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

2021 ◽  
pp. 291-303
Author(s):  
János Sztrik ◽  
Ádám Tóth ◽  
Elena Yu. Danilyuk ◽  
Svetlana P. Moiseeva
Keyword(s):  
Queueing System ◽  
Impatient Customers ◽  
Unreliable Server ◽  
Retrial Queueing System ◽  
Retrial Queueing

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 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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