A D/D/1 queueing process with varying service times (Q1574266)

A single-server queue with deterministic interarrival time \(a\) and service times \(\{b_n\}\) is considered under the assumption that \(b_n<a\) for all \(n\) (service times are constants which vary from one customer to another). Explicit expressions are obtained for the queue-size as a function of time and waiting time for each customer. A necessary and sufficient condition that queue-size is at or above a predefined level (instability criterion) is given.