Premium
Analysis of a discrete‐time queue with integrated bursty inputs in ATM networks
Author(s) -
Zhang Zhensheng
Publication year - 1991
Publication title -
international journal of digital and analog communication systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.344
H-Index - 49
eISSN - 1099-1131
pISSN - 1047-9627
DOI - 10.1002/dac.4510040303
Subject(s) - markovian arrival process , markov chain , markov process , queueing theory , queue , computer science , mathematics , discrete time and continuous time , boundary (topology) , function (biology) , mathematical optimization , algorithm , mathematical analysis , statistics , computer network , evolutionary biology , biology
In this paper, we carry out an exact analysis of a discrete‐time queue system with a number of independent Markov modulated inputs in ATM networks, using a generating function approach. We assume that the queueing system has an infinite buffer with M servers. The cell arrival process is characterized by a number of independent Markov modulated geometrical batch arrival processes. We first obtain the generating function of the queue‐size distribution at steady‐state in vector form, then derive an expression for the average queue‐size in terms of the unknown boundary probabilities. To obtain those unknown probabilities, we use the technique proposed in Reference 1. This involves decomposing the system characteristic function to evaluate the roots and solving a set of linear equations. One of the contributions of this paper is presented in Lemma 1, which characterizes the property of the underlying eigenvalues. For one special case of at least M ‐1 cell arrivals during one slot at one Markov state and of at least M arrivals at all other states, the determination of the unknowns is straightforward. If every Markov modulated arrival process can be further decomposed into a number of i.i.d. two‐state, or three‐state, or even four‐state Markov modulated arrival processes, then each root can be obtained separately using an iterative algorithm. Numerical results are presented to validate the proposed traffic models against actual traffic measurements.