On transient queue-size distribution in the batch-arrivals system with a single vacation policy

Abstract

A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated.As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained.The approach consists of few stages.Firstly, some results for a "usual" system without vacations corresponding to the original one are derived.Next, applying the formula of total probability, the analysis of the original system on a single vacation cycle is brought to the study of the "usual" system.Finally, the renewal theory is used to derive the general result.Moreover, a numerical approach to analytical results is discussed and some illustrative numerical examples are given.

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 — 18 citations exist upstream.

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