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Transient analysis of M/M/1 queues in discrete time by general server vacations

Part of: Special processes Combinatorics

Published online by Cambridge University Press:  14 July 2016

W. Böhm  and
S. G. Mohanty
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Abstract

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

Keywords

T-POLICYCOMBINATORIAL METHODSDISCRETE-TIME QUERIES

MSC classification

Primary: 60K25: Queueing theory
Secondary: 05A15: Exact enumeration problems, generating functions
Type
Part 3 Queueing Theory
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 115 - 129
Copyright
Copyright © Applied Probability Trust 1994 

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References

Böhm, W. and Mohanty, S. G. (1991) On discrete time Markovian N-policy queues involving batches. Sankya A.Google Scholar
Böhm, W. and Mohanty, S. G. (1993) The transient solution of M/M/1 queues under (M, N) policy. A combinatorial approach. J. Statist. Planning Inf. 34, 23–33.Google Scholar
Doshi, B. T. (1985) Stochastic decomposition in a GI/G/1 queue with vacations. J. Appl. Prob. 22, 419–428.Google Scholar
Ethier, S. N. and Kurtz, T. G. (1986) Markov Processes. Characterization and Convergence. Wiley, New York.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and Its Applications , Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and Its Applications , Vol. 2, 2nd edn. Wiley, New York.Google Scholar
Heyman, D. P. (1977) The T-policy for the M/G/Ì queue. Management Sci. 23, 7, 775–778.Google Scholar
Mohanty, S. G. and Panny, W. (1989) A discrete time analogue of the M/M/1 queue and the transient solution: an analytic approach. In Colloq. Math. Soc. János Bolyai 57, Limit Theorems in Probability and Statistics , ed. Révész, P., pp. 417–424. North-Holland, Amsterdam.Google Scholar
Mohanty, S. G. and Panny, W. (1990) A discrete time analogue of the M/M/1 queue and the transient solution: a geometric approach. Sankya A52, 364–370.Google Scholar
Takács, L. (1961) The probability law of the busy period for two types of queueing processes. Operat. Res. 9, 402–407.Google Scholar
Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar
Takács, L. (1975) Combinatorial and analytic methods in the theory of queues. Adv. Appl. Prob. 7, 607–635.CrossRefGoogle Scholar
Takagi, H. (1991) Queueing Analysis . Vol. 1, A Foundation of Performance Analysis. North-Holland, Amsterdam.Google Scholar