Impatient Customers in a Markovian Queue with Multiple Working Vacation

2018 ◽  
Vol 9 (12) ◽  
pp. 1979-1989
Author(s):  
P. Manoharan ◽  
A. Ashok
Keyword(s):  
Impatient Customers ◽  
Working Vacation ◽  
Markovian Queue

scholarly journals Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Cosmika Goswami ◽  
N. Selvaraju
Keyword(s):  
Blocking Probability ◽  
Death Process ◽  
Impatient Customers ◽  
Working Vacation ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
The One ◽  
Vacation Period ◽  
Stationary Probability Vector

We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.

scholarly journals On Probability Characteristics for a Class of Queueing Models with Impatient Customers

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 594 ◽  
Author(s):  
Yacov Satin ◽  
Alexander Zeifman ◽  
Alexander Sipin ◽  
Sherif I. Ammar ◽  
Janos Sztrik
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Markov Model ◽  
Queueing Models ◽  
Impatient Customers ◽  
Numerical Examples ◽  
Markovian Queue ◽  
Proposed Model ◽  
System Characteristics ◽  
Individual Requirement

In this paper, a class of queueing models with impatient customers is considered. It deals with the probability characteristics of an individual customer in a non-stationary Markovian queue with impatient customers, the stationary analogue of which was studied previously as a successful approximation of a more general non-Markov model. A new mathematical model of the process is considered that describes the behavior of an individual requirement in the queue of requirements. This can be applied both in the stationary and non-stationary cases. Based on the proposed model, a methodology has been developed for calculating the system characteristics both in the case of the existence of a stationary solution and in the case of the existence of a periodic solution for the corresponding forward Kolmogorov system. Some numerical examples are provided to illustrate the effect of input parameters on the probability characteristics of the system.

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.

STRATEGIC CUSTOMERS IN MARKOVIAN QUEUES WITH VACATIONS AND SYNCHRONIZED ABANDONMENT

2020 ◽  
Vol 62 (1) ◽  
pp. 89-120
Author(s):  
GOPINATH PANDA ◽  
VEENA GOSWAMI
Keyword(s):  
Cost Structure ◽  
Social Benefits ◽  
Single Server ◽  
Impatient Customers ◽  
Strategic Customers ◽  
Markovian Queue ◽  
The Social ◽  
Queues With Vacations ◽  
First Come First Serve ◽  
System Information

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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