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

Part of: Operations research and management science Special processes Markov 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 service 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
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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