Optimal vacation period with cost analysis of an interdependence fuzzy queue model to a communication system

Mathematical study of queue model provides the basic frame work in communication system as there is a close resemblance between queue networks and communication systems. This paper deals with the application of an interdependence fuzzy queue model to a communication system which have the voice packetized statistical multiplexing. The objective of the paper is intended to review the state of affairs of analytical methods, queuing analytical techniques essential to modeling of communication system. By approximating the arrival of packets, transmission and the covariance between them under a bi-variate Poisson process, the performance of statistical multiplexing is measured. The steady state solution and system characteristics are derived. The model mechanism reduces the idle time of transmitter and enhances the system utilization capacity. A unified treatment of buffer storage over flow problem has been discussed as an application example in which we call attention to the analogy between buffer problem and waiting time.

The ratio of the cost associated with shifting the transmitter from voice buffer to data buffer and the cost associated with waiting time of voice packets is compared with idle time of transmitter in consideration of the dependence between arrival of messages and service transmission. The vacation period has been calculated with respect to cost ratio and change in interdependence between arrival of packets and number of transmission completion.