Queueing model with non-homogeneous bulk arrivals having state-dependent service rates

Abstract

This paper considers a single-server queueing model with non-homogeneous bulk arrivals and state-dependent service rates. The bulk arrival queueing model is important in developing optimal operating policies for queueing in transportation systems and communication systems. Arrivals are assumed to be characterised by a non-homogeneous compound Poisson process, and the service rate depends on the content of the buffer connecting to the service station. Using difference-differential equations and a probability generating function, the system’s behaviour is analysed. Explicit expressions are derived for performance measures including average number of customers in the queue and probability of queue emptiness, etc. Sensitivity analysis of the model revealed that assuming non-homogeneous arrival significantly influences the system performance measures. The state-dependent service rate strategy can control queue congestion and mean delay in transmission. This model is effective in evaluating the performance of time-dependent communication systems.