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 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.

Analysis of a queueing system in random environment with an unreliable server and geometric abandonments

2018 ◽  
Vol 52 (3) ◽  
pp. 903-922 ◽  
Author(s):  
Tao Jiang ◽  
Baogui Xin ◽  
Baoxian Chang ◽  
Liwei Liu
Keyword(s):  
Performance Measures ◽  
Random Environment ◽  
Queueing System ◽  
Geometric Approach ◽  
Repair Process ◽  
Single Server ◽  
Steady State Distribution ◽  
Server Breakdown ◽  
Multi Phase ◽  
The Impact

This paper studies a single server queueing model in a multi-phase random environment with server breakdowns and geometric abandonments, where server breakdowns only occur while the server is in operation. At a server breakdown instant (i.e., an abandonment opportunity epoch), all present customers adopt the so-called geometric abandonments, that is, the customers decide sequentially whether they will leave the system or not. In the meantime, the server abandons the service and a repair process starts immediately. After the server is repaired, the server resumes its service, and the system enters into the operative phaseiwith probabilityqi,i= 1, 2, …,d. Using probability generating functions and matrix geometric approach, we obtain the steady state distribution and various performance measures. In addition, some numerical examples are presented to show the impact of parameters on the performance measures.

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 M/M/1 Queueing system with Customer Balking and Reneging

2019 ◽  
Vol 8 (9) ◽  
pp. 2636-2646
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Queueing System ◽  
Probability Generating Functions ◽  
Multiple Vacation ◽  
Steady State Probabilities ◽  
Explicit Expressions

This paper deals with an M/M/1 queueing system with customer balking and reneging. Balking and reneging of the customers are assumed to occur due to non-availability of the server during vacation and breakdown periods. Steady state probabilities for both the single and multiple vacation scenarios are obtained by employing probability generating functions. We evaluate the explicit expressions for various performance measures of the queueing system.

A queueing system with impatient customers

1985 ◽  
Vol 22 (3) ◽  
pp. 688-696 ◽  
Author(s):  
A. G. De Kok ◽  
H. C. Tijms
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Fixed Time ◽  
Single Server ◽  
Impatient Customers ◽  
Average Delay ◽  
Practical Applications ◽  
Poisson Input ◽  
General Service Times ◽  
General Service

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

scholarly journals Analysis of a Discrete-Time Queueing Model with Disasters

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3283
Author(s):  
Mustafa Demircioglu ◽  
Herwig Bruneel ◽  
Sabine Wittevrongel
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Time Slot ◽  
Probability Distributions ◽  
Single Server ◽  
Bernoulli Process ◽  
Tail Probabilities ◽  
Mean Values ◽  
The Mean ◽  
The Impact

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

scholarly journals Geo/Geo/1/N Queue with In-Immune and Immune Service Killing Discipline

2012 ◽  
Vol 23 (1) ◽  
pp. 129-148
Author(s):  
Madhu Jain Madhu Jain
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Relaxation Method ◽  
Single Server ◽  
Finite Capacity ◽  
Single Server Queue ◽  
Stationary Probability Distribution ◽  
Negative Customers ◽  
Server Queue ◽  
Successive Over Relaxation

The present investigation studies a discrete time single server queue with both positive and negative arrival streams in accordance with removal of the customer from the end (RCE)-in immune and immune service killing policy. This study is a generalization of the queue with negative customers, wherein only positive customers need a service and negative customers arriving to the system can kill the already present positive customers from any where in the queue, otherwise get lost. The concept of both in-immune and immune service killing are taken into consideration. According to the in-immune killing policy, the negative customer is allowed to kill the most recent positive customer inspite of whether it is in service or not, while the immune service killing discipline suggests that the customer currently being served is immune from killing by the negative arrival. We analyze a queue with geometric arrivals of both positive and negative customers for a finite capacity system. The stationary probability distribution and other performance measures are derived in terms of the generating functions. The results so obtained are validated by the numerical method based on successive over relaxation method (SOR). We have also employed the neurro fuzzy approach for exhibiting the approximate results for various performance measures.

scholarly journals Continuous-Service M/M/1 Queuing Systems

2019 ◽  
Vol 2 (2) ◽  
pp. 16
Author(s):  
Song Chew
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Queuing Systems ◽  
Simulation Experiments ◽  
Steady State Analysis ◽  
System A ◽  
Continuous Service ◽  
Service Priority

In this paper, we look into a novel notion of the standard M/M/1 queueing system. In our study, we assume that there is a single server and that there are two types of customers: real and imaginary customers. Real customers are regular customers arriving into our queueing system in accordance with a Poisson process. There exist infinitely many imaginary customers residing in the system. Real customers have service priority over imaginary customers. Thus, the server always serves real (regular) customers one by one if there are real customers present in the system. After serving all real customers, the server immediately serves, one at a time, imaginary customers residing in the system. A newly arriving real customer presumably does not preempt the service of an imaginary customer and hence must wait in the queue for their service. The server immediately serves a waiting real customer upon service completion of the imaginary customer currently under service. All service times are identically, independently, and exponentially distributed. Since our systems are characterized by continuous service by the server, we dub our systems continuous-service M/M/1 queueing systems. We conduct the steady-state analysis and determine common performance measures of our systems. In addition, we carry out simulation experiments to verify our results. We compare our results to that of the standard M/M/1 queueing system, and draw interesting conclusions.

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