Optimal balking strategies for high-priority customers in M/G/1 queues with 2 classes of customers

Abstract

This paper studies the optimal balking strategies of customers with a higher priority in the single-server M/G/1 queue, where there are two classes of customers who have different priorities. When a low-priority customer is being served, the high-priority customer joins in the system and will be served immediately while the low-priority customer will go back to the head of the queue of its class. Upon arrival, the high-priority customers decide for themselves whether to join or balk based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness to wait. We identify equilibrium strategies and socially optimal strategies under one information assumption. The high-priority customers make individual decisions in a unobservable queue. By deriving and solving a set of system equations, we obtain equilibrium strategies and socially optimal strategies. Finally we illustrate our results via numerical experiments.