System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation

In many queueing systems the server processes several customers simultaneously. Although the capacity of a batch, that is the number of customers that can be processed simultaneously, is often variable in practice, nearly all batch-service queueing models in literature consider a constant capacity. In this paper, we extend previous work on a batch-service queueing model with variable server capacity, where customers of two classes are accommodated in a common first-come-first-served single-server queue. We include correlation between the classes of consecutive customers, and the service times are geometrically distributed. We establish the equations that govern the system behaviour, the stability condition, and an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. In addition, some numerical results are shown to study the impact of the mean service times and of the customer-based correlation in the arrival process on the performance of the queueing system.