Equilibrium and Optimal Strategies in M/M/1 Queues with Working Vacations and Vacation Interruptions

Tian, Ruiling; Hu, Linmin; Wu, Xijun

doi:10.1155/2016/9746962

Cited by 12 publications

(7 citation statements)

References 15 publications

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“…Laxmi and Jyothsna [10] dealt with balking and reneging multiple working vacations queue with heterogeneous servers. Later, Tian et al [19] presented equilibrium and optimal strategies in M/M/1 queueing model with working vacations and vacation interruptions. Recently, in Bouchentouf and Yahiaoui [2], a study on queueing system with Bernoulli feedback, reneging and retention of reneged customers, multiple working vacations, and Bernoulli schedule vacation interruption has been done.…”

Section: Introductionmentioning

confidence: 99%

The $$M^{X}/M/c$$ Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis

Bouchentouf

Guendouzi

2019

Arab. J. Math.

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The present paper deals with an M X /M/c Bernoulli feedback queueing system with variant multiple working vacations and impatience timers which depend on the states of the servers. Whenever a customer arrives at the system, he activates an random impatience timer. If his service has not been completed before his impatience timer expires, the customer may abandon the system. Using certain customer retention mechanism, the impatient customer can be retained in the system. After getting incomplete or unsatisfactory service, with some probability, each customer may comeback to the system as a Bernoulli feedback. Using the probability generating functions (PGFs), we derive the steady-state solution of the model. Then, we obtain useful performance measures. Moreover, we carry out an economic analysis. Finally, numerical study is performed to explore the effects of the model parameters on the behavior of the system.

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Section: Introductionmentioning

confidence: 99%

The $$M^{X}/M/c$$ Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis

Bouchentouf

Guendouzi

2019

Arab. J. Math.

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“…They studied equilibrium balking strategies of rational customers in an M/M/1 queue with setup times under four information cases. Variants of Markovian vacation queues with optimal strategic behaviour have been discussed in the literature (see [8,14,15,19,21] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Strategic Customers in Markovian Queues With Vacations and Synchronized Abandonment

Panda¹,

Goswami²

2020

ANZIAM J.

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We study impatient customers’ joining strategies in a single-server Markovian queue with synchronized abandonment and multiple vacations. Customers receive the system information upon arrival, and decide whether to join or balk, based on a linear reward-cost structure under the acquired information. Waiting customers are served in a first-come-first-serve discipline, and no service is rendered during vacation. Server’s vacation becomes the cause of impatience for the waiting customers, which leads to synchronous abandonment at the end of vacation. That is, customers consider simultaneously but independent of others, whether to renege the system or to remain. We are interested to study the effect of both information and reneging choice on the balking strategies of impatient customers. We examine the customers’ equilibrium and socially optimal balking strategies under four cases of information: fully/almost observable and fully/almost unobservable cases, assuming the linear reward-cost structure. We compare the social benefits under all the information policies.

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“…Wang and Zhang [15] discussed the equilibrium strategies in the Markovian queues with a single working vacation. Then, Tian et al [16] studied equilibrium and optimal strategies in M/M/1 queues with multiple working vacations and vacation interruptions under three different levels of system information. Doo Ho Lee [17] observed customer's equilibrium joining/balking behaviors in M/M/1 queues with a single working vacation and vacation interruptions.…”

Section: Introductionmentioning

confidence: 99%

Social Optimization and Pricing Strategies in Unobservable Queues with Delayed Multiple Vacations

Tian

2019

Mathematical Problems in Engineering

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The paper considers the single-server Markovian queues with delayed multiple vacations. Once the system becomes empty, the server will experience a changeover time to begin the vacation. By using the matrix-geometric solution method, we obtain the stationary probability distribution and the mean queue length under almost unobservable and fully unobservable cases. Based on the system status information and a linear reward-cost structure reflecting the desire of customers for service and their unwillingness for waiting, the social welfare function is determined. We also investigate optimal pricing strategies of the server under the ex-postpayment scheme and the ex-antepayment scheme, and we get the customer’s equilibrium strategy under optimal pricing strategy. Finally, we illustrate the effect of several parameters and information levels on socially optimal strategies and optimal social benefit by numerical examples.

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Equilibrium and Optimal Strategies in M/M/1 Queues with Working Vacations and Vacation Interruptions

Cited by 12 publications

References 15 publications

The $$M^{X}/M/c$$ Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis

The $$M^{X}/M/c$$ Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis

Strategic Customers in Markovian Queues With Vacations and Synchronized Abandonment

Social Optimization and Pricing Strategies in Unobservable Queues with Delayed Multiple Vacations

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