A tandem of discrete-time queues with arrivals and departures at each stage

A discrete-time system of a tandem of queues with exogenous arrivals and departures at each stage is considered. A customer leaving queue k − 1 departs the system with probability 1 − ρ^[k] and continues to queue k with probability ρ^[k]. Exogenous arrivals to each stage are independent, identically distributed at each time slot. An approximate analysis of the occupancy and busy-period distributions of each stage based on a General Busy-period with batches and Memoryless (geometric) Idle period renewal Process provides improved performance over two-state Markov approximations and gives exact results when there are no interstage departures.