The Second Order Asymptotic Analysis Under Heavy Load Condition for Retrial Queueing System MMPP/M/1

2015 ◽  
pp. 344-357 ◽  
Author(s):  
Ekaterina Fedorova
Keyword(s):  
Asymptotic Analysis ◽  
Queueing System ◽  
Load Condition ◽  
Second Order ◽  
Heavy Load ◽  
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 Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

2020 ◽  
Vol 20 (4) ◽  
pp. 534-547
Author(s):  
Ekaterina A. Fedorova ◽  
◽  
Anatoly A. Nazarov ◽  
Mais P. Farkhadov ◽  
◽  
...  
Keyword(s):  
Asymptotic Analysis ◽  
Retrial Queue ◽  
Load Condition ◽  
System Capacity ◽  
Stationary Mode ◽  
Single Server ◽  
Numerical Comparison ◽  
Heavy Load ◽  
Retrial Queueing System ◽  
Asymptotic Characteristic

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed. It is proved that the asymptotic characteristic function of a number of calls on the orbit has the gamma distribution with the obtained parameters. The value of the system capacity is obtained, so, the condition of the system stationary mode is found. The results of a numerical comparison of the asymptotic distribution and the distribution obtained by simulation are presented. Conclusions about the method applicability area are made.

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