Workload distribution of discrete-time parallel queues with two servers

We study discrete-time, parallel queues with two identical servers. Custome rs arrive randomly at the system and join the queue with the shortest workl oad that is defined as the total service time required for the server to co mplete all the customers in the queue. The arrivals are assumed to follow a geometric distribution and the service times are assumed to have a general distribution. It is a no-jockeying queue. The two-dimensional state space is truncated into a banded array. The resulting modified queue is studied u sing the method of probability generating function (pgf). The workload dist ribution in steady state is obtained in form of pgf. A special case where t he service time is a deterministic constant is further investigated. Numeri cal examples are illustrated. (C) 2000 John Wiley & Sons, Inc.