scholarly journals Modelling customers’ impatience with discouraged arrival and retention of reneging

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Pallabi Medhi
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Stochastic Modelling ◽  
Steady State Solution ◽  
Single Server ◽  
Finite Buffer ◽  
System Parameters ◽  
Retention Of Reneged Customers

This paper presents stochastic modelling of a single server, finite buffer Markovian queuing system with discouraged arrivals, balking, reneging, and retention of reneged customers. Markov process is used to derive the steady-state solution of the model. Closed form expressions using probability generating functions (PGFs) are derived and presented for both classical and novel performance measures. In addition, a sensitivity analysis is carried out to study the effect of the system parameters on performance measures. A numerical problem is also presented to demonstrate the derived results and some design aspects.

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.

Sensitivity analysis for stationary and ergodic queues

1992 ◽  
Vol 24 (03) ◽  
pp. 738-750 ◽  
Author(s):  
P. Konstantopoulos ◽  
Michael A. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Perturbation Analysis ◽  
Service Process ◽  
Single Server ◽  
Stationary Version ◽  
Major Interest ◽  
Regenerative Approach ◽  
Steady State Performance

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

Sensitivity analysis for stationary and ergodic queues

1992 ◽  
Vol 24 (3) ◽  
pp. 738-750 ◽  
Author(s):  
P. Konstantopoulos ◽  
Michael A. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Perturbation Analysis ◽  
Service Process ◽  
Single Server ◽  
Stationary Version ◽  
Major Interest ◽  
Regenerative Approach ◽  
Steady State Performance

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

Analysis of Feedback Retrial Queue with Starting Failure and Server Vacation

2016 ◽  
pp. 71-96
Author(s):  
K. Sathiya Thiyagarajan ◽  
G. Ayyappan
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Retrial Queue ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Steady State Analysis ◽  
Starting Failure ◽  
Dependent Probability ◽  
Bernoulli Vacation

In this chapter we discusses a batch arrival feedback retrial queue with Bernoulli vacation, where the server is subjected to starting failure. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of each service, the server either goes for a vacation with probability or may wait for serving the next customer. Repair times, service times and vacation times are assumed to be arbitrarily distributed. The time dependent probability generating functions have been obtained in terms of their Laplace transforms. The steady state analysis and key performance measures of the system are also studied. Finally, some numerical illustrations are presented.

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.

COST ANALYSIS OF THE R-UNRELIABLE-UNLOADER QUEUEING SYSTEM

2008 ◽  
Vol 25 (01) ◽  
pp. 57-73
Author(s):  
KUO-HSIUNG WANG ◽  
CHUN-CHIN OH ◽  
JAU-CHUAN KE
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Queueing System ◽  
Cost Model ◽  
Analytic Solutions ◽  
Queueing Model ◽  
Exponential Distributions ◽  
System Parameters ◽  
Optimal Values ◽  
The Cost

This paper analyzes the unloader queueing model in which N identical trailers are unloaded by R unreliable unloaders. Steady-state analytic solutions are obtained with the assumptions that trip times, unloading times, finishing times, breakdown times, and repair times have exponential distributions. A cost model is developed to determine the optimal values of the number of unloaders and the finishing rate simultaneously, in order to minimize the expected cost per unit time. Numerical results are provided in which several steady-state characteristics of the system are calculated based on assumed numerical values given to the system parameters and the cost elements. Sensitivity analysis is also studied.

Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment

2016 ◽  
Vol 33 (05) ◽  
pp. 1650036 ◽  
Author(s):  
Gopinath Panda ◽  
Veena Goswami ◽  
Abhijit Datta Banik
Keyword(s):  
Performance Measures ◽  
Numerical Experiments ◽  
Optimal Strategies ◽  
Cost Structure ◽  
Single Server ◽  
System Parameters ◽  
Optimal Behavior ◽  
Markovian Queue ◽  
Queues With Vacations ◽  
The Individual

In this paper, we consider customers’ equilibrium and socially optimal behavior in a single-server Markovian queue with multiple vacations and sequential abandonments. Upon arrival customers decide for themselves whether to join or balk, based on the level of information available to them. During the server’s vacation, present customers become impatient and decide sequentially whether they will abandon the system or not upon the availability of a secondary transport facility. Assuming the linear reward-cost structure, we analyze the equilibrium balking strategies of customers under four cases: fully and almost observable as well as fully and almost unobservable. In all the above cases, the individual and social optimal strategies are derived. Finally, the dependence of performance measures on system parameters are demonstrated via numerical experiments.

Performance analysis of the discrete-time GI/Geom/1/N queue

1996 ◽  
Vol 33 (01) ◽  
pp. 239-255 ◽  
Author(s):  
M. L. Chaudhry ◽  
U. C. Gupta
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Interarrival Time ◽  
Single Server ◽  
Finite Buffer ◽  
Supplementary Variable ◽  
Time Analysis ◽  
Variable Technique ◽  
Early Arrival ◽  
Finite Buffer Queue

This paper presents an analysis of the single-server discrete-time finite-buffer queue with general interarrival and geometric service time,GI/Geom/1/N. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variations of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both cases, steady-state distributions for outside observers as well as at random and prearrival epochs have been obtained. The waiting time analysis has also been carried out. Results for theGeom/G/1/Nqueue with LAS-DA have been obtained from theGI/Geom/1/Nqueue with EAS. We also give various performance measures. An algorithm for computing state probabilities is given in an appendix.

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