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We consider the problem of customer equilibrium strategies in an M/M/1 queueunder dynamic service control. The service rate switches between a low and ahigh value depending on system congestion. Arriving customers do not observethe system state at the moment of arrival. We show that due to service ratevariation, the customer equilibrium strategy is not generally unique, andderive an upper bound on the number of possible equilibria. For the problem ofsocial welfare optimization, we numerically analyze the relationship betweenthe optimal arrival rate, which maximizes the overall welfare of the customers,and the equilibrium ones as a function of various parameter values. We finallyderive analytic solutions for the special case where the service rate switchoccurs when the queue ceases to be empty.

Customer Equilibrium and Optimal Strategies in an M/M/1 Queue with Dynamic Service Control