scholarly journals A single-server Markovian queuing system with discouraged arrivals and retention of reneged customers

2014 ◽  
Vol 24 (1) ◽  
pp. 119-126 ◽  
Author(s):  
Rakesh Kumar ◽  
Kumar Sharma
Keyword(s):  
Negative Impact ◽  
Steady State Solution ◽  
Queuing System ◽  
Point Of View ◽  
Single Server ◽  
Queuing Model ◽  
Queuing Models ◽  
Special Cases ◽  
Retention Of Reneged Customers ◽  
Measures Of Effectiveness

Customer impatience has a very negative impact on the queuing system under investigation. If we talk from business point of view, the firms lose their potential customers due to customer impatience, which affects their business as a whole. If the firms employ certain customer retention strategies, then there are chances that a certain fraction of impatient customers can be retained in the queuing system. A reneged customer may be convinced to stay in the queuing system for his further service with some probability, say q and he may abandon the queue without receiving the service with a probability p(=1? q). A finite waiting space Markovian single-server queuing model with discouraged arrivals, reneging and retention of reneged customers is studied. The steady state solution of the model is derived iteratively. The measures of effectiveness of the queuing model are also obtained. Some important queuing models are derived as special cases of this model.

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.

Development of a Heuristics Model for Simplifying a Multi-Channel Queuing System

2011 ◽  
Vol 367 ◽  
pp. 647-652
Author(s):  
B. Kareem ◽  
A. A. Aderoba
Keyword(s):  
Waiting Time ◽  
Channel Model ◽  
Single Channel ◽  
Queuing System ◽  
Queuing Model ◽  
Average Waiting Time ◽  
Queuing Models ◽  
Significant Difference ◽  
Number Of Customers ◽  
Proportionality Principle

Queuing model has been discussed widely in literature. The structures of queuing systems are broadly divided into three namely; single, multi-channel, and mixed. Equations for solving these queuing problems vary in complexity. The most complex of them is the multi-channel queuing problem. A heuristically simplified equation based on relative comparison, using proportionality principle, of the measured effectiveness from the single and multi-channel models seems promising in solving this complex problem. In this study, six different queuing models were used from which five of them are single-channel systems while the balance is multi-channel. Equations for solving these models were identified based on their properties. Queuing models’ performance parameters were measured using relative proportionality principle from which complexity of multi-channel system was transformed to a simple linear relation of the form = . This showed that the performance obtained from single channel model has a linear relationship with corresponding to multi-channel, and is a factor which varies with the structure of queuing system. The model was tested with practical data collected on the arrival and departure of customers from a cocoa processing factory. The performances obtained based on average number of customers on line , average number of customers in the system , average waiting time in line and average waiting time in the system, under certain conditions showed no significant difference between using heuristics and analytical models.

scholarly journals Transient performance analysis of a single server queuing model with retention of reneging customers

2018 ◽  
Vol 28 (3) ◽  
pp. 315-331 ◽  
Author(s):  
Rakesh Kumar ◽  
Sapana Sharma
Keyword(s):  
Performance Analysis ◽  
Probability Generating Function ◽  
Time Dependent ◽  
Function Technique ◽  
Single Server ◽  
Transient Solution ◽  
Transient Performance ◽  
Queuing Model ◽  
Special Cases ◽  
Mean And Variance

In this paper, we study a single server queuing model with retention of reneging customers. The transient solution of the model is derived using probability generating function technique. The time-dependent mean and variance of the model are also obtained. Some important special cases of the model are derived and discussed. Finally, based on the numerical example, the transient performance analysis of the model is performed.

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.

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.

Availability and maintenance modeling of a batch service queuing system

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shweta Agarwal ◽  
S.B. Singh
Keyword(s):  
Distribution System ◽  
Renewal Theory ◽  
Realistic Model ◽  
Queuing System ◽  
Batch Service ◽  
Single Server ◽  
Queuing Model ◽  
Content Type ◽  
Poisson Input ◽  
Reliability Characteristics

PurposeThe purpose of the paper is to analyze reliability characteristics of batch service queuing system with a single server model that envisages Poisson input process and exponential service times under first come, first served (FCFS) queue discipline.Design/methodology/approachWith the help of renewal theory and stochastic processes, a model has been designed to discuss the reliability and its characteristics.FindingsThe instantaneous and steady-state availability along with the maintenance model of the systems subject to generalized M/Mb/1 queuing model is derived, and a few particular cases for availability are obtained as well. For supporting the developed model, a case study on electrical distribution system (EDS) has been illustrated, which also includes a comparison for the system subject to M/Mb/1 queuing model and the system without any queue (delay).Originality/valueIt is a quite realistic model that may aid to remove congestion in the system while repairing.

scholarly journals Self-Similar Characteristics of COVID-19 Patient arrival at Healthcare Centre – A Study Using Queuing Models

2021 ◽  
Vol 12 (3) ◽  
pp. 4776-4791
Author(s):  
AM Girija, D.Mallikarjuna Reddy, Pushpalatha Sarla
Keyword(s):  
Health Care ◽  
Care Center ◽  
Local Area ◽  
Single Server ◽  
Self Similarity ◽  
Queuing Model ◽  
Health Care Center ◽  
Queuing Models ◽  
Detection And Identification ◽  
Patient Arrival

The entire world is spreading of coronavirus-COVID-19 has increased exponentially across the globe, and still, no vaccine is available for the treatment of patients. The crowd has grown tremendously in the hospitals where the facilities are minimal. The queue theory is applied for the Single-server system and its self-similarity existence in a queue used to identify the queue time, waiting time, and Hurst parameter by different patient arrivals methods Health care center in our local area located in Hosapete, Ballari district, Karnataka. Due to more arrivals to the health care center for the identification and confirmation of disease covid-19. This study paper presents a sequential queuing model for estimating infections' detection and identification in severe loading conditions. The goal is to offer a simplified probabilistic model to determine the general behavior to predict how long the treatment cycle will diagnose and classify people already tested and get negative or positive results. For this type of Method, there are some graphical representations of the various measurement criteria. The modelling results showed that the patient's waiting period in the course of inquiries, detections, detecting, or treating COVID-19 in the event of imbalances in the system as a whole rise following the logarithm rule.

ON A QUEUING MODEL WITH SERVICE INTERRUPTIONS

2008 ◽  
Vol 22 (4) ◽  
pp. 537-555 ◽  
Author(s):  
Onno Boxma ◽  
Michel Mandjes ◽  
Offer Kella
Keyword(s):  
Queue Length ◽  
Production Systems ◽  
Single Server ◽  
Queuing Model ◽  
Computer Communication ◽  
Polling Models ◽  
Special Cases ◽  
Wide Range ◽  
Workload Distribution ◽  
Almost All

Single-server queues in which the server takes vacations arise naturally as models for a wide range of computer, communication, and production systems. In almost all studies on vacation models, the vacation lengths are assumed to be independent of the arrival, service, workload, and queue length processes. In the present study, we allow the length of a vacation to depend on the length of the previous active period (viz. the period since the previous vacation). Under rather general assumptions regarding the offered work during active periods and vacations, we determine the steady-state workload distribution, both for single and multiple vacations. We conclude by discussing several special cases, including polling models, and relate our findings to results obtained earlier.

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