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Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts

Published online by Cambridge University Press:  14 July 2016

Thomas Hanschke*
Affiliation:
Joh annes Gutenberg-Universität Mainz
*
Postal address Fachbereich Mathematik, Saarstr. 21, 6500 Mainz, W. Germany.

Abstract

In this paper we study the M/M/2/2 queue with repeated attempts. It is shown that the part generating functions of the steady state probabilities can be expressed in of generalized hypergeometric unctions.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1987 

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References

Cohen, J. W. (1957) Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommun. Rev. 18, 49100.Google Scholar
Erdélyi, A. et al. (1953) Higher Transcendental Functions, Vol. I, McGraw-Hill, New York.Google Scholar
Falin, G. I. (1984a) On sufficient conditions for ergodicity of multichannel queueing systems with repeated calls. Adv. Appl. Prob. 16, 447448.CrossRefGoogle Scholar
Falin, G. I. (1984b) Double-channel queueing system with repeated calls. The paper is deposited with the All-Union Institute for Scientific and Technical Information, Moscow, USSR, No. 4221–84, June 21 (in Russian).Google Scholar
Jonin, G. L. and Sedol, J. J. (1970) Telephone systems with repeated calls. Proc. 6th Internat. Teletraffic Congr., Munich, 435/1435/5.Google Scholar
Keilson, J., Cozzolino, J. and Young, H. (1968) A service system with unfilled requests repeated. Operat. Res. 16, 11261137.CrossRefGoogle Scholar
Kendall, D. G. and Reuter, G. E. H. (1957) The calculation of the ergodic projection for Markov chains and processes with a countable infinity of states. Acta Math. 97, 103144.CrossRefGoogle Scholar
Little, J. D. C. (1961) A proof for the queueing formula L = ?W. Operat Res. 9, 383387.CrossRefGoogle Scholar
Reuter, G. E. H. (1957) Denumerable Markov processes and the associated contraction semigroups on 1. Acta Math. 97, 146.CrossRefGoogle Scholar
Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.Google Scholar
Tweedie, R. L. (1975) Sufficient conditions for regularity, recurrence and ergodicity of Markov processes. Math. Proc. Camb. Phil. Soc. 78, 125136.CrossRefGoogle Scholar