.
Iglehart, D. L., andShedler, G. S.,Regenerative Simulation of Response Times in Networks of Queues, Springer-Verlag, New York, New York, 1980.
Cao, X. R.,Convergence of Parameter Sensitivity Estimates in a Stochastic Experiment, IEEE Transactions on Automatic Control, Vol. 30, pp. 845–853, 1985.
Little, J. D. C.,A Proof of the Queueing Formula L = λ W, Operations Research, Vol. 9, pp. 383–387, 1961.
Jackson, J. R.,Networks of Waiting Lines, Operations Research, Vol. 5, pp. 518–522, 1957.
Sevcik, K. C., andMitrani, I.,The Distribution of Queueing Network States at Input and Output Instants, Journal of the Association for Computing Machinery, Vol. 28, pp. 358–371, 1981.
Buzen, J. P.,Computational Algorithms for Closed Queueing Networks with Exponential Servers, Communications of the ACM, Vol. 16, pp. 527–531, 1973.
Williams, A. C., andBandiwad, R. A.,A Generating Function Approach to Queueing Network Analysis of Multiprogrammed Computers, Networks, Vol. 6, pp. 1–22, 1976.
Ho, Y. C.,On the Perturbation Analysis of Discrete-Event Dynamic Systems, Journal of Optimization Theory and Applications, Vol. 46, pp. 535–545, 1985.
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This work was supported by the US Office of Naval Research, Contracts N00014-84-K-0465 and N00014-79-C-0776, and by the National Science Foundation, Grant No. ENG-78-15231.
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Cao, X.R., Ho, Y.C. Estimating the sojourn time sensitivity in queueing networks using perturbation analysis. J Optim Theory Appl 53, 353–375 (1987). https://doi.org/10.1007/BF00938944
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DOI: https://doi.org/10.1007/BF00938944