Shadow-Routing Based Control of Flexible Multiserver Pools in Overload

We consider a general parallel server system model with multiple customer classes and several flexible multiserver pools, in the many-server asymptotic regime where the input rates and server pool sizes are scaled up linearly to infinity. Service of a customer brings a constant reward, which depends on its class. The objective is to maximize the long-run reward rate. Our primary focus is on overloaded systems. Unlike in the case when the system is non-overloaded, where the main decision is how to allocate resources to incoming customers, in this case it is also crucial to determine which customers will be admitted to the system. We propose a real-time, parsimonious, robust routing policy, SHADOW-RM, which does not require the knowledge of customer input rates and does not solve any optimization problem explicitly, and prove its asymptotic optimality. Then, by combining SHADOW-RM with another policy, SHADOW-LB, proposed in Stolyar and Tezcan (2010) for systems that are not overloaded, we suggest policy SHADOW-TANDEM, which automatically and seamlessly detects overload and reduces to one of the schemes, SHADOW-RM or SHADOW-LB, accordingly. Extensive simulations demonstrate a remarkably good performance of proposed policies.