Queues with postponed work

Abstract

In this paper a queueing system in which work gets postponed due to finiteness of the buffer is considered. When the buffer is full (capacityK) further arrivals are directed to a pool of customers (postponed work). An arrival encountering the buffer full, will join the pool with probability γ (0<γ<1); else it is lost to the system forever. When, at a departure epoch the buffer size drops to a preassigned levelL−1 (1<L<K) or below, a postponed work is transferred with probabilityp (0<p<1) and positioned as the last among the waiting customers. If at a service completion epoch the buffer turns out to be empty and there is at least one customer in the pool, then the one ahead of all waiting in the pool gets transferred (with probability one) to the buffer and its service commences immediately. This ensures conservation of work. With arrival forming a Poisson process and service time having PH-distribution we study the long run behaviour of the system. Several system performance measures are obtained. A control problem is discussed and some numerical illustrations are provided.