Infinite server queues with synchronized departures driven by a single point process
The paper considers a system where groups of customers arrive at the epochs of a point process \(\{ T_n ,n \in Z\} \) defined on the whole real line. The \(n\)th group arrives at time \(T_n \) and consists of \(\beta _n \) customers. The \(i\)th customer of the \(n\)th group remains in the system for \(\sigma _{i,n} \) time units, and then departs at the next arrival point after his service completion. For this system the queue length process and the statistics of the departing batches of customers are investigated. Results for the asymptotic distribution of the departing batches when the service times are long compared to the interarrival times are also derived.
scientific article; zbMATH DE number 2153995