Admission Control Policies in Loss Networks

Abstract

This article addresses the admission control of a loss queueing network, or shortly loss network, of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> parallel multiserver stations with no waiting rooms. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> classes of customers arrive at a Poisson rate and require an exponential service time with common mean. A customer can be served by any free server of a station in the set of stations determined by the class of the customer. Admission of a customer to a station brings different rewards that depend on customer class and the preference order of that station. Our objective is to find the optimal admission control policy that maximizes the average reward. We adopt a research strategy that evolves from simpler networks to more complicated ones. First, we consider a one-station <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -class loss network whose results form a fundamental basis for the analysis of more complicated networks. Second, we consider a two-station <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -class loss network for which we establish the existence of an optimal threshold admission policy. Finally, we consider a general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> -station <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -class loss network and propose an iterative approximation policy (IAP) and a mixed-integer linear programming model that is proven to compute an upper bound. We demonstrate the near-optimal performance of the proposed IAP and the tightness of the upper bound on several numerical instances motivated by real-life networks, such as healthcare emergency service networks and emergency call centers. Note to Practitioners—This article is mainly motivated by real-time scheduling of emergency service networks, such as emergency healthcare and telecommunication networks. In such networks, emergent demands need to be served promptly and are lost otherwise. They can be served by multiple hospitals/operator groups but have their own preferences. The decision maker has to decide dynamically whether to keep the capacity of a hospital/operator for its own customers to meet customer preference or serve the incoming demand to improve the resource utilization. We set the problem as the admission control of a multiclass multistation loss network, study the properties of the optimal policy, and propose an iterative approximation policy that is proven to be near-optimal for large-size loss networks. The proposed policy is found to improve by up to 16% and 52% the no-control policy admitting the customer to the most preferred available station and the no-overflow policy with admission to only the most preferred station, respectively. Managerial insights and extensions are also discussed.