Understanding the marginal impact of customer flexibility

Authors:
Osman T. Akgun;Rhonda Righter;Ronald Wolff
Affiliations:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA 94720;Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA 94720;Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA 94720
Venue:
Queueing Systems: Theory and Applications
Year:
2012

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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.