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Busy period of queues with state dependent arrival and service rates

Published online by Cambridge University Press:  14 July 2016

Nasser Hadidi
Nasser Hadidi*
Affiliation:
Pahlavi University, Shiraz, Iran
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Abstract

A technique is derived providing for the analysis of busy period processes in the queueing models M/Mn/1 and Mn/M/1; queueing models with state dependent service and arrival rates respectively. A single treatment covers both models and no separate analysis is required.

Keywords

POISSON QUEUESBUSY PERIODSTATE DEPENDENT RATESINTEGRAL DIFFERENCE EQUATIONPARTIAL DIFFERENTIAL EQUATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 842 - 848
Copyright
Copyright © Applied Probability Trust 1974 

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References

Conolly, B. W. (1959) The busy period in relation to the queueing process GI/M/1. Biometrica 46, 246–251.Google Scholar
Conolly, B. W. (1974) The generalised state dependent Erlangian queue: the busy period. J. Appl. Prob. 11, 618–623.Google Scholar
Conway, R. W. and Maxwell, W. L. (1961) A queueing model with state dependent service rates. J. Indust. Engr. 10, 131–142.Google Scholar
Cox, D. R. and Smith, W. L. (1961) Queues. Methuen, London.Google Scholar
Hadidi, N. (1969) On the service time distribution and the waiting time process of a potentially infinite capacity queueing system. J. Appl. Prob. 6, 594–603.Google Scholar
Hadidi, N. (1972) On the output process of a state dependent queue. Skand. Aktuartidskr. 10, 182–186.Google Scholar
Hadidi, N. (1973) A queueing model with variable arrival rates. Hungarica Mathematica Periodica To appear.Google Scholar
Hadidi, N. and Conolly, B. W. (1969a) On the improvements of the operational characteristics of single server queues by the use of a queue length dependent service mechanism. Applied Statist. 18, No. 3, 229–240.Google Scholar
Hadidi, N. and Conolly, B. W. (1969b) On the reduction of congestion. Statist. Research Report No. 6, Institute of Mathematics, University of Oslo.Google Scholar
Harris, C. M. (1967) Queues with state dependent stochastic service rates. ORSA Journal 15, 117–130.Google Scholar
Jackson, J. R. (1963) Jobshop-like queueing systems. Management Sci. 10, 131–142.Google Scholar
Natvig, B. (1973) A queueing model where potential customers are discouraged by queue length. Scand. Journ. Statist. To appear.Google Scholar
Scott, N. (1970) A queueing process with varying degree of service. Nav. Res. Log. Quart. 17, 515–523.Google Scholar
Yadin, M. and Naor, P. (1963) Queueing systems with a removable service station. Oper. Res. Quart. 14, 393–405.Google Scholar
Yadin, M. and Naor, P. (1967) On queueing systems with variable service capacities. Nav. Res. Log. Quart. 14, 43–53.Google Scholar