On a single-server queue with group arrivals

1 September 1976

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 13 (3) , 619-622
https://doi.org/10.2307/3212485

Abstract

The queueing system GI/G/1 with group arrivals and individual service of the customers is considered. For the stable situation the limiting distribution of the waiting time distribution of the kth served customer for k → ∞ is derived by using the theory of regenerative processes. It is assumed that the group sizes are i.i.d. variables of which the distribution is aperiodic. The relation between this limiting distribution and the stationary distribution of the virtual waiting time is derived.

Keywords

This publication has 3 references indexed in Scilit:

On Regenerative Processes in Queueing Theory
Published by Springer Nature ,1976
Technical Note—Delays in Single-Server Queues with Batch Input
Operations Research, 1975
Regenerative processes in the theory of queues, with applications to the alternating-priority queue
Advances in Applied Probability, 1972