Multi Node Tandem Queuing Model with Bulk Arrivals Having Geometric Arrival Distribution

Abstract

In this paper a K-node forked queuing model with load dependent service rates is analysed. Here it is assumed that the customers arrive to the first queue in batches and wait for service. After getting service at first service station with some probability they may 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. The influence of Geometrically distributed bulk arrivals on this queuing model is studied. Sensitivity analysis of the system behaviour with regards to the arrival rates and load dependent service distribution parameters is carried out. The influence of these parameters on system performance measures such as average number of customers, waiting time of customer, variation of number of customers in each queue, throughput of each service station, utilization of each server are derived explicitly when arrivals follow a Geometric distribution. Simulations are carried out to illustrate the result.