Abstract
An appropriate state vector for simulation of closed networks of queues with priorities among job classes is a linear “job stack”, an enumeration of service center and job class of all the jobs. Simulation for passage times can be based on observation of an augmented job stack process which maintains the position of an arbitrarily chosen “marked job”. Using a representation of the augmented job stack process as a generalized semi-Markov process, we develop an estimation procedure for passage times in networks with general service times. We also describe an estimation procedure for passage times which correspond to the passage through a subnetwork of a given network of queues. With this “labelled jobs method”, observed passage times for all the jobs are used to construct point and interval estimates. Our results apply to networks with “single states” for passage times. Based on a single simulation run, the procedures provide point estimates and confidence intervals for characteristics of limiting passage times.
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References
Cox, D.R. (1955). A use of complex probabilities in the theory of queues. Proc. Cambridge Philos. Soc. 51, 313–319.
Crane, M.A. and Iglehart, D.L. (1975). Simulating stable stochastic systems: III, Regenerative processes and discrete event simulation. Operations Res. 23, 33–45.
Crane, M.A. and Lemoine, A.J. (1977). An Introduction to the Regenerative Method for Simulation Analysis. Lecture Notes in Control and Information Sciences, Vol. 4, Springer-Verlag, Berlin, Heidelberg, New York.
Fishman, G.S. (1978). Principles of Discrete Event Simulation. John Wiley, New York.
Fossett, L.D. (1979). Simulating generalized Semi-Markov process. Technical Report No. 2. Department of Operations Res., Stanford, Wisconsin.
Glynn, P.W. (1983). Forthcoming technical report. Department of Industrial Engineering. University of Wisconsin, Madison, Wisconsin.
Heidelberger, P. and Welch, P.D. (1981). A spectral method for confidence, interval generation and run length control in simulations. Comm. Assoc. Comput. Mach. 24, 233–245.
Iglehart, D.L. and Shedler, G.S. (1980). Regenerative Simulation of Response Times in Networks of Queues. Lecture Notes in Control and Information Sciences, Vol. 26. Springer-Verlag, Berlin, Heidelberg, New York.
Iglehart, D.L. and Shedler, G.S. (1981). Regenerative simulation of response times in networks of queues: statistical efficiency. Acta Informatica 15, 347–363.
Iglehart, D.L. and Shedler, G.S. (1983). Statistical efficiency of regenerative simulation methods for networks of queues. Adv. Appl. Probability 15, 183–197.
König, D., Matthes, K. and Nawrotzki, K. (1967). Verallgemeinerungen der Erlangschen und Engsetschen Formeln. Akademie-Verlag, Berlin.
König, D., Matthes, K. and Nawrotzki, K. (1974). Unempfindlichkeitseigenschaften von Bedienungsprozessen. Appendix to Gnedenko, B.V. and Kovalenko, I.N., Introduction to Queueing Theory, German edition.
Lavenberg, S.S. and Shedler, G.S. (1976). Stochastic modelling of processor scheduling with application to data base amangement systems. IBM J. Res. Develop. 19, 437–448.
Law, A.M. and Carson, J. (1979). A sequential procedure for determining the length of a steady-state simulation. Operations Res. 27, 1011–1025.
Lewis, P.A.W., Goodman, A.S. and Miller, J.M. (1969). A pseudo-random number generator for the System/360. IBM Systems J. 8, 199–220.
Matthes, K. (1962). Zur Theorie der Bedienungsprozesse. Trans. 3rd Prague Conference on Information Theory and Statistical Decision Functions. Prague.
Miller, D.R. (1972). Existence of limits in regenerative processes. Ann. Math. Statist. 43, 1275–1282.
Schmeiser, B. (1982). Batch size effects in the analysis of simulation output. Operations Res. 30, 556–568.
Shedler, G.S. and Slutz, D.R. (1981). Irreducibility in closed multi-class networks of queues with priorities: passage times of a marked job. Performance Eval. 1, 334–343.
Shedler, G.S. and Southard, H. (1982). Regenerative simulation of networks of queues with general service times: passage through subnetworks. IBM J. Res. Develop. 26, 625–633.
Smith, W.L. (1958). Renewal theory and its ramifications. J. Roy. Statist. Soc. Ser. B 20, 243–302.
Whitt, W. (1980). Continuity of generalized semi-Markov processes. Math. Operations Res. 5, 494–501.
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© 1986 Springer-Verlag
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Iglehart, D.L., Shedler, G.S. (1986). Simulation for passage times in non-Markovian networks of queues. In: Archetti, F., Di Pillo, G., Lucertini, M. (eds) Stochastic Programming. Lecture Notes in Control and Information Sciences, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006860
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DOI: https://doi.org/10.1007/BFb0006860
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