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 Performance Characteristics of Discrete-Time Queue With Variant Working Vacations

2020 ◽  
Vol 11 (2) ◽  
pp. 1-21
Author(s):  
P. Vijaya Laxmi ◽  
Rajesh P.
Keyword(s):  
Discrete Time ◽  
Cost Model ◽  
Probability Generating Function ◽  
System Size ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Optimal Service ◽  
Working Vacations ◽  
Vacation Period

This article analyzes an infinite buffer discrete-time single server queueing system with variant working vacations in which customers arrive according to a geometric process. As soon as the system becomes empty, the server takes working vacations. The server will take a maximum number K of working vacations until either he finds at least on customer in the queue or the server has exhaustively taken all the vacations. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. The probability generating function of the steady-state probabilities and the closed form expressions of the system size when the server is in different states have been derived. In addition, some other performance measures, their monotonicity with respect to K and a cost model are presented to determine the optimal service rate during working vacation.

scholarly journals Variant vacation queueing system with Bernoulli feedback, balking and server's states-dependent reneging

2021 ◽  
pp. 3-3
Author(s):  
Amina Bouchentouf ◽  
Mohamed Boualem ◽  
Mouloud Cherfaoui ◽  
Latifa Medjahri
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Queueing System ◽  
Steady State Solution ◽  
Single Server ◽  
Multiple Vacation ◽  
Retention Of Reneged Customers ◽  
The Impact ◽  
System Characteristics ◽  
Feedback Queue

We consider a single server Markovian feedback queue with variant of multiple vacation policy, balking, server's states-dependent reneging, and retention of reneged customers. We obtain the steady-state solution of the considered queue based on the use of probability generating functions. Then, the closed-form expressions of different system characteristics are derived. Finally, we present some numerical results in order to show the impact of the parameters of impatience timers on the performance measures of the system.

scholarly journals Variant vacation queueing system with Bernoulli feedback, balking and server's states-dependent reneging

2021 ◽  
pp. 3-3
Author(s):  
Amina Bouchentouf ◽  
Mohamed Boualem ◽  
Mouloud Cherfaoui ◽  
Latifa Medjahri
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Queueing System ◽  
Steady State Solution ◽  
Single Server ◽  
Multiple Vacation ◽  
Retention Of Reneged Customers ◽  
The Impact ◽  
System Characteristics ◽  
Feedback Queue

We consider a single server Markovian feedback queue with variant of multiple vacation policy, balking, server's states-dependent reneging, and retention of reneged customers. We obtain the steady-state solution of the considered queue based on the use of probability generating functions. Then, the closed-form expressions of different system characteristics are derived. Finally, we present some numerical results in order to show the impact of the parameters of impatience timers on the performance measures of the system.

scholarly journals An M/G/1 Retrial Queue with Fluctuating Modes of Services

2018 ◽  
Vol 7 (4.10) ◽  
pp. 762
Author(s):  
P. Rajadurai ◽  
S. Venkatesh ◽  
K. Parameswari
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
Single Server ◽  
Supplementary Variable ◽  
Working Vacation ◽  
Variable Technique ◽  
Retrial Queueing System ◽  
Retrial Queueing

In this paper, we consider a single server retrial queueing system with working vacation and two classes of customers, which are priority customers and ordinary customers. The single server provides fluctuating modes (optional phases) of services. Using the method of Probability Generating Function (PGF) approach and supplementary variable technique, the steady state results are obtained. 

scholarly journals Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

2018 ◽  
Vol 10 (2) ◽  
pp. 218-241
Author(s):  
Amina Angelika Bouchentouf ◽  
Abdelhak Guendouzi ◽  
Abdeldjebbar Kandouci
Keyword(s):  
Queueing System ◽  
Numerical Study ◽  
Cost Model ◽  
Probability Generating Function ◽  
Impatient Customers ◽  
Bernoulli Feedback ◽  
Single Vacation ◽  
Impatient Customer ◽  
Steady State Probabilities ◽  
Random Amount

Abstract This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

scholarly journals Single server queues with modified service mechanisms

1962 ◽  
Vol 2 (4) ◽  
pp. 499-507 ◽  
Author(s):  
G. F. Yeo
Keyword(s):  
Time Distribution ◽  
Busy Period ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Period Distribution ◽  
Time Dependent Problem ◽  
Stationary Waiting Time ◽  
Special Case

SummaryThis paper considers a generalisation of the queueing system M/G/I, where customers arriving at empty and non-empty queues have different service time distributions. The characteristic function (c.f.) of the stationary waiting time distribution and the probability generating function (p.g.f.) of the queue size are obtained. The busy period distribution is found; the results are generalised to an Erlangian inter-arrival distribution; the time-dependent problem is considered, and finally a special case of server absenteeism is discussed.

Transient and steady-state analysis of a queuing system having customers’ impatience with threshold

2019 ◽  
Vol 53 (5) ◽  
pp. 1861-1876 ◽  
Author(s):  
Sapana Sharma ◽  
Rakesh Kumar ◽  
Sherif Ibrahim Ammar
Keyword(s):  
Steady State ◽  
Probability Generating Function ◽  
Threshold Value ◽  
Steady State Solution ◽  
Function Technique ◽  
Single Server ◽  
Queuing Model ◽  
Queuing Models ◽  
Special Cases ◽  
Number Of Customers

In many practical queuing situations reneging and balking can only occur if the number of customers in the system is greater than a certain threshold value. Therefore, in this paper we study a single server Markovian queuing model having customers’ impatience (balking and reneging) with threshold, and retention of reneging customers. The transient analysis of the model is performed by using probability generating function technique. The expressions for the mean and variance of the number of customers in the system are obtained and a numerical example is also provided. Further the steady-state solution of the model is obtained. Finally, some important queuing models are derived as the special cases of this model.

scholarly journals A bulk queueing system under N-policy with bilevel service delay discipline and start-up time

1993 ◽  
Vol 6 (4) ◽  
pp. 359-384 ◽  
Author(s):  
David C. R. Muh
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Numerical Examples ◽  
Queueing Process ◽  
Poisson Input ◽  
Service Delay ◽  
Start Up ◽  
Bulk Arrival

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r(≥1), the system, with server capacity R, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥r). Two cases, with N≤R and N≥R, are studied.The author finds explicitly the probability generating function of the stationary distribution of the queueing process and gives numerical examples.

Sign in / Sign up

Export Citation Format

Share Document