General discrete-time queueing systems with correlated batch arrivals and departures

Discrete time queueing systems have gained attention recently due to their applications in the performance analysis of ATM and other systems. In this paper, we analyze generic discrete-time queueing models with general distribution for batch arrivals and departures. Our models allow correlation and distributions with arbitrary rational probability generating functions. Our solution methodology is significantly different, compared with the traditional methods. We provide a state-space representation of the model resulting in an exact simple matrix geometric solution of the system probability vector. Our approach is algorithmic, numerically robust and efficient. Applications in ATM systems and classical (discrete) G/G/1 queues with semi-Markovian arrival and departure processes are immediate and are discussed