The Discrete-Time Queue with Geometrically Distributed Service Capacities Revisited

We analyze a discrete-time queue with variable service capacity, such that the total amount of work that can be performed during each time slot is a stochastic variable that is geometrically distributed. We study the buffer occupancy by constructing an analogous model with fixed service capacity. In contrast with classical discrete-time queueing models, however, the service times in the fixed-capacity model can take the value zero with positive probability (service times are non-negative). We study the late arrival models with immediate and delayed access, the first model being the most natural model for a system with fixed capacity and non-negative service times and the second model the more practically relevant model for the variable-capacity model.