Waiting Time Asymptotic Analysis of a M/M/1 Retrial Queueing System Under Two Types of Limiting Condition

2021 ◽  
pp. 171-185
Author(s):  
Anatoly Nazarov ◽  
Maria Samorodova
Keyword(s):  
Asymptotic Analysis ◽  
Waiting Time ◽  
Queueing System ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Limiting Condition

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

ASYMPTOTIC WAITING TIME ANALYSIS OF A FINITE-SOURCE M/M/1 RETRIAL QUEUEING SYSTEM

2018 ◽  
Vol 33 (3) ◽  
pp. 387-403 ◽  
Author(s):  
E. Sudyko ◽  
A.A. Nazarov ◽  
J. Sztrik
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Simulation Software ◽  
Generalized Exponential Distribution ◽  
Time Analysis ◽  
Asymptotic Results ◽  
Retrial Queueing System ◽  
Software Packages ◽  
Finite Source ◽  
Retrial Queueing

The aim of the paper is to derive the distribution of the number of retrial of the tagged request and as a consequence to present the waiting time analysis of a finite-source M/M/1 retrial queueing system by using the method of asymptotic analysis under the condition of the unlimited growing number of sources. As a result of the investigation, it is shown that the asymptotic distribution of the number of retrials of the tagged customer in the orbit is geometric with given parameter, and the waiting time of the tagged customer has a generalized exponential distribution. For the considered retrial queuing system numerical and simulation software packages are also developed. With the help of several sample examples the accuracy and range of applicability of the asymptotic results in prelimit situation are illustrated showing the effectiveness of the proposed approximation.

scholarly journals On the virtual waiting time for an M/G/1 retrial queue with two types of calls

1993 ◽  
Vol 6 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Bong Dae Choi ◽  
Dong Hwan Han ◽  
Guennadi Falin
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Retrial Queue ◽  
Arrival Rate ◽  
Switching System ◽  
Stieltjes Transform ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Virtual Waiting Time ◽  
Incoming Call

We consider an M/G/1 retrial queueing system with two types of calls which models a telephone switching system. In the case that arriving calls are blocked due to the channel being busy, the outgoing calls are queued in priority group whereas the incoming calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the Laplace-Stieltjes transform of the distribution of the virtual waiting time for an incoming call. When the arrival rate of outgoing calls is zero, it is shown that our result is consistent with the known result for a retrial queueing system with one type of call.

Sign in / Sign up

Export Citation Format

Share Document