Recursive Markovian analysis for the occupancy distribution of M/G/1 queuing systems

Abstract

M/G/1 queuing analysis has a critical role in the performance evaluation of different communication systems. Traditional approaches for M/G/1 queuing analysis employ the Laplace transform and are generally used to estimate only the mean and variance of the queue length distribution. These parameters are not adequate for comprehensive assessment of system performance. Furthermore, these techniques occasionally become limited when dealing with the queuing analysis of data-type of traffic that has heavy-tailed service time distributions. In this paper, a one-dimensional embedded Markov model is developed to derive the exact queue length distribution of M/G/1 queues without any restrictions on the type of the service distribution. Transition probabilities of the developed Markov chain are derived with the use of a recursive method. The analytical approach is then applied to derive the queue occupancy distribution of an M/G/1 queuing system with heavy-tailed Weibull distribution service time.