Algorithm for waiting time distribution of a discrete-time multiserver queue with deterministic service times and multi-threshold service policy

In this paper, a discrete-time multiserver queueing system with infinite buffer size is studied. Packets arrive at the system according to a Bernoulli arrival process, and the service times of the packets are assumed to be constant equal to an integer multiple of slots. The number of active servers in the system is controlled by a so-called multi-threshold service policy with a set of thresholds predefined. For this multiserver system, we derive its stationary waiting time distribution by using the stochastic complement and Crommelin's techniques. We also present an algorithm for computing the stationary waiting time distribution.