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Gaussian approximations to service problems: a communication system example

Published online by Cambridge University Press:  14 July 2016

Donald P. Gaver  and
John P. Lehoczky
Donald P. Gaver
Affiliation:
Naval Postgraduate School, Monterey, California
John P. Lehoczky
Affiliation:
Carnegie-Mellon University, Pittsburgh, Pennsylvania
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Abstract

Messages arrive at a group of service channels in accordance with a time-dependent Poisson process. An arrival either (i) immediately begins k -stage Markovian service if an empty channel is reached, or (ii) balks and enters a retrial population if the channel sought is busy. Diffusion approximations to the number of messages in service (each stage) and in the retrial population are derived by writing stochastic differential equations (I + 0). Steady-state distributions are found and compared with certain simulation results.

Keywords

QUEUESDIFFUSIONSERVICE SYSTEMRETRIALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 768 - 780
Copyright
Copyright © Applied Probability Trust 1976 

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References

Arnold, L. (1974) Stochastic Differential Equations. Wiley, New York.Google Scholar
Barbour, A. (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Prob. 6, 21–29.CrossRefGoogle Scholar
Feller, W. (1967) An Introduction to Probability Theory and Its Applications, II. Wiley, New York.Google Scholar
Gaver, D. P., Lehoczky, J. P. and Perlas, M. (1975) Service systems with transitory demand. Studies in the Management Sciences, Vol. I, Logistics. North-Holland/TIMS.Google Scholar
Gordon, W. and Newell, G. F. (1967) Closed queueing systems with exponential servers. Opns. Res. 15, 254–265.Google Scholar
Kingman, J. F. C. (1969) Markov population processes. J. Appl. Prob. 6, 1–18.Google Scholar
Kurtz, T. G. (1971) Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Prob. 8, 344–356.Google Scholar
McNeil, D. R. (1973) Diffusion limits for congestion problems. J. Appl. Prob. 10, 368–376.Google Scholar
McNeil, D. R. and Schach, S. (1973) Central limit analogues for Markov population processes. J. R. Statist. Soc. B 35, 1–23.Google Scholar
Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.Google Scholar
Whittle, P. (1968) Equilibrium distributions for an open migration process. J. Appl. Prob. 5, 567–571.CrossRefGoogle Scholar