Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation

Gao, Shan; Dong, Hanwu; Wang, Xianchao

doi:10.1007/s12351-018-0437-7

Cited by 14 publications

(6 citation statements)

References 26 publications

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“…Yang et al [29] considered an unreliable retrial queue with J optional vacations, where the server is subject to random breakdowns and repairs when he is working. Gao et al [13] treated an M/M/1 retrial queue with an unreliable server from the economic viewpoint.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Retrial Queue With Two-Type Breakdowns and Delayed Repairs

2020

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This paper studies an M/G/1 retrial queue with two types of breakdowns. When the server is idle, it is subject to breakdowns according to a Poisson process with rate δ and it cannot be repaired immediately. While when the server is busy, it may break down according to a Poisson process with rate θ and can be immediately repaired. Firstly, based on embedded Markov chain technique and probability generating function (PGF) method, we present the necessary and sufficient condition for the system to be stable and the PGF of the orbit size at the departure epochs. Secondly, we give the steady-state joint queue length distribution by supplementary variable method, and present some important performance measures and reliability indices. Thirdly, we provide the analysis of sojourn time of an arbitrary customer in the system when the system is in stable state. Finally, some numerical examples are presented to illustrate the effect of the some system parameters on important performance measures and reliability indices.

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Section: Introductionmentioning

confidence: 99%

Analysis of a Retrial Queue With Two-Type Breakdowns and Delayed Repairs

2020

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“…Bontali and Economou [1] considered equilibrium joining strategy for batch service queueing systems in unobservable and observable cases. Gao et al [6] dealt with an M/M/1 retrial queue with unreliable servers from an economic point of view. Do et al [2] studied M/M/1 retrial queues with working vacation and constant retrial rates and obtained customer equilibrium and socially optimal strategies for different information levels.…”

Section: Introductionmentioning

confidence: 99%

On a retrial queue with negative customers, passive breakdown, and delayed repairs

Han,

Tian,

et al. 2023

Prob. Eng. Inf. Sci.

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This paper studies an M/M/1 retrial queue with negative customers, passive breakdown, and delayed repairs. Assume that the breakdown behavior of the server during idle periods is different from that during busy periods. Passive breakdowns may occur when the server is idle, due to the lack of monitoring of the server during idle periods. When the passive breakdown occurs, the server does not get repaired immediately and enters a delayed repair phase. Negative customers arrive during the busy period, which will cause the server to break down and remove the serving customers. Under steady-state conditions, we obtain explicit expressions of the probability generating functions for the steady-state distribution, together with some important performance measures for the system. In addition, we present some numerical examples to illustrate the effects of some system parameters on important performance measures and the cost function. Finally, based on the reward-cost structure, we discuss Nash equilibrium and socially optimal strategy and numerically analyze the influence of system parameters on optimal strategies and optimal social benefits.

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“…Later, Edelson and Hilderbrand [2] considered the case when the queue length is unobservable and showed that the optimal social toll is equal to the revenue-maximizing toll. Subsequently, many scholars published their works on the customer behaviour in various queueing systems, such as unreliable queueing systems [3,4], retrial queueing systems [5][6][7][8][9], queueing systems with catastrophe [10,11], vacation queueing systems [12][13][14][15][16][17], queueing system with egalitarian processor-sharing [18], queueing systems with priority customer [19,20], and service inventory systems [21][22][23][24]. And the following excellent monographs: Hassin and Haviv [25], Stidham [26], Hassin [27], summarized achievements in recent years.…”

Section: Introductionmentioning

confidence: 99%

The Effect of a Service Experience Cost on a Queueing System

Zhang

2021

Discrete Dynamics in Nature and Society

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In this work, the authors consider the effect of a service experience cost (SE cost) on customer behaviour in the M/M/1 queueing system. Based on customer individual equilibrium strategy, social welfare is also analyzed in unobservable and observable cases. The SE cost decreases the equilibrium joining probability and social welfare in an unobservable case. However, there might exist multiple individual equilibrium thresholds in an observable case. Furthermore, numerical results show that the SE cost can be used as a feasible policy to make an incentive for customers and regulate the system for improved social welfare in some scenarios.

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Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation

Cited by 14 publications

References 26 publications

Analysis of a Retrial Queue With Two-Type Breakdowns and Delayed Repairs

Analysis of a Retrial Queue With Two-Type Breakdowns and Delayed Repairs

On a retrial queue with negative customers, passive breakdown, and delayed repairs

The Effect of a Service Experience Cost on a Queueing System

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