St. Josephs College Irinjalakuda

ON A THREE-SERVER QUEUE WITH CONSULTATION BY MAIN SERVER CONTROLLED BY AN UPPER BOUND ON NUMBER OF INTERRUPTIONS

This paper analyses a queueing model with three servers, namely a main server and two identical regular servers. The main server not only serves customers but also provides consultation to the regular servers with a preemptive priority over customers. The customer sat the main server undergo interruptions

during their service. The consultations are limited by an upper bound on the number of interruptions to a customer at the main server. The arrivals to the system and requirement of consultation follow independent Poisson processes. The service times at the main server and the regular servers are assumed to follow mutually independent phase type distributions. The stability of the system is established. Some performance measures are studied numerically.