Workload distribution of discrete-time parallel queues with two servers

We study discrete-time, parallel queues with two identical servers. Customers arrive randomly at the system and join the queue with the shortest workload that is defined as the total service time required for the server to complete all the customers in the queue. The arrivals are assumed to flow 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 using the method of probability generating function (pgf). The workload distribution in steady state is obtained in form of pgf. A special case where the service time is a deterministic constant is further investigated. Numerical examples are illustrated.