On the Application of Mean Value Analysis Without the Normalization Constant in the Closed Queuing Networks

Abstract

An example of closed queue network could be view when patients arrive at a doctor’s office to update their medical records, then it’s off to the nurse’s station for various measurements like weight, blood pressure, and so on. The next stop is generally to queue (i.e., wait patiently) for one of the doctors to arrive and begin the consultation and examination. Perhaps it may be necessary to have some X-rays taken, an ultrasound may be called for, and so on. After these procedures have been completed, it may be necessary to talk with the doctor once again. The final center through which the patient must pass is always the billing office. In this work, multiple-node” system in which a customer requires service at more than one node, which may be viewed as a network of nodes, and each node is a service center having storage room for queues to form and perhaps with multiple servers to handle customer requests is investigated in order to provide some insight into the performance measure analysis. Our quest is to exempt the normalization constant in the computation of performance measure in the closed queueing network. The arrival properties and Little’s law are use with the help of some existing equations and formulas in queueing network. Performance measures, such as Mean number of customers, response time, throughput, and marginal probability distribution are obtained for central server and load dependent server closed queuing networks for nodes 4 and 5, and also for k = 3 and k = 10.