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On Queue-Length Information when Customers Travel to a Queue

Authors: Refael Hassin; Ricky Roet-Green;

On Queue-Length Information when Customers Travel to a Queue

Abstract

Problem definition: We consider a service system in which customers must travel to the queue to be served. In our base model, customers observe the queue length and then decide whether to travel. We also consider alternative information models and investigate how the availability of queue-length information affects customer-equilibrium strategies, throughput, and social welfare. Academic/practical relevance: A common assumption in queueing models is that once a customer decides to join the queue, joining is instantaneous. This assumption does not fit real-life settings, where customers possess online information about the current wait time at the service, but while traveling to the service, its queue length may change. Motivated by this realistic setting, we study how queue-length information prior to traveling affects customers’ decision to travel. Methodology: We prove that a symmetric equilibrium exists in our base model. We perform the calculation numerically as a result of the model complexity, which is due to the fact that the arrival rate to the traveling queue depends on the current state of the service queue, and vice versa. The alternative models are tractable, and we present their analytical solution. Results: When customers can observe the service-queue length prior to traveling, their probability of traveling is monotonically nonincreasing with the observed queue length. We find that customers may adopt a generalized mixed-threshold equilibrium strategy: Travel when observing short queue lengths, avoid traveling when observing long queue lengths, and mix between traveling and not traveling when observing intermediate queue lengths, with a decreasing probability of traveling. Managerial implications: Our results imply that when system congestion is high, the provider can increase throughput by disclosing the queue-length information, whereas at low congestion, the provider benefits from concealing the information. With respect to social welfare, queue-length information prior to departure is beneficial when congestion is at intermediate to high levels and yields the same social welfare otherwise.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
47
Top 10%
Top 10%
Top 1%
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