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Queues with delayed feedback

Published online by Cambridge University Press:  01 July 2016

Robert D. Foley  and
Ralph L. Disney
Robert D. Foley*
Affiliation:
Virginia Polytechnic Institute and State University
Ralph L. Disney*
Affiliation:
Virginia Polytechnic Institute and State University
*
∗Postal address: Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A.
∗Postal address: Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A.
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Abstract

Queues with delayed feedback have been little studied in queueing theory. Presented here is a rather complete discussion of such problems including queue length processes, busy period processes and several customer flow processes (e.g., departure processes). The case in which the delay mechanism is an M-server queue is studied in detail but it is shown later that many of the results carry over to a more general delay mechanism.

Keywords

M/G/1 QUEUES WITH FEEDBACKDELAYED FEEDBACKQUEUEBUSY PERIODMARKOV RENEWAL PROCESSESDEPARTURE PROCESSQUEUEING NETWORK
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 162 - 182
Copyright
Copyright © Applied Probability Trust 1983 

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References

Berman, M. (1978) Multivariate Point Processes. Doctoral Dissertation, Imperial College, London.Google Scholar
ÇInlar, E. (1969) Markov renewal processes. Adv. Appl. Prob. 1, 123–187.CrossRefGoogle Scholar
ÇInlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
Cohen, J. W. (1969) The Single Server Queue. Wiley, New York.Google Scholar
Daley, D. J. and Vere-Jones, D. (1972) A summary of the theory of point processes. In Stochastic Point Processes: Statistical Analysis, Theory, and Applications, ed. Lewis, P. A. W., Wiley, New York, 299–383.Google Scholar
Disney, R. L. and Hannibalsson, I. (1977) Networks of queues with delayed feedback. Naval Res. Logist. Quart. 24, 281–291.Google Scholar
Disney, R. L., McNickle, D., and Simon, B. (1980) The M/G/1 queue with instantaneous, Bernoulli feedback. Naval Res. Logist. Quart. 27, 635–644.CrossRefGoogle Scholar
Foley, R. D. (1979) The M/G/1 Queue with Delayed Feedback. Doctoral Dissertation, University of Michigan, Ann Arbor.Google Scholar
Jackson, J. R. (1957) Networks of waiting lines. Operat. Res. 5, 518–521.CrossRefGoogle Scholar
Kelly, F. P. (1976) Networks of queues. Adv. Appl. Prob. 8, 416–432.Google Scholar
Kemeny, J. and Snell, L. (1960) Finite Markov Chains. Van Nostrand, Princeton, N.J.Google Scholar
Kingman, J. F. C. (1961) The ergodic behaviour of random walks. Biometrika 48, 391–396.CrossRefGoogle Scholar
Melamed, B. (1979a) On Poisson traffic processes in discrete state Markovian systems with applications to queueing theory. Adv. Appl. Prob. 11, 218–239.CrossRefGoogle Scholar
Melamed, B. (1979b) Characterizations of Poisson traffic streams in Jackson queueing networks. Adv. Appl. Prob. 11, 422–438.CrossRefGoogle Scholar
Nakamura, G. (1971) A feedback queueing model for an interactive computer system. AFIPS Proceedings of the Fall Joint Conference. CrossRefGoogle Scholar
Serfozo, R. (1971) Functions of semi-Markov processes. SIAM J. Appl. Math. 20, 530–535.CrossRefGoogle Scholar
Simon, B. (1979) Equivalent Markov Renewal Processes. Doctoral Dissertation, University of Michigan, Ann Arbor.Google Scholar