A single server queue with gated processor-sharing discipline
The authors study a single-line queueing system with an infinite capacity buffer in which customers arrive in a Poisson process and service times have exponential distribution. When a customer arrives into an empty system, he begins to be served immediately and until service completion newly arriving customers must wait in the buffer. After service completion a batch of at most m of the waiting customers from the head of the queue occupies the server and starts to be served in accordance with processor-sharing discipline. As before newly arriving customers are not allowed to join the batch which receives service. The authors study waiting time, queue length, etc. It should be noted that for finite m the conditional mean response time is not a linear function.
scientific article; zbMATH DE number 4107895