Infinite Server Queues with Synchronized Departures Driven by a Single Point Process

We analyze an infinite-server queueing model with synchronized arrivals and departures driven by the point process {Tn} according to the following rules. At time Tn, a single customer (or a batch of size βn) arrives to the system. The service requirement of the ith customer in the nth batch is σi,n. All customers enter service immediately upon arrival but each customer leaves the system at the first epoch of the point process {Tn} which occurs after his service requirement has been satisfied. For this system the queue length process and the statistics of the departing batches of customers are investigated under various assumptions for the statistics of the point process {Tn}, the incoming batch sequence {βn}, and the service sequence {σi,n}. Results for the asymptotic distribution of the departing batches when the service times are long compared to the interarrival times are also derived.