International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 589-597

Identification of waiting time distribution of M/G/1, Mx/G/1, GIr/M/1 queueing systems

A. Ghosal and S. Madan

Council of Scientific and Industrial Research Complex, New Delhi 110012, India

Received 17 March 1986; Revised 12 November 1986

Copyright © 1988 A. Ghosal and S. Madan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper brings out relations among the moments of various orders of the waiting time of the 1st customer and a randomly selected customer of an arrival group for bulk arrivals queueing models, and as well as moments of the waiting time (in queue) for M/G/1 queueing system. A numerical study of these relations has been developed in order to find the (β1,β2) measures of waiting time distribution in a comutable form. On the basis of these measures one can look into the nature of waiting time distribution of bulk arrival queues and the single server M/G/1 queue.