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Transient Analysis for a Queuing System with Impatient Customers and Its Applications to the Pricing Strategy of a Video Website

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  • Qihui Bu

    (School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China)

Abstract

In this paper, we consider a queuing system with impatient customers, which includes infinite servers and two types of customers. During the service process, Type-1 customers may leave the system or upgrade to be Type-2 customers due to their impatience. By solving the partial differential equations, we obtain the generating functions of the transient distribution of the queue length, and many stationary performance measures are further derived. Then, as an application, we formulate an expected profit function for a video website, and maximize it by determining the optimal pricing strategy. Finally, numerical examples are provided to demonstrate the impacts of parameters on the optimal website profit.

Suggested Citation

  • Qihui Bu, 2024. "Transient Analysis for a Queuing System with Impatient Customers and Its Applications to the Pricing Strategy of a Video Website," Mathematics, MDPI, vol. 12(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2030-:d:1425674
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    References listed on IDEAS

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    Cited by:

    1. Eimutis Valakevičius & Mindaugas Bražėnas & Tomas Ruzgas, 2025. "Comparison of Continuous-Time Partial Markov Chain Construction by Heuristic Algorithms for Purpose of Approximate Transient Analysis," Mathematics, MDPI, vol. 13(2), pages 1-19, January.
    2. Vinay Kumar & Neelesh Shankar Upadhye, 2025. "Modeling and simulation of first-come, first-served queueing system with impatient multiclass customers," Operational Research, Springer, vol. 25(1), pages 1-37, March.

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