Service scheduling for random requests with fixed waiting costs

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