Equilibrium strategies in an M/M/1 queue with setup times and a single vacation policy

We consider equilibrium strategies in an Markovian queue with setup times and a single vacation policy. Arriving customers decide either to enter the system or to balk based on their desire for service and their unwillingness for waiting. We derive equilibrium strategies for both cases of fully observable queue and fully unobservable queue. Then, for fully unobservable queue, we consider socially optimal strategy and illustrate the effects of several parameters on equilibrium strategy and socially optimal balking strategy using numerical examples.