Prediction of Two-Node Tandem Queue with Feedback Having State and Time Dependent Service Rates

Abstract

Queuing networks are current area of great research and application interest, in view of their increased applicability in - modelling manufacturing facilities and computer/communication networks, production and assembly lines, hospitals, transport systems, banks and so forth. The present paper develops and analyses a tandem queuing model having two nodes with feedback. Such type of model finds its application in many fields, e.g. telecommunication, inventory, hospitals, traffic control and so on. For example, in hospitals, a patient first visits the doctor and goes through a series of examinations, after which he revisits the doctor for medication. The inter-arrival time is exponentially distributed, whereas the service rate for each node depends on the aggregate of customers in the respective queues and thus follows non-homogeneous Poisson process. After constructing the difference –differential equations, and using PGF technique, we have obtained the joint probability distribution for queue size. Some key measures such as the “average number of customers in queue”, “utilization time of each queue”, “average waiting time in each queue” are computed.