RETRACTED ARTICLE: Transient behavior of a Markovian queue with working vacation variant reneging and a waiting server

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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Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy

Operations Research and Decisions ◽

10.37190/ord200401 ◽

2020 ◽

Vol 30 (4) ◽

Author(s):

Amina Angelika Bouchentouf ◽

Lahcene Yahiaoui ◽

Mokhtar Kadi ◽

Shakir Majid

Keyword(s):

Queueing System ◽

Cost Model ◽

Probability Generating Function ◽

Steady State Solution ◽

Stochastic Decomposition ◽

Single Server ◽

Working Vacation ◽

Bernoulli Feedback ◽

Markovian Queue ◽

Retention Of Reneged Customers

This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using probability generating function (PGF) technique, we obtain the steady-state solution of the system. In addition, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using quadratic fit search method (QFSM). Finally, numerical examples are provided in order to visualize the analytical results.

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Impatient Customers in a Markovian Queue with Multiple Working Vacation

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/946 ◽

2018 ◽

Vol 9 (12) ◽

pp. 1979-1989

Author(s):

P. Manoharan ◽

A. Ashok

Keyword(s):

Impatient Customers ◽

Working Vacation ◽

Markovian Queue

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Variant working vacation Markovian queue with second optional service, unreliable server and retention of reneged customers

International Journal of Mathematics in Operational Research ◽

10.1504/ijmor.2021.115447 ◽

2021 ◽

Vol 19 (1) ◽

pp. 45

Author(s):

Vijaya Laxmi Pikkala ◽

Girija Bhavani Edadasari

Keyword(s):

Working Vacation ◽

Unreliable Server ◽

Markovian Queue ◽

Optional Service ◽

Second Optional Service ◽

Retention Of Reneged Customers

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Equilibrium analysis of cloud user request based on the Markov queue with variable vacation and vacation interruption

RAIRO - Operations Research ◽

10.1051/ro/2021130 ◽

2021 ◽

Vol 55 (5) ◽

pp. 2807-2825

Author(s):

Yitong Zhang ◽

Xiuli Xu

Keyword(s):

Social Benefit ◽

Equilibrium Analysis ◽

Service Rate ◽

Single Server ◽

Working Vacation ◽

Idle Period ◽

Markovian Queue ◽

User Request ◽

Vacation Interruption ◽

The Individual

This paper considers the equilibrium balking behavior of customers in a single-server Markovian queue with variable vacation and vacation interruption, where the server can switch across four states: vacation, working vacation, idle period, and busy period. Once the queue becomes empty, the server commences a working vacation and slows down its service rate. However, this period may be interrupted anytime by the vacation interruption. Upon the completion of a working vacation, the server takes a vacation in a probability-based manner and stops service if the system is empty. The system stays idle after a vacation until a new customer arrives. The comparisons between the equilibrium balking strategy of customers and the optimal expected social benefit per time unit for each type of queue are elucidated and the inconsistency between the individual optimization and the social optimization is revealed. Moreover, the sensitivity of the expected social benefit and the equilibrium threshold with respect to the several parameters as well as diverse precision levels is illustrated through numerical examples in a competitive cloud environment.

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