The on-line transfer rule for queueing with arrivals

Abstract

We consider the queueing problem with arrivals, or the arrival queueing problem, where agents arrive at different (time) slots to process their jobs in a service facility and each job requires the same amount of processing time which is normalized to one. Each agent has one job to process and the facility can process only one job at each slot. We introduce a rule for the arrival queueing problem, which we call the on-line transfer rule, by adapting the minimal transfer rule of the static queueing problem (Maniquet, 2003) but incorporating the time span which each agent observes. We provide axiomatic characterizations of the on-line transfer rule by imposing the axioms of efficiency, Pareto indifference, equal treatment of equals, independence of larger costs, and consistency from later-arrived-later-served agents. We also introduce and characterize an alternative rule for the arrival queueing problem which adapts the maximal transfer rule of the static queueing problem (Chun, 2006a).