Abstract:

This paper studies customers' equilibrium joining strategy in an M/M/1 constant retrial queue with an unreliable server, where the server may break down under the busy and idle states. In this system, there is no waiting space in front of the server. If a customer finds the server idle upon arrival, he occupies the server immediately. Otherwise, if the server is found busy, the customer can choose to leave a message so that the server can search for customers in the retrial orbit who have left messages before in order to serve them when it is free. Once the server breaks down, the customer being served will be squeezed out of the system and new customers are not allowed to join again. According to the different information provided for customers, this paper investigates the system characteristics at steady state and customers' equilibrium joining strategies based on a reward-cost function. Further, the server's revenue and social welfare functions are established. Through comparisons, it is found revealing the queue length may not bring a greater revenue for the server or a larger social welfare.

Key words: retrial queue, breakdown, equilibrium joining strategy, server's revenue, social welfare