Transient Behavior of a Single-Server Markovian Queue with Balking and Working Vacation Interruptions

2020 ◽  
Author(s):  
Arumugam Azhagappan ◽  
Thirunavukkarasu Deepa
Keyword(s):  
Transient Behavior ◽  
Single Server ◽  
Working Vacation ◽  
Markovian Queue

ON MARKOVIAN QUEUES WITH SINGLE WORKING VACATION AND BERNOULLI INTERRUPTIONS

2021 ◽  
pp. 1-28
Author(s):  
Ruiling Tian ◽  
Zhe George Zhang ◽  
Siping Su
Keyword(s):  
Optimal Strategies ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Markovian Queue ◽  
Rate Period ◽  
System Information ◽  
Vacation Period ◽  
Maintenance Process ◽  
Different Levels

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.

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

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.

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

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.

Time-dependent single server Markovian queue with catastrophe

2015 ◽  
Vol 9 ◽  
pp. 3275-3283
Author(s):  
R. Sudhesh ◽  
A. Vaithiyanathan
Keyword(s):  
Time Dependent ◽  
Single Server ◽  
Markovian Queue

q-SERIES IN MARKOV CHAINS WITH BINOMIAL TRANSITIONS

2008 ◽  
Vol 23 (1) ◽  
pp. 75-99 ◽  
Author(s):  
Antonis Economou ◽  
Stella Kapodistria
Keyword(s):  
Busy Period ◽  
Hypergeometric Series ◽  
Binomial Coefficients ◽  
Single Server ◽  
Transition Rates ◽  
Extensive Analysis ◽  
Service Completion ◽  
Markovian Queue ◽  
Number Of Customers ◽  
Sojourn Time Distributions

We consider a single-server Markovian queue with synchronized services and setup times. The customers arrive according to a Poisson process and are served simultaneously. The service times are independent and exponentially distributed. At a service completion epoch, every customer remains satisfied with probability p (independently of the others) and departs from the system; otherwise, he stays for a new service. Moreover, the server takes multiple vacations whenever the system is empty.Some of the transition rates of the underlying two-dimensional Markov chain involve binomial coefficients dependent on the number of customers. Indeed, at each service completion epoch, the number of customers n is reduced according to a binomial (n, p) distribution. We show that the model can be efficiently studied using the framework of q-hypergeometric series and we carry out an extensive analysis including the stationary, the busy period, and the sojourn time distributions. Exact formulas and numerical results show the effect of the level of synchronization to the performance of such systems.

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