A LCFS finite buffer model with batch input and non-exponential services (Q582714)

A single server can hold at most N jobs in service or waiting. Randomly sized batches of jobs arrive at Poisson times. A batch of size k is accepted at its time of arrival if k places are free, lost otherwise. An accepted batch starts getting served at once, interrupting the service (if any) going on at the time of acceptance. For each job a service time is drawn from a general distribution. When all jobs of a batch are completely served, the service of the batch last interrupted (if any), is resumed. A job departs once its service is completed. Using a phase-type approximation of the service time distribution, the author computes the steady-state distribution of the queue length, which turns out to depend only on the mean and not on any other parameters of the service time distribution.