Last in line

Abstract

Queueing is a common praxis in banks, hospitals and transportation, just to name a few. One common performance metric is the mean sojourn time. However, humans experience waiting time in a more complex manner — they dislike being the last in line. We study queueing systems subject to such a cost structure. For the single M/G/1 queue, we derive the corresponding mean costs, value functions and admission costs, which are then applied to route customers to parallel servers.