Queues with Redundancy: Is Waiting in Multiple Lines Fair?

56 Pages Posted: 3 Sep 2016 Last revised: 24 Aug 2017

See all articles by Leela Nageswaran

Leela Nageswaran

University of Washington - Michael G. Foster School of Business

Alan Andrew Scheller-Wolf

Carnegie Mellon University

Date Written: August 23, 2017

Abstract

In a service system, a redundant customer is one who may join multiple queues simultaneously and is "served" when any one of her copies completes service; systems with redundant customers range from multiple listing for organ transplants to supermarkets with multiple checkout lines. By considering two queues serving two classes of customers, one of which is redundant, our model provides fundamental insights on fairness, optimal queue-joining policies, and the value of information in such systems, from the non-redundant customers' perspective. Specifically, we prove that non-redundant customers forming independent Poisson streams to each queue actually benefit under redundancy of the other class compared to when the other class joins the shortest queue (JSQ) if the queues are symmetric (i.e., in this case redundancy is fair); however, there are situations where they are worse off if the queues are asymmetric. In this latter case redundancy may be seen as unfair. We also prove that JSQ does not always result in the lowest delay for a non-redundant customer if complete system state information (including which customers are redundant) is available, but that JSQ is optimal if only queue length information is observable. We extend several of our results to include unequal service rates and customer abandonments, and to systems with more than two servers.

Keywords: redundancy, optimal policy, multiple listing, fairness

Suggested Citation

Nageswaran, Leela and Scheller-Wolf, Alan Andrew, Queues with Redundancy: Is Waiting in Multiple Lines Fair? (August 23, 2017). Available at SSRN: https://ssrn.com/abstract=2833549 or http://dx.doi.org/10.2139/ssrn.2833549

Leela Nageswaran (Contact Author)

University of Washington - Michael G. Foster School of Business

Seattle, WA 98195-3226
United States

Alan Andrew Scheller-Wolf

Carnegie Mellon University ( email )

Pittsburgh, PA 15213-3890
United States

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