Control of systems with flexible multi-server pools: a shadow routing approach

• Published in: Queueing systems Vol. 66; no. 1; pp. 1 - 51
• Main Authors: Stolyar, Alexander L., Tezcan, Tolga
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.09.2010; Springer Nature B.V
• Subjects: Business and Management; Call centers; Computer Communication Networks; Control; Control algorithms; Customer services; Literature reviews; Load; Operations Research/Decision Theory; Optimization; Probability Theory and Stochastic Processes; Scheduling; Servers; Supply Chain Management; Systems stability; Systems Theory; Large flexible server pools; Halfin–Whitt regime; Many server asymptotics; 90B15; Routing and scheduling; 60J70; Queueing networks; Shadow routing; 60K25; Order-optimality; Diffusion limit
• ISSN: 0257-0130; 1572-9443
• DOI: 10.1007/s11134-010-9183-0

A general model with multiple input flows (classes) and several flexible multi-server pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queueing system. We study the behavior of our scheme in the Halfin–Whitt (or, QED) asymptotic regime, when server pool sizes and the input rates are scaled up simultaneously by a factor r growing to infinity, while keeping the system load within of its capacity. The main results are as follows. (i) We show that, in general, a system in a stationary regime has at least average queue lengths, even if the so called null-controllability (Atar et al., Ann. Appl. Probab. 16, 1764–1804, 2006 ) on a finite time interval is possible; strategies achieving this growth rate we call order-optimal . (ii) We show that some natural algorithms, such as MaxWeight , that guarantee stability, are not order-optimal. (iii) Under the complete resource pooling condition, we prove the diffusion limit of the arrival processes into server pools, under the Shadow routing. (We conjecture that result (iii) leads to order-optimality of the Shadow routing algorithm; a formal proof of this fact is an important subject of future work.) Simulation results demonstrate good performance and robustness of our scheme.