SIMULTANEITY IN DISCRETE-TIME SINGLE-SERVER QUEUES WITH BERNOULLI INPUTS

In discrete-time systems, arrivals and departures occur simultaneously. The present work focuses on the scheduling of arrivals and departures in discrete-time queues with Bernoulli arrivals and general independent service times. Both finite and infinite capacity queues are analysed. The waiting-room management policy takes care of the simultaneity problem. Two waiting-room management policies, AF (Arrivals First) and DF (Departures First) are singled out and their influence on the derivation of the state probabilities is investigated. Furthermore, the outside observer's distribution is shown to be identical to the arriving customer's distribution in the AF queue and a formula relating both distributions is provided for the DF queues.