STEADY STATE SOLUTION OF INTERDEPENDENT FORKED QUEUE OF BULK ARRIVALS WITH LOAD DEPENDENT SERVICE RATE

Abstract

In this paper a forked two node tandem queueing model with load dependent service rates having bulk arrivals is introduced and analyzed under equilibrium conditions. The system performance measures like probability of emptiness of the system, the probabilities of emptiness of marginal queues, the average number of customers in each queue, the average waiting time of the customer in each queue, the throughput of each node, the utility of servers, and the variance of the number of customers in each queue are derived and analyzed. The sensitivity analysis of a model reveals that the bulk size distribution parameters have a significant influence on system performance measures. Through numerical studies, it is observed that the load dependent service rates can reduce the congestion in queues and mean delay. This model also includes some of the earlier models as particular cases for specific values of the parameters.