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On the MX/G/∞ queue by heterogeneous customers in a batch

Part of:Markov processesOperations research and management scienceSpecial processes

Published online by Cambridge University Press:  14 July 2016

Tang Dac Cong
Tang Dac Cong*
Affiliation:
University of Amsterdam
*
∗ Postal address: Faculty of Mathematics and Computer Science, P1. Muidergracht 24, 1018 TV Amsterdam, The Netherlands.
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Abstract

We consider the Mx/G/∞ queue in which customers in a batch belong to k different types, and a customer of type i requires a non-negative service time with general distribution function Bi (s) (1 ≦ i ≦ k). The number of customers in a batch is stochastic. The joint probability generating function of the number of customers of type i being served at a fixed time t > 0 is derived by the method of collective marks.

Keywords

BATCH ARRIVAL QUEUEJOINT PROBABILITY GENERATING FUNCTIONCOLLECTIVE MARKS

MSC classification

Primary:60K25: Queueing theory
Secondary:90B22: Queues and service60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994, pp. 280 - 286
Copyright
Copyright © Applied Probability Trust 1994 

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References

Choi, B. D. and Park, K. K. (1992) The Mk/M/8 queue with heterogeneous customers in a batch. J. Appl. Prob. 29, 477–481.Google Scholar
Danieljan, E. A. and Liese, F. (1991) The analysis of a Mr/Gr/1/8 model with time dependent priorities. Rostock. Math. Kolloq. 43, 39–54.Google Scholar
Van Dantzig, D. (1949) Sur la méthode des fonctions génératrices. Colloques internationaux du CNRS 13, 29–45.Google Scholar
Falin, G. and Fricker, C. (1991) On the virtual waiting time in an M/G/1 retrial queue. J. Appl. Prob. 28, 446–460.CrossRefGoogle Scholar
Holman, D. F., Chaudhry, M. L. and Kashyap, B. R. K. (1983) On the service system Mx/G/8. Eur. J. Operat. Res. 13, 142–145.Google Scholar
Liu, L., Kashyap, B. R. K. and Templeton, J. G. C. (1990) On the GIx/G/8 system. J. Appl. Prob. 27, 671–683.CrossRefGoogle Scholar
Runnenburg, J. Th. (1965) On the use of the method of collective marks in queueing theory. Chapter 13 in Congestion Theory, ed. Smith, W. L. and Wilkinson, W. E., University of North Carolina Press, Chapel Hill.Google Scholar
Runnenburg, J. Th. (1979) Van Dantzig's Collective Marks revisited. MC tract 101, Proceedings of the Bicentennial Congress Wiskundig Genootschap, Part II, pp. 309–329, ed. Baayen, P. C., van Dulst, D. and Oosterhoff, J., Mathematisch Centrum, Amsterdam.Google Scholar
Whittaker, E. T. and Watson, G. N. (1920) A Course of Modern Analysis, 3rd edn. Cambridge University Press.Google Scholar