Poisson winner queues

Abstract

Kleinrock, L. and F. Mehović, Poisson winner queues, Performance Evaluation 14 (1992) 79–101. We study special types of queues, winner queues, in which all customers are served concurrently. A customer in a winner queue will successfully finish his service (i.e. “win”) and leave if no other customer leaves during his current service. Once a customer wins, all others in service at that time “lose”; thus we have a situation in which concurrent customers conflict, yielding a single “winner”. There are four disciplines considered: silent-redraw, silent-noredraw, broadcast-redraw, and broadcast-noredraw. The winner queues considered have an infinite number of servers. We assume that service times consist of a deterministic part and an exponential part. This type of service time distribution includes pure deterministic and pure exponential service times as special cases. Using a one-dimensional imbedded Markov chain and a recursive formula for the state probabilities, we obtain numerical results for certain disciplines and distributions of requested and restarted service time. For some broadcast winner queues we show analytic results. In all cases we also give simulation results which indicate the correctness and accuracy of our numerical calculations. The results obtained are given in terms of the normalized average system time and the normalized power (defined as the system load divided by the normalized average system time). One application of this model is to study the performance of optimistic concurrency control schemes in databases.