Multi Node Tandem Queuing Model with Binomial Bulk Size Distribution Having Load Dependent Service

Abstract

In this article we study a multi node tandem queuing model consisting of K-nodes in which the customers arriving in batches to the first queue and after receiving service they will be directed with some node specific probability to join any one of the (K-1) parallel queues which are connected to first queue in series and exit from the system after getting service. It is assumed that the arrival and service completions follow Poisson processes and service rates depend on number of customers in the queue connected to it. Here the bulk arrivals are assumed to be Binomially distributed. Using difference differential equations the joint probability function is derived and performance measures such as average number of customers, waiting time of customer, throughput of each service station, utilization of each server, variance of number of customers in each queue are derived explicitly. A numerical illustration is provided to understand the theoretical results. Sensitivity analysis of the system behavior with regards to the arrival rates and load dependent service distribution parameters is carried out. A comparison between transient and study state behavior is also done .