Equilibrium balking strategies of customers in Markovian queues with two-stage working vacations

Sun, Wei; Li, Shiyong; Li, Quan‐Lin

doi:10.1016/j.amc.2014.09.116

Cited by 24 publications

(6 citation statements)

References 21 publications

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“…As for the work studying customers behavior in queueing systems with working vacations, Zhang et al [14] and Sun and Li [15] obtained equilibrium balking strategies in M/M/1 queues with working vacations for four cases with respect to different levels of information. Sun et al [16] also considered the customers equilibrium balking behavior in some single-server Markovian queues with two-stage working vacations.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

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

Tian¹,

Wu³

2016

Mathematical Problems in Engineering

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We consider the customers equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with multiple working vacations and vacation interruptions. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. We consider that the system states are observable, partially observable, and unobservable, respectively. For these cases, we first analyze the stationary behavior of the system and get the equilibrium strategies of the customers and compare them to socially optimal balking strategies numerically.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

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

Tian¹,

Wu³

2016

Mathematical Problems in Engineering

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“…One recently very active direction is the consideration of queues with different kinds of classic vacations(see e.g., Guo and Hassin [4], Sun et al [5], Economou et al [6], Liu et al [7]). Similar economic studies have been also implemented in the queueing systems with various working vacations (see e.g., Zhang et al [8], Sun and Li [9], Sun et al [10], Sun et al [11]). Another direction in the economic analysis of queueing systems concerns the study for the M/M/1 queue with an unreliable server (see e.g., Wang and zhang [12], Li et al [13], Yu et al [14], Chen and Zhou [15]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Equilibrium Strategies in Markovian Queues With Negative Customers and Working Breakdowns

Tian

Wang

2019

IEEE Access

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We consider the customers' strategic behavior in Markovian queues with negative customers and working breakdowns. when a negative customer arrives, the customer being served is forced to leave the system. At the same time, the server breaks down and the service rate decreases. Arriving customers decide whether to enter the system or balk based on a natural reward-cost structure and the information of the system. By using the probability generating functions, we analyze the steady-state distribution and obtain the mean sojourn time of the arriving customers. We investigate the customers' behavior under different information levels of the system and derive equilibrium strategy for the customers in the fully observable, almost observable, almost unobservable and fully unobservable cases. Finally, some numerical results are provided to illustrate the effect of the system parameters on equilibrium strategies of the observable case and customers' sojourn time for unobservable cases.

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“…For work on customers' choice behavior in queueing systems with working vacations, Zhang et al [27] and Sun and Li [14] studied equilibrium balking strategies in M/M/1 queues with multiple working vacations under different information scenarios. Subsequently, Sun et al [17,18] considered customers' optimal balking behavior in some single-server Markovian queues with two-stage working vacations and double adaptive working vacations, respectively. Wang and Zhang [24] considered equilibrium strategies in Markovian queues with a single working vacation.…”

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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Equilibrium balking strategies of customers in Markovian queues with two-stage working vacations

Cited by 24 publications

References 21 publications

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

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

Analysis of Equilibrium Strategies in Markovian Queues With Negative Customers and Working Breakdowns

On Markovian Queues With Single Working Vacation and Bernoulli Interruptions

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