On queues in which customers are served in random order

Abstract

The queue M |G| l is considered in the case in which customers are served in random order. A formal solution is obtained for the waiting time distribution in the steady state, and is used to consider the exponential decay of the distribution. The moments of the waiting time are examined, and the asymptotic form of the distribution in heavy traffic is found. Finally, the problem is related to those of the busy period and the approach to the steady state.