The General Bulk Queue as a Hilbert Problem

Abstract

SUMMARY Bulk queues are those in which customers arrive and are served in groups, with the size of the groups governed by given probability distributions. A general theory for arbitrary group size distributions is developed for Poisson arrival epochs and arbitrary service-time distribution. Phase space methods and devices for solving the Hilbert problem on the unit circle play a key role. Treated are both the ordinary queue in which the server finding an empty queue waits for new arrivals and the transportation queue in which the service epochs form a renewal process. Formal expressions are given for the server busy period and the equilibrium waiting-time distributions for the general case. The formalism is applied to several queueing situations untreated in the literature.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 34 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.