Service Scheduling for Random Requests with Fixed Waiting Costs

TL;DR

This paper investigates optimal service scheduling in a stochastic environment with fixed waiting costs, characterizing policies and equilibria in complex, state-dependent, quadratic cost systems.

Contribution

It introduces a novel analysis of scheduling with fixed waiting costs, deriving optimal policies and Nash equilibria in a complex, state-dependent control setting.

Findings

Characterized optimal policies for the scheduling problem.

Derived Nash equilibrium for the game-theoretic setting.

Analyzed the impact of fixed waiting costs on system performance.

Abstract

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.