Optimal decentralized queuing system with diversion: Using incentives to influence behavior

Abstract

We are interested in the modeling of people's queueing behavior and influencing this behavior through the use of incentives. This setting is motivated by applications wherein a customer may choose to postpone his entry into a queue by accepting to take a so-called diversion, where this diversion is in some way more pleasant than waiting in the queue. The goal is thus to determine the minimal incentive to be provided by the queue organizing agent to entice users to take the diversion, to an extent sufficient to reduce the overall waiting time of the queue. We propose a formulation for this problem using stochastic dynamic programming. The goal is to determine the optimal strategy in terms of the incentive and service level so as to reduce overall waiting time while limiting the cost borne by organizing agent. We further propose a decentralized version of the model where the service agent and the organizing agent do not wish to share all the state information. We show that it is possible to ensure that the solution of the decentralized problem is as efficient as that of the centralized system through the use of transfer contracts between the two agents.