Equilibrium analysis of observable express service with customer choice

Zhou, Jiaqi; Ryzhov, Ilya O.

doi:10.1007/s11134-021-09720-z

Cited by 2 publications

(1 citation statement)

References 34 publications

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“…In the following, we make a brief review on the progress of these methods. [15] In 1953, Kendall used the embedded chain method to study queuing theory. And for the first time, symbols composed of letters were used to represent queuing system, laying a theoretical foundation for the development of queuing theory.…”

Section: Introductionmentioning

confidence: 99%

Research on M/M/1/WV Queuing System with Single Working Vacation

Huang,

2024

Preprint

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In this paper, we discuss the applications of queuing theory in working vacation state and normal busy state, then establish a M/M/1 queuing model with impatient customers and single working vacation. The model provides theoretical guidance for practical problems such as library reservation system. In a queuing system, the customers' arrival follows Poisson distribution, while the service time is a negative exponential distribution. We consider the situation that there is a stationary distribution when the queuing system reaches steady state at any time. Using the constant variation method of differential equation (Bernoulli equation) to solve the stationary equation, the average queue length in two states of probability generation function is obtained. Finally, we improve the model to acquire Q matrix of the single working vacation model, which can be used to calculate the average queue staying time of the system in two states. By construction and improvement of M/M/1/WV queuing models, ingenious proofs of three important theorems are given accordingly, which will definitely make a difference in many practical problems.

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Section: Introductionmentioning

confidence: 99%

Research on M/M/1/WV Queuing System with Single Working Vacation

Huang,

2024

Preprint

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Demand Equilibria in Spatial Service Systems

Gunnar Carlsson,

Peng,

Ryzhov

2024

M&SOM

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Problem definition: A service is offered at certain locations (“facilities”) in a geographical region. Customers can appear anywhere in the region, and each customer chooses a facility based on travel distance as well as expected waiting time. Customer decisions affect waiting times by increasing the load on a facility, and thus, they impact other customers’ decisions. The service provider can also influence service quality by adjusting service rates at each facility. Methodology/results: Using a combination of queueing models and computational geometry, we characterize demand equilibria in such spatial service systems. An equilibrium can be visualized as a partition of the region into service zones that form as a result of customer decisions. Service rates can be set in a way that achieves the best-possible social welfare purely through decentralized customer behavior. Managerial implications: We provide techniques for computing and visualizing demand equilibria as well as calculating optimal service rates. Our analytical and numerical results indicate that in many situations, resource allocation is a far more significant source of inefficiency than decentralized behavior. Funding: J. G. Carlsson was funded by the METRANS Transportation Consortium [Grant NCST-USC-RR-24-12] and the Office of Naval Research [Grant N00014-24-1-2277-P00001]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0434 .

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Equilibrium analysis of observable express service with customer choice

Cited by 2 publications

References 34 publications

Research on M/M/1/WV Queuing System with Single Working Vacation

Research on M/M/1/WV Queuing System with Single Working Vacation

Demand Equilibria in Spatial Service Systems

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