Busy period density of M/ C 2 b /1 queueing system through lattice path approach: a special case

Abstract

Abstract We consider M/ C 2 b / lqueueing system which is a queueing system with arrival rate follows a Poisson distribution, service rate follows an exponential distribution which is approximated by Coxian 2-phase distribution, service is performed in b -size, and the number of service facility is one. This paper aims to derive the properties of M/ C 2 b / 1 queueing system when the system is in busy pea riod using latticea path combinatorics approach. We consider a special case which is called pure incomplete busy period (PIBP) Through this approach, the queue system is represented in the form of lattice path. Furthermore, we have determined the number of lattice paths and finally, the probability function in the queue system M/ C 2 b / 1 in PIBP is derived.