Transient analysis of K-node tandem queuing model with load dependent service rates

Abstract

This paper deals with the development and analysis of K-node series and parallel queueing model with load dependent service rates. Here it is assumed that the customers arrive to the initial queue and waiting line for service. After completing the service at first service station they may join one of the (K-1) queues which are parallel and connected to first queue in series. After getting service from the service station they leave the system. Here it is assumed that the service rates in each service station are dependent on number of customers in the queue connected to it .The arrival and service completions in each queue are assumed to follow Poisson processes. Using difference-differential equations the joint probability function of number of customers in each queue are derived. The system performance measures such as average number of customers in each queue, throughput of each service station, the probability of idleness of each server, the waiting time of customer in each queue are derived explicitly. The sensitivity of the model with respect to parameters are analysed through numerical illustration. It is observed that the state dependent service rates has significant influence on performance measures. This model also includes the earlier models as particular cases for specific values of the parameters. This model is useful in analysing the communication networks, transportation systems, production processes and cargo handling.