Dynamic Control of Unreliable Flexible Servers : The 'W' Network and Beyond

Assigning partially flexible resources (servers) effectively to various jobs (customers or products) in real-time is a fundamental problem in many applications such as service centers, manufacturing systems, and communication networks. Although the potential benefits of using flexible servers to improve the performance of such systems is generally acknowledged, policies for controlling such networks in real-time to extract this potential benefit are not well understood. We address this problem in a general framework where servers are heterogeneous and also subject to stochastic disruptions. We consider the average holding cost as the performance criterion, and first analyze parallel queueing systems with general structures. To gain more insights, we then focus on a structure with two servers and three customer classes forming a "W." In this structure, servers are trained to serve a shared task in addition to their fixed (specialized) task. We find that the "W" design is highly ecient; it requires only a small amount of cross-training, but performs almost as well as a fully cross-trained system. We then show that (even allowing disruptions) a version of the cµ rule, which prioritizes serving the "fixed task before the shared," is optimal under some conditions. However, our results show that, in general, the optimal policy is complex, and not well-structured for implementation in practice. Hence, we propose a powerful and yet very simple policy to control the servers in parallel queueing systems. This new heuristic (which can be implemented in any parallel queueing system) eectively combines the intuition underlying two widely used policies: (1) the load balancing objective in serving the Longest Queue (LQ), and (2) the greedy cost minimization emphasis of the cµ rule. Our proposed control policy, termed as "LEWC," defines a simple and intuitive measure of workload costs and assigns each server to the queue with the Largest Expected Workload Cost (LEWC) among its skill set. Our extensive numerical tests show that the proposed policy performs well in comparison with three key policies: optimal, cµ and LQ. LEWC is also a very robust policy which makes it suitable for strategic design purposes