M/G/1 Queue with Self Generating Priorities
by
A. Krishnamoorthy
Department of Mathematics, Cochin Univ. of Science & Tech., Kochi 682022, India
Coauthors: P.V. Ushakumari (Department of Mathematics, Cochin Univ. of Science and Tech., Kochi 682022 INDIA), B. Krishnakumar (Department of Mathematics, Anna University, Chennai 600025, India), N. Raju (Department of Statistics, University of Calicut, Calicut University P.O. 673635, India)

In this paper we consider a single server queue to which customers arrive according to a homogeneous Poisson process. Service times of customers are independent and identically distributed random variables following an arbitrary distribution. While in the system, customers generate into priority units which occurs at exponentially distributed time intervals. The intensity of priority generation depends on the number of waiting customers. At a time at most one priority unit can wait in the queue. Any unit that generates into priority at the time when one is already waiting will leave the system in search of service else where. The service discipline is preemptive priority. That is if the unit in service is NOT a priority and if a waiting customer generates into priority the unit undergoing service is preempted to provide service for the one that generated into priority. However, if the one in service is already a priority unit, any priority generating unit will have to wait for the present unit to complete its service. The model under discussion is seen to occur at several service stations, especially in Hospitals, Telegraph office and communications in general and so on. The analysis is by the use of supplementary variable technique. We consider a two dimensional Continuous time Markov Chain whose first coordinate represents the number in the system, with the second one representing the type of unit in service- the symbol 0 stands for nonpriority unit in service and 1 represents priority unit in service. We derive several system state characteristics, in addition to obtaining system state probabilities in the long run.

Date received: March 1, 2003