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An efficient solution technique for discrete‐time queues fed by heterogeneous traffic
Author(s) -
Steyaert Bart,
Bruneel Herwig,
Xiong Yijun
Publication year - 1997
Publication title -
international journal of communication systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.344
H-Index - 49
eISSN - 1099-1131
pISSN - 1074-5351
DOI - 10.1002/(sici)1099-1131(199703)10:2<73::aid-dac325>3.0.co;2-t
Subject(s) - computer science , queueing theory , queue , expression (computer science) , state space , markov chain , markov process , boundary (topology) , mathematical optimization , asynchronous communication , probability generating function , multiplexer , discrete time and continuous time , joint probability distribution , algorithm , probability mass function , mathematics , computer network , mathematical analysis , telecommunications , statistics , machine learning , multiplexing , programming language
During the past couple of years, a lot of effort has been put into solving all kinds of Markov modulated discrete‐time queueing models, which occur, almost in a natural way, in the performance analysis of slotted systems, such as asynchronous transfer mode (ATM) multiplexers and switching elements. However, in most cases, the practical application of such solutions is limited, because of the large state space that is usually involved. In this paper we try to take a first step towards obtaining approximate solutions for a discrete‐time multiserver queueing model with a general heterogeneous Markove modulated cell arrival process, which allows accurate predictions concerning the behaviour of the buffer occupancy in such a model and still remains tractable, both from an analytical and a computational point of view. We first introduce a solution technique which leads to a closed‐form expression for the joint probability generating function of the buffer occupancy and the state of the arrival process, from which an expression for V(z), the probability generating function of the buffer occupancy is easily derived. On the basis of this result we propose an approximation for the boundary probabilities, which reduces all calculations to an absolute minimum. In addition, we show how accurate data for the distribution of the buffer occupancy can be obtained, by using multiple poles of V(z) in the geometric‐tail approximation of the distribution. ©1997 by John Wiley & Sons, Ltd.