Expected waiting times in a multiclass batch arrival retrial queue

Abstract

Expressions are derived for the expected waiting times for the customers of two types who arrive in batches (in a compound Poisson fashion) at a single-server queueing station with no waiting room. Those who cannot get served immediately keep returning to the system after random exponential amounts of time until they get served. The result is shown to agree with similar results for three special cases studied in the literature.