K. C. Madan and W. Abu-Dayyeah, “On a Combination of M/G/1 and M/D/1 Queues in Non-Preemptive Priority Queueing System,” Far East Journal of Theoretical Statistics, Vol. 10, No. 2, 2003, pp. 133-146.

has been cited by the following article:

• TITLE: A Non-Preemptive Priority Queueing System with a Single Server Serving Two Queues M/G/1 and M/D/1 with Optional Server Vacations Based on Exhaustive Service of the Priority Units

  AUTHORS: Kailash C. Madan

  KEYWORDS: Non Preemptive Priority Queueing System, Modified Server Vacations, Combination of General Service and Deterministic Service, Steady State, Queue Size Distribution

  JOURNAL NAME: Applied Mathematics, Vol.2 No.6, June 22, 2011

  ABSTRACT: We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.