Simulating Stable Stochastic Systems, II: Markov Chains

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

Simulating Stable Stochastic Systems, II: Markov Chains

Full text

Pdf (559 KB)

Source

Journal of the ACM (JACM) archive
Volume 21 , Issue 1 (January 1974) table of contents

Pages: 114 - 123

Year of Publication: 1974

ISSN:0004-5411

Authors

Michael A. Crane	Control Analysis Corporation, 800 Welch Rd., Palo Alto, California
Donald L. Iglehart	Department of Operations Reserach, Stanford University, Stanford, California

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 32, Citation Count: 29

Additional Information:

abstract references cited by index terms collaborative colleagues peer to peer

Tools and Actions:	Request Permissions Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/321796.321806 What is a DOI?

ABSTRACT

A technique for simulating GI/G/s queues is shown to apply to simulations of discrete and continuous-time Markov chains. It is possible to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of observations which produces independent identically distributed blocks from the start of the simulation. This grouping allows confidence intervals to be obtained for a general function of the steady-state distribution of the Markov chain. The technique is illustrated with simulation of an (s, S) inventory model in discrete time and the classical repairman problem in continuous time. Consideration is also given to determining system sensitivity to errors and uncertainty in the input parameters.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	CHUNG, K.L. Markov Chaius with Stationary Transition Probabilities. Springer, Berlin, 1960.
	2	CuuNa, K. L. A Course in Probability. Harcourt, Brace and World, New York, 1968.
	3	Michael A. Crane , Donald L. Iglehart, Simulating Stable Stochastic Systems, I: General Multiserver Queues, Journal of the ACM (JACM), v.21 n.1, p.103-113, Jan. 1974 [doi>10.1145/321796.321805]
	4	FISRMAN, G., AND K~WA% P. The analysis of simulation generated time series. Management Sci. 13 (1967), 525-557.
	5	WAGN~a, H. Principles of Operations Research. Prentice-Hall, Englewood Cliffs, N. J., 1969.

CITED BY 29

	Donald L. Iglehart, Simulating Stable Stochastic Systems, VI: Quantile Estimation, Journal of the ACM (JACM), v.23 n.2, p.347-360, April 1976
	Averill M. Law, A tutorial on statistical analysis of simulation output data, Proceedings of the 12th conference on Winter simulation, p.361-370, December 03-05, 1980, Orlando, FL
	Philip Heidelberger, Variance reduction techniques for simulating Markov chains, Proceedings of the 9th conference on Winter simulation, p.160-164, December 05-07, 1977, Gaitherburg, Maryland, United States
	Averill M. Law, Confidence intervals in discrete event simulation: A state-of-the-art survey, Proceedings of the 76 Bicentennial conference on Winter simulation, p.53-54, December 06-08, 1976, Gaithersburg, MD
	Viatcheslav B. Melas, On the efficiency of the splitting and roulette approach for sensitivity analysis, Proceedings of the 29th conference on Winter simulation, p.269-274, December 07-10, 1997, Atlanta, Georgia, United States
	Herbert D. Schwetman , Steven C. Bruell, When to stop a simulation run: A case study, ACM SIGSIM Simulation Digest, v.7 n.4, p.131-137, July 1976
	W. R. Franta, Simulation, Proceedings of the 1975 annual conference, p.279-280, January 1975
	Donald L. Iglehart , Peter A. W. Lewis, Regenerative Simulation with Internal Controls, Journal of the ACM (JACM), v.26 n.2, p.271-282, April 1979
	George S. Fishman, Achieving specific accuracy in simulation output analysis, Communications of the ACM, v.20 n.5, p.310-315, May 1977
	Boo Ho Rho, A comparison on two techniques for collecting statistics in simulation, ACM SIGSIM Simulation Digest, v.9 n.1, p.54-58, Fall-Winter 1977
	Michael A. Crane , Donald L. Iglehart, Statistical analysis of discrete—event simulations, Proceedings of the 7th conference on Winter simulation, p.513-521, January 14-16, 1974, Washington, DC
	W. David Kelton, Simulation analysis, Proceedings of the 15th conference on Winter simulation, p.159-168, December 12-14, 1983, Arlington, Virginia, United States
	George S. Fishman , Louis R. Moore, Estimating the Mean of a Correlated Binary Sequence with an Application to Discrete Event Simulation, Journal of the ACM (JACM), v.26 n.1, p.82-94, Jan. 1979
	Robert G. Sargent, Statistical analysis of simulation output data, ACM SIGSIM Simulation Digest, v.7 n.4, p.39-50, July 1976
	Richard P. King, Disk arm movement in anticipation of future requests, ACM Transactions on Computer Systems (TOCS), v.8 n.3, p.214-229, Aug. 1990
	Robert G. Sargent, Statistical analysis of simulation output data, ACM SIGSIM Simulation Digest, v.8 n.3, p.21-31, April 1977
	Christos Alexopoulos, Advanced simulation output analysis for a single system, Proceedings of the 25th conference on Winter simulation, p.89-96, December 12-15, 1993, Los Angeles, California, United States
	Christos Alexopoulos, Advanced methods for simulation output analysis, Proceedings of the 27th conference on Winter simulation, p.101-109, December 03-06, 1995, Arlington, Virginia, United States
	Christos Alexopoulos, A review of advanced methods for simulation output analysis, Proceedings of the 26th conference on Winter simulation, p.133-140, December 11-14, 1994, Orlando, Florida, United States
	Christos Alexopoulos , Andrew F. Seila, Output analysis: output analysis for simulations, Proceedings of the 32nd conference on Winter simulation, December 10-13, 2000, Orlando, Florida
	Christos Alexopoulas , Andrew F. Seila, Advanced methods for simulation output analysi8, Proceedings of the 30th conference on Winter simulation, p.113-120, December 13-16, 1998, Washington, D.C., United States
	C. H. Sauer , M. Reiser , E. A. MacNair, RESQ: a package for solution of generalized queueing networks, Proceedings of the June 13-16, 1977, national computer conference, June 13-16, 1977, Dallas, Texas
	Christos Alexopoulos , Andrew F. Seila, Output analysis: output data analysis for simulations, Proceedings of the 33nd conference on Winter simulation, December 09-12, 2001, Arlington, Virginia
	L P Clare, Control procedures for slotted Aloha systems that achieve stability, ACM SIGCOMM Computer Communication Review, v.16 n.3, p.302-309, Aug. 5, 1986
	Christos Alexopoulos , Seong-Hee Kim, Statistical analysis of simulation output: output data analysis for simulations, Proceedings of the 34th conference on Winter simulation: exploring new frontiers, December 08-11, 2002, San Diego, California
	Steven E. Shladover, Simulation of merge junctions in a dynamically entrained automated guideway transit system, Proceedings of the 11th conference on Winter simulation, p.527-539, December 03-05, 1979, San Diego, CA, United States
	William Farrell, Literature review bibliography of simulation optimitation, Proceedings of the 9th conference on Winter simulation, p.116-124, December 05-07, 1977, Gaitherburg, Maryland, United States
	K. Mani Chandy, Models of distributed systems, Proceedings of the third international conference on Very large data bases, p.105-120, October 06-08, 1977, Tokyo, Japan
	J. C. Browne, A critical overview of computer performance evaluation, Proceedings of the 2nd international conference on Software engineering, p.138-145, October 13-15, 1976, San Francisco, California, United States