Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 1, 159--174

On the $M^X/G/1$ Queue with a Waiting Server and Vacations

By

Uri Yechiali, Tel Aviv University, Israel

SUMMARY. We analyse the $M^X/G/1$ queue with server vacations and an {\it additional} feature, reflecting various real-life situations, in which the server, upon finding an empty system at the end of a vacation, activates a timer of duration $T$ and {\it waits} dormant.  If a batch arrives during the dormant period, a new busy period starts, but if no arrivals occur, the server waits no more and takes another vacation. The $M^X/G/1$ queues with multiple or with single vacations become limiting cases of the above model when $T \to 0$ or $T\to \infty$, respectively.

AMS (1991) subject classification}. 90B22, 60K25.

Key words and phrases. $M^X/G/1$ queue, vacations, waiting server.

Full paper (PDF)