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The optimal admission policy to a multiserver queue with finite horizon

Published online by Cambridge University Press:  14 July 2016

H. Emmons
H. Emmons*
Affiliation:
Cornell University
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Abstract

An M/M/s queueing system with a simple cost structure is considered, under the assumption that the system will close in a finite time after which any remaining customers will require extra overtime service costs. We determine the optimal policy for admitting customers to the queue, as a function of the time, t, to closing and the current queue length, i. It is shown to have the form: admit if and only if f 1(t) ≦ i ≦ f 2(t). The bounds f 1(t) and f 2(t) are specified, and it is shown under what conditions f 1(t) = 0 (a control limit rule) or f 2(t) = ∞ (an inverse control limit rule).

Keywords

QUEUEING CONTROLMULTIPLE SERVER QUEUEADMISSION TO QUEUETRANSIENT QUEUEING CONTROLDYNAMIC QUEUEING CONTROLFINITE TIME QUEUEING CONTROLMARKOV DECISION PROCESS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 103 - 116
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Adler, I. and Naor, P. (1969) Social optimization versus self-optimization in waiting lines. Technical Report No. 126, Dept. of Operations Research, Stanford.Google Scholar
[2] Blackwell, D. (1962) Discrete dynamic programming. Ann. Math. Statist. 33, 719–726.CrossRefGoogle Scholar
[3] Crabill, T. B. (1969) Optimal control of a queue with variable service rates. Technical Report No. 75, Department of Operations Research, Cornell.Google Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York.Google Scholar
[5] Howard, R. A. (1960) Dynamic Programming and Markov Processes. Wiley, New York.Google Scholar
[6] Howard, R. A. (1964) Research in semi-Markovian decision structures. J. Operat. Res. Soc. Japan 6, No. 4.Google Scholar
[7] Jewell, W. S. (1963). Markov-renewal programming: I and II. Operat. Res. 11, 938–971.CrossRefGoogle Scholar
[8] Kakumanu, P. V. (1969) Continuous time Markov decision models with applications to optimization problems. Technical Report No. 63, Department of Operations Research, Cornell.Google Scholar
[9] Keilson, J. (1970) A simple algorithm for contract acceptance. Opsearch 7, 157–166.Google Scholar
[10] Knudsen, N. C. (1970) Individual versus social optimization in queuing systems. Technical Report No. 108, Department of Operations Research, Cornell.Google Scholar
[11] Lippman, S. A. and Ross, S. M. (1971) The streetwalker's dilemma: A job shop model. SIAM J. Appl. Math. 20, 336–342.CrossRefGoogle Scholar
[12] Mcgill, J. T. (1969) Optimal control of queuing systems with variable number of exponential servers. Technical Report No. 123, Department of Operations Research, Stanford.Google Scholar
[13] Miller, B. L. (1968) Finite state continuous time Markov decision processes with a finite planning horizon. SIAM J. Control 6, 266–280.CrossRefGoogle Scholar
[14] Miller, B. L. (1969) A queuing reward system with several customer classes. Management Sci. 16, 234–245.CrossRefGoogle Scholar
[15] Mine, H. and Ohno, K. (1971) An optimal rejection time for an M/G/1 queuing system. Operat. Res. 19, 194–207.CrossRefGoogle Scholar
[16] Naor, P. (1969) The regulation of queue size by levying tolls. Econometrica 37, 15–24.CrossRefGoogle Scholar
[17] Sabeti, H. (1970) Optimal decision in queuing. ORC 70–12, Operations Research Center, University of California, Berkeley.CrossRefGoogle Scholar
[18] Scott, M. (1970). A queueing process with varying degree of service. Naval Res. Logist. Quart. 17, 515–523.CrossRefGoogle Scholar
[19] Sobel, M. J. (1969) Optimal average-cost policy for a queue with start-up and shut-down costs. Operat. Res. 17, 145–162.CrossRefGoogle Scholar
[20] Yechiali, U. (1971) On optimal balking rules and toll charges in the GI/M/1 queueing process. Operat. Res. 19, 349–370.CrossRefGoogle Scholar