Forked queueing model with load dependent service rate and bulk arrivals

In this paper a forked two‐node tandem queueing model with load dependent service rates having bulk arrivals is introduced and analysed under transient and 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 analysed. The sensitivity analysis of a model reveals that the bulk size distribution parameters has 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. A comparative study of the model with respect to equilibrium and transient conditions reveal that the time has significant influence on the performance measures. This model also includes some of the earlier models as particular cases for specific values of the parameters.