scholarly journals A study on transient solution of single server queueing system with repair process by using generating functions of the system under the system down

2018 ◽  
Vol 1139 ◽  
pp. 012025
Author(s):  
S. Anand Gnana Selvam ◽  
D. Moganraj ◽  
M. Reni Sagayaraj
Keyword(s):  
Generating Functions ◽  
Queueing System ◽  
Repair Process ◽  
Single Server ◽  
Transient Solution

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.

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 A transient solution to an M/M/1 queue: a simple approach

1987 ◽  
Vol 19 (04) ◽  
pp. 997-998 ◽  
Author(s):  
P. R. Parthasarathy
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Single Server ◽  
Transient Solution ◽  
Poisson Arrivals ◽  
Service Times ◽  
Time Dependent Solution

A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.

scholarly journals Transient analysis of a single server queueing system with infinite buffer

2020 ◽  
Author(s):  
Huixia Huo ◽  
Houbao XU ◽  
Zhuoqian Chen ◽  
Thet Thet Win
Keyword(s):  
Spectral Distribution ◽  
Transient Analysis ◽  
Manufacturing System ◽  
Queueing System ◽  
Transient Behavior ◽  
Intelligent Manufacturing ◽  
Computer Integrated Manufacturing ◽  
Single Server ◽  
Transient Solution ◽  
Numerical Examples

As a typical single server queueing system, computer integrated manufacturing system (CIMS) has been widely used in the field of intelligent manufacturing. Howerve, how to derive its instantaneous index is still an imporant issue. This paper investigates the transient behavior of the CIMS with spectral method. By constructing an asymptotic system and analyzing the spectral distribution, we derive the explicit transient solution of the asymptotic system. Trottter-Kato theorem is used to prove that the transient solution of the CIMS is just the limitation of explicit transient solution of the asymptotic system. At the end of the paper, numerical examples are shown to illustrate the effectiveness of the proposed approximation.

scholarly journals A transient solution to an M/M/1 queue: a simple approach

1987 ◽  
Vol 19 (4) ◽  
pp. 997-998 ◽  
Author(s):  
P. R. Parthasarathy
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Single Server ◽  
Transient Solution ◽  
Poisson Arrivals ◽  
Service Times ◽  
Time Dependent Solution

A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.

scholarly journals STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

2014 ◽  
Vol 31 (02) ◽  
pp. 1440002 ◽  
Author(s):  
K. AVRACHENKOV ◽  
E. MOROZOV ◽  
R. NEKRASOVA ◽  
B. STEYAERT
Keyword(s):  
Queueing System ◽  
Stability Domain ◽  
Single Server ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Single Orbit ◽  
Transmission Control Protocols ◽  
Regenerative Approach ◽  
The Stability ◽  
Multi Access

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate [Formula: see text]) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

Sign in / Sign up

Export Citation Format

Share Document