Service scheduling for random requests with fixed waiting costs

We study service scheduling problems in a slotted system in which agents arrive with service requests according to a Bernoulli process and have to leave within two slots after arrival, service costs are quadratic in service rates, and there is also a waiting cost. We consider fixed waiting costs. We frame the problem as an average cost Markov decision process. While the studied system is a linear system with quadratic costs, it has state dependent control. Moreover, it also possesses a non-standard cost function structure rendering the optimization problem complex. Here, we characterize the optimal policy. We also consider a system in which the agents make scheduling decisions for their respective service requests keeping their own cost in view. We frame this scheduling problem as a stochastic game. Here, we provide Nash equilibrium.