WAITING TIME IN THE M/M/ FCFS NONPREEMPTIVE
PRIORITY QUEUE WITH IMPATIENT CUSTOMERS

Abstract. As a possible model for a service center with multiple servers and prioritized impatient customers, we study an M/M/ nonpreemptive priority (first-come, first-served within the same class) queueing system with impatient customers in the steady state. We analyze the waiting time for those customers who are served successfully and the time to abandonment for those customers who leave the system while waiting. Explicit formulas are given for the probabilities of service and abandonment as well as the mean and second moment of the waiting time for customers of each class. The distribution of the waiting time is derived only for customers of the highest priority class. Numerical examples are shown in order to demonstrate the feasibility of computation from theoretical formulas.

Received: June 28, 2014

AMS Subject Classification: 60K25, 68M20, 90B22

Key Words and Phrases: queue, waiting time, multiserver, nonpreemptive priority, impatient customers, abandonment

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