Optimal routing in two-queue polling systems

TL;DR

This paper analyzes optimal routing policies in a two-queue polling system with exponential service times, focusing on minimizing waiting costs under different information scenarios and proposing new algorithms and conjectures for optimal policies.

Contribution

It introduces a new iterative algorithm for determining individually optimal routing policies and conjectures a linear switching curve as socially optimal, proving it for the fluid model.

Findings

Developed an iterative algorithm for individual optimal policies.

Proposed a conjecture that a linear switching curve is socially optimal.

Proved the linear switching curve is optimal in the fluid model.

Abstract

We consider a polling system with two queues, exhaustive service, no switch-over times and exponential service times. The waiting cost depends on the position of the queue relative to the server: It costs a customer c per time unit to wait in the busy queue (where the server is) and d per time unit in the idle queue (where no server is). Customers arrive according to a Poisson process. We study the control problem of how arrivals should be routed to the two queues in order to minimize expected waiting costs and characterize individually and socially optimal routing policies under three scenarios of available information at decision epochs: no, partial and complete information. In the complete information case, we develop a new iterative algorithm to determine individually optimal policies, and show that such policies can be described by a switching curve. We conjecture that a linear switching curve is socially optimal, and prove that this policy is indeed optimal for the fluid version of the two-queue polling system.