On transient behavior of M/C₂/1 interdependent queueing model with (0, K) control policy using lattice path technique

Interdependent queueing models have wide applicability in many practical systems like manufacturing processes, computer communication networks etc. In the present paper, we give analysis of M/C₂/1 interdependent queueing model with (0,k) control policy using lattice path technique. (0,k) control policy represents the system in which the service counter is closed whenever the system becomes empty and reopens for service immediately at arrival of k ^th customer. In the model arrivals are according to Poisson distribution and service time distribution is two phase Coxian distribution C₂. Cox distribution C₂ has Markovian property. Hence lattice path combinatorics can be used. Kanwar Sen et. al. (1993) used this approximation and lattice path technique for analysing such queueing models. Transient solutions for the performance characteristics of model namely queue length distribution, busy period distribution and waiting time distribution are derived for the model. Mean dependence rate η > 0, between arrival and service process has an influence on the system behavior of the model. The effect of this parameter η is studied on all the three distributions.