Abstract
We study the marginal impact of customer flexibility in service systems. We consider a queueing system with multiple parallel servers, in which a proportion of customers are flexible and can go to any server, while the remainder require service at a particular server. We show that the stationary expected waiting time is decreasing and convex in the proportion of flexible customers. We also show, for a related Inventory Model, in which servers are never idle and can build up inventory, that convexity holds in a strong sample-path sense. Our results reinforce the idea that a little flexibility goes a long way.
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Akgun, O.T., Righter, R. & Wolff, R. Understanding the marginal impact of customer flexibility. Queueing Syst 71, 5–23 (2012). https://doi.org/10.1007/s11134-011-9271-9
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DOI: https://doi.org/10.1007/s11134-011-9271-9