Compensating for Failures with Flexible Servers

• Published in: Operations research Vol. 55; no. 4; pp. 753 - 768
• Main Authors: Andradottir, Sigrun, Ayhan, Hayriye, Down, Douglas G
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.07.2007; Institute for Operations Research and the Management Sciences
• Subjects: Applied sciences; Assembly lines; Carrying costs; Evaluation; Exact sciences and technology; File servers; flexible manufacturing; Flexible manufacturing systems; Inventory control, production control. Distribution; Learning models (Stochastic processes); line balancing; Linear programming; Machinery; manufacturing; Markov analysis; Markov processes; Network servers; networks; Operational research and scientific management; Operational research. Management science; Optimal solutions; optimization; Production scheduling; productivity; Queueing networks; queues; Queuing theory; Queuing theory. Traffic theory; Scheduling; Servers; Stochastic models; Studies; United States; Markov process; optimization; manufacturing: performance; Round robin test; Dynamical system; Queueing network; Flexibility; Modeling; Optimization; Bounded solution; Network servers; line balancing; Queue; Productivity; Balancing; Probabilistic approach; Rupture; Linear programming; Routing; Scheduling; productivity; production/scheduling: flexible manufacturing; Failures; Production management; Service time; Flexible manufacturing system; queues: networks
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1070.0437

We consider the problem of maximizing capacity in a queueing network with flexible servers, where the classes and servers are subject to failure. We assume that the interarrival and service times are independent and identically distributed, that routing is probabilistic, and that the failure state of the system can be described by a Markov process that is independent of the other system dynamics. We find that the maximal capacity is tightly bounded by the solution of a linear programming problem and that the solution of this problem can be used to construct timed, generalized round-robin policies that approach the maximal capacity arbitrarily closely. We then give a series of structural results for our policies, including identifying when server flexibility can completely compensate for failures and when the implementation of our policies can be simplified. We conclude with a numerical example that illustrates some of the developed insights.