Decentralized Control of a Stochastic Multi-Agent Queueing System

This paper concerns decentralized control of a multi-agent stochastic queueing system. The system consists of two agents, a pricing agent and a service agent. The pricing agent controls the arrival rate by dynamically setting the fee that is paid by customers who would like to receive service, while the service agent controls the rate at which customers in the system are processed. Each agent optimizes his/her own objective subject to a model which accurately specifies the component of the system that he/she is controlling but potentially mis-specifies the component that is controlled by the other agent. We are interested in optimizing the efficiency of the aggregate system when control decisions are made in this way. Decentralized agents are coordinated using transfer contracts, which define a price for occupying unit of buffer space in the system as a function of time and available capacity. Transfer contracts lead to cash transfers between agents whenever a customer enters or departs, and serve to modify each of their incentives. We characterize the contract that maximizes the efficiency of the aggregate system under decentralized control, and show that it achieves the efficiency of a centralized agent who jointly optimizes over pricing and service policies with an accurate model of the integrated system. We also show that optimal centralized efficiency is robust to mis-specification by each agent of the dynamics induced by the other in his/her model. An iterative decentralized algorithm for constructing the optimal contract and a proof of convergence is also presented.