Mathematical Problems in Engineering
Volume 2 (1996), Issue 2, Pages 95-106
doi:10.1155/S1024123X96000257
Abstract
The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less than
r
and not greater than
R(≥r). The server takes vacations each time the queue level falls below
r(≥1)
in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics for the queueing process in an analytically tractable form. Some examples and applications are given.