Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment

We study the optimal demand allocation policies to induce high service capacity and achieve minimum expected sojourn times in equilibrium in a queueing system with multiple strategic servers. We propose the mixed threshold allocation policy as an optimal state-dependent policy that induces optimal service capacity from strategic servers. Compensation to the server can be paid at customer allocation or upon job completion. Our study focuses on the use of a multiple-server mixed threshold allocation policy to replicate the demand of a given state-independent policy to achieve a symmetric equilibrium with lower expected sojourn time. The results indicate that, under both payment schemes, for any given multiple-server state-independent policy, there exists a multiple-server threshold policy that produces identical demand allocation and Nash equilibrium (if any). Moreover, the policy can be designed to minimize the expected sojourn time at a symmetric equilibrium. Further-more, under the payment-at-allocation scheme, our results, combining with existing results on the optimality of the multiple-server linear allocation policy, show that the mixed threshold policy can achieve the maximum feasible service capacity and thus the minimum feasible equilibrium expected sojourn time. Hence, our results agree with previous two-server results and affirm that a trade-off between incentives and efficiency need not exist in the case of multiple servers.published_or_final_versio

Optimality of the Fastest Available Server Policy

We give sufficient conditions under which a policy that assigns customers to the Fastest Available Server, labelled FAS, is optimal in queueing models with multiple independent Poisson arrival processes and heterogeneous parallel exponential servers. The criterion is to minimize the long-run average cost per unit time. We obtain results for loss models and for queueing systems with a finite-capacity or infinite-capacity buffer under a head-of-the-line priority scheme. The results depend on cost assumptions, so we analyze the robustness of the cost structure and present counter-examples to illustrate when FAS is not optimal

On the incomplete results for the heterogeneous server problem

In this article, we show that the arguments in Rykov [9] on the optimality of a threshold routing policy when there are more than two heterogeneous servers are incomplete. © Springer Science + Business Media, LLC 2006.link_to_subscribed_fulltex