A generalized neyman's type a contribution for the busy period of queues

Abstract

This paper consider the probability distribution of the busy period of a single server queuing system with constant servicing time for each customer when customer arrive condonly in varying batch sizes and the batch size is distributed according to the Poisson law. First four moments and a few limiting forms of the distribution are also given.

Keywords:

• busy period
• single-server queue
• batch arrival
• constant service times
• probability generating functions
• moments
• the Borel-Tamer
• generalized negative binomial