  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 are also waiting costs. We consider fixed waiting costs. We frame the
problems as average cost Markov decision processes. 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 in the case of fixed
waiting costs, rendering the optimization problem complex. Here, we
characterize 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 again consider fixed waiting costs and frame this scheduling
problem as a stochastic game. Here, we provide Nash equilibrium.
