The paper studies a queue with Poisson arrivals and a bulk service rule with two thresholds N and m on the group sizes. No group of fewer than N or more than m customers is served. When the number of available customers is between N and m, all customers are served together. The principal results deal with the joint stationary distribution of the waiting time of an arriving customer and of the size of the group in which he is eventually served. After prior computation of the stationary queue length density, the evaluation of the waiting time distribution is reduced to the solution of a system of linear differential equations and a single integral equation. The process describing the waiting time is in general non-Markovian.
