RESIDUAL SERVICE TIME BASED ANALYSIS OF MULTI-CLASS MULTI-SERVER PRIORITY . QUEUING SYSTEMS

Abstract

ABSTRACT In this research, Multi-Class Multi-Server Priority Queuing Systems. service times for all priority classes are assumed to be identically and exponentially distributed. This assumption led to the possibility of extending the analysis of non- preemptive priority queuing systems to the multiple servers case (similarly to multiple communication channels). ' The extension is based on the developed fomiula for the residual service time R. This on its part, was achieved by utilizing the analysis of M/M/m systems in which the service times are identically and exponentially distributed, combining this with the analysis of non-preemptive queuing systems for single server systems based on M/G/l system. Making all necessary modifications for the system to fit the multiple servers case, the necessary mathematical analysis and derivations were given. The Preemptive Priority queues with Multiple Servers and Multiple priority classes were treated in the same manner. Here the assumption that the service times - for all priority classes — are identically and exponentially distributed _is put forward. Again, a formula for the residual service time is developed and utilized in calculating the average customer waiting time and other related parameters. In the light of this assumption the author presents the relations necessary to derive an expression for the mean residual service time which is then used in developing a mathematical model for the analysis of preemptive priority queues with multiple servers and multiple priority classes. The research includes some comparative studies between the proposed model (multi-class multi-servers priority queuing systems) and some prior related works.