On parallel and series non homogeneous bulk arrival queueing model

Abstract

Queueing models create lot of importance due to their ready applicability. Much work has reported in literature regarding queueing models with homogeneous Poisson arrivals. But in many practical situations arising at places like transportation, communication networks, production processes, etc., the arrivals are non homogeneous and time dependent. Hence, in this paper we develop and analyze a queueing model with non homogeneous (time dependent) bulk arrivals under parallel and series configuration. Using the difference differential equations the joint probability density function of the number of customers in each queue is obtained. The performance of the model is evaluated by deriving the explicit expressions of the system characteristics like the probability of the system emptiness, average number of customers in each queue, the mean waiting time of the customer, the throughput of the nodes, etc. The sensitivity analysis of the model revealed that the bulk size distribution parameters and non homogeneous arrivals have significant influence on the system performance measures. The utility of the model in congestion control is demonstrated through a numerical illustration.