scholarly journals Finite M/M/1 retrial model with changeable service rate

2021 ◽  
Vol 56 (1) ◽  
pp. 96-102
Author(s):  
M.S. Bratiichuk ◽  
A.A. Chechelnitsky ◽  
I.Ya. Usar
Keyword(s):  
Queueing System ◽  
Service Rate ◽  
Numerical Examples ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Explicit Formulae ◽  
Number Of Customers ◽  
Theoretical Results

The article deals with M/M/1 -type retrial queueing system with finite orbit. It is supposedthat service rate depends on the loading of the system. The explicit formulae for ergodicdistribution of the number of customers in the system are obtained. The theoretical results areillustrated by numerical examples.

scholarly journals An M/G/1 Retrial Queueing System with Phase Type Services and Working Vacations

2018 ◽  
Vol 7 (4.10) ◽  
pp. 758
Author(s):  
P. Rajadurai ◽  
R. Santhoshi ◽  
G. Pavithra ◽  
S. Usharani ◽  
S. B. Shylaja
Keyword(s):  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
Multi Phase ◽  
Number Of Customers

A multi phase retrial queue with optional re-service and multiple working vacations is considered. The Probability Generating Function (PGF) of number of customers in the system is obtained by supplementary variable technique. Various system performance measures are discussed. 

scholarly journals Asymptotic Analysis of Retrial Queueing System M/M/1 with Impatient Customers, Collisions and Unreliable Server

2020 ◽  
pp. 218-230 ◽  
Author(s):  
Elena Yu. Danilyuk ◽  
Svetlana P. Moiseeva ◽  
Janos Sztrik
Keyword(s):  
Asymptotic Analysis ◽  
Queueing System ◽  
Analysis Method ◽  
Impatient Customers ◽  
Heavy Load ◽  
Gaussian Form ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Long Time ◽  
Number Of Customers

The retrial queueing system of M=M=1 type with Poisson flow of arrivals, impatient cus- tomers, collisions and unreliable service device is considered in the paper. The novelty of our contribution is the inclusion of breakdowns and repairs of the service into our previous study to make the problem more realistic and hence more complicated. Retrial time of customers in the orbit, service time, impa- tience time of customers in the orbit, server lifetime (depending on whether it is idle or busy) and server recovery time are supposed to be exponentially distributed. An asymptotic analysis method is used to find the stationary distribution of the number of customers in the orbit. The heavy load of the system and long time patience of customers in the orbit are proposed as asymptotic conditions. Theorem about the Gaussian form of the asymptotic probability distribution of the number of customers in the orbit is formulated and proved. Numerical examples are given to show the accuracy and the area of feasibility of the proposed method

scholarly journals A Feedback Retrial Queueing System with Two Types of Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
R. Kalyanaraman
Keyword(s):  
Queueing System ◽  
Numerical Study ◽  
Priority Queue ◽  
Type I ◽  
Type Ii ◽  
Operating Characteristics ◽  
Batch Arrivals ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Number Of Customers

A retrial queueing system with two types of batch arrivals, called type I and type II customers, is considered. Type I customers and type II customers arrive in batches of variable sizes according to two different Poisson processes. Service time distributions are identical and independent and are different for both types of customers. If the arriving customers are blocked due to the server being busy, type I customers are queued in a priority queue of infinite capacity, whereas type II customers enter into a retrial group in order to seek service again after a random amount of time. A type I customer who has received service departs the system with a preassigned probability or returns to the priority queue for reservice with the complement probability. A type II call who has received service leaves the system with a preassigned probability or rejoins the retrial group with complement probability. For this model, the joint distribution of the number of customers in the priority queue and in the retrial group is obtained in a closed form. Some particular models and operating characteristics are obtained. A numerical study is also carried out.

M/M/1 Retrial Queueing System with Variable Service Rate

2020 ◽  
Vol 72 (3) ◽  
pp. 403-415
Author(s):  
M. S. Bratiichuk ◽  
A. A. Chechelnitsky ◽  
I. Ya. Usar
Keyword(s):  
Queueing System ◽  
Service Rate ◽  
Retrial Queueing System ◽  
Retrial Queueing

scholarly journals Transient Analysis of M[X1],M[X2]/G1,G2/1 retrial queueing system with priority services, working breakdown, start up/close down time, Bernoulli vacation, reneging and balking

2020 ◽  
pp. 203-216
Author(s):  
Govindhan Ayyappan ◽  
Udayageetha J
Keyword(s):  
Transient Analysis ◽  
Queueing System ◽  
Variable Technique ◽  
Retrial Queueing System ◽  
System A ◽  
Retrial Queueing ◽  
Start Up ◽  
Set Up ◽  
Number Of Customers ◽  
Bernoulli Vacation

This paper considers  M[X1],M[X2]/G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the pre-emptive priority rule subject to working breakdown, startup/closedown time and Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there are no priority customers present in the system the server may go for a vacation or close down the system. On completion of the close down, the server needs some time to set up the system. The priority customers who find the server busy are queued in the system. A low-priority customer who find the server busy are routed to a retrial (orbit) queue that attempts to get the service. The system may breakdown at any point of time when it is in operation. However, when the system fails, instead of stopping service completely, the service is continued only to the high priority customers at a slower rate. We consider balking to occur to the low priority customer while the server is busy or idle, and reneging to occur at the high priority customers during server’s vacation, start up/close down time. Using the supplementary variable technique, we derive the joint distribution of the server state and the number of customers in the system. Finally, some performance measures and numerical examples are presented.

Sensitivity analysis of an M/G/1 retrial queueing system with disaster under working vacations and working breakdowns

2018 ◽  
Vol 52 (1) ◽  
pp. 35-54 ◽  
Author(s):  
P. Rajadurai
Keyword(s):  
Queueing System ◽  
Cost Optimization ◽  
Probability Generating Function ◽  
System Size ◽  
Service Rate ◽  
Steady State Probability ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Working Vacations ◽  
Busy Server

This paper deals with the new type of retrial queueing system with working vacations and working breakdowns. The system may become defective by disasters at any point of time when the regular busy server is in operation. The occurrence of disasters forces all customers to leave the system and causes the main server to fail. At a failure instant, the main server is sent to the repair and the repair period immediately begins. As soon as the orbit becomes empty at regular service completion instant or disaster occurs in the regular busy server, the server goes for a working vacation and working breakdown (called lower speed service period). During this period, the server works at a lower service rate to arriving customers. Using the supplementary variable technique, we analyze the steady state probability generating function of system size. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.

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.

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