Strategic behavior in the partially observable Markovian queues with partial breakdowns

Yu, Senlin; Liu, Zaiming; Wu, Jinbiao

doi:10.1016/j.orl.2017.07.007

Cited by 13 publications

(5 citation statements)

References 5 publications

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“…Moreover, Li et al [5] obtained the equilibrium balking strategies and socially optimal behavior in an M/M/1 queue with partial breakdowns and immediate repairs, where the systems can continue the service at a lower rate during the breakdowns. Yu et al [16] compensated the game analysis in [5] by studying the corresponding partially observable cases. Xu and Xu [12] further discussed the individual Nash equilibrium in an M/M/1 queue with partial failures and delayed repairs.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium analysis of the fluid model with two types of parallel customers and incomplete fault

Zhang,

Xu,

Zhao

et al. 2024

Prob. Eng. Inf. Sci.

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This article considers the individual equilibrium behavior and socially optimal strategy in a fluid queue with two types of parallel customers and incomplete fault. Assume that the working state and the incomplete fault state appear alternately in the buffer. Different from the linear revenue and expenditure structure, an exponential utility function can be constructed to obtain the equilibrium balking thresholds in the fully observable case. Besides, the steady-state probability distribution and the corresponding expected social benefit are derived based on the renewal process and the standard theory of linear ordinary differential equations. Furthermore, a reasonable entrance fee strategy is discussed under the condition that the fluid accepts the globally optimal strategies. Finally, the effects of the diverse system parameters on the entrance fee and the expected social benefit are explicitly illustrated by numerical comparisons.

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Section: Introductionmentioning

confidence: 99%

Equilibrium analysis of the fluid model with two types of parallel customers and incomplete fault

Zhang,

Xu,

Zhao

et al. 2024

Prob. Eng. Inf. Sci.

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“…Two cases are considered: totally observable and totally unobservable. This work [16] was extended by Yu et al (2017) [29] to the almost observable and almost unobservable cases. Boudali and Economou (2012) [3] studied the behavior of customers who decide whether to join or not a Markovian queueing system with catastrophes.…”

Section: Introductionmentioning

confidence: 99%

The service pricing strategies and the strategic behavior of customers in an unobservable Markovian queue with unreliable server

2022

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A Stackelberg game is used to study the service pricing and the strategic behavior of customers in an unreliable and totally unobservable M/M/1 queue under a reward-cost structure. At the first stage, the server manager, acting as a leader, chooses a service price and, at the second stage, a customer, arriving at the system and acting as a follower, chooses to join the system or an outside opportunity, knowing only the service price imposed by the server manager and the system parameters. We show that the constructed game admits an equilibrium and we give explicit forms of server manager and customers equilibrium behavioral strategies. The results of the proposed model show that the assumption that customers are risk-neutral is fundamental for the standard approach usually used. Moreover, we determine the socially optimal price that maximizes the social welfare and we compare it to the Stackelberg equilibrium. We illustrate, by numerical examples, the effect of some system parameters on the equilibrium service price and the revenue of the server manager.

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“…Sun et al [15,16] studied customers' equilibrium and socially optimal balking strategies in observable and unobservable queues with several types of setup/closedown policies, respectively. More research in this area can be referred to Guo and Hassin [6,7], Tian et al [22], Yu et al [25,26], Liu and Wang [11], Doo [8], and references therein.…”

Section: Introductionmentioning

confidence: 99%

On Markovian Queues With Single Working Vacation and Bernoulli Interruptions

Tian¹,

Zhang

2021

Prob. Eng. Inf. Sci.

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This paper considers the customers’ equilibrium and socially optimal joining–balking behavior in a single-server Markovian queue with a single working vacation and Bernoulli interruptions. The model is motivated by practical service systems where the service rate can be adjusted according to whether or not the system is empty. Specifically, we focus on a single-server queue in which the server's service rate is reduced from a regular to a lower one when the system becomes empty. This lower rate period is called a working vacation for the server which may represent that part of the service facility is under a maintenance process or works on other non-queueing job, or simply for saving the energy (for a machine server case). In this paper, we assume that the working vacation period is terminated after a random period or with probability p after serving a customer in a non-empty system. Such a system is called a queue with single working vacation and Bernoulli interruptions. Customers are strategic and can make choice of joining or balking based on different levels of system information. We consider four scenarios: fully observable, almost observable, almost unobservable, and fully unobservable queue cases. Under a reward-cost structure, we analyze the customer's equilibrium and social-optimal strategies. In addition, the effects of system parameters on optimal strategies are illustrated by numerical examples.

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Strategic behavior in the partially observable Markovian queues with partial breakdowns

Cited by 13 publications

References 5 publications

Equilibrium analysis of the fluid model with two types of parallel customers and incomplete fault

Equilibrium analysis of the fluid model with two types of parallel customers and incomplete fault

The service pricing strategies and the strategic behavior of customers in an unobservable Markovian queue with unreliable server

On Markovian Queues With Single Working Vacation and Bernoulli Interruptions

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