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This paper studies a queueing system with horizontally differentiated servers. Each customer decides whether to join the queues of multiple servers simultaneously (“multi-list”), join the queue exclusively served by her preferred server, or balk. Such a multi-listing system contrasts a single-listing system, which allows for server choice but prohibits multi-listing, and a pooling system, which precludes server choice by requiring every joining customer to multi-list. We build queueing-game-theoretic models of the three systems above and compare their throughput and social welfare in equilibrium. Between a single-listing system and a pooling system, the former better facilitates matching between customers and servers, whereas the latter excels at reducing waiting time through load balancing. Accordingly, we find that either system can outperform the other in either throughput or social welfare. One may expect the multi-listing system to beat both single-listing and pooling as it marries the matching value of the former with the operational advantage of the latter. We find that multi-listing indeed outperforms pooling in both throughput and social welfare. While multi-listing also achieves higher throughput than single-listing, it can strikingly underperform single-listing in social welfare. In contrast to the equilibrium, the socially optimal routing policy of the multi-listing system can be asymmetric across the servers even when the servers are ex-ante symmetric. Relative to the social optimum, customers under-choose multi-listing in equilibrium when the congestion level is low but may over-multi-list otherwise. The social planner can charge nonnegative, asymmetric prices to restore efficiency in equilibrium. Our paper provides design guidance for the configuration of multi-server service systems.

This is a joint work with Zhou Chen and Luyi Yang.