Asymptotic Analysis of the Output Process in Retrial Queue with Markov-Modulated Poisson Input Under Low Rate of Retrials Condition

2019 ◽  
pp. 315-324 ◽  
Author(s):  
Ivan Lapatin ◽  
Anatoly Nazarov
Keyword(s):  
Asymptotic Analysis ◽  
Retrial Queue ◽  
Output Process ◽  
Poisson Input ◽  
Markov Modulated ◽  
Low Rate

An Asymptotic Analysis of a Queueing System with Markov-Modulated Arrivals

1986 ◽  
Vol 34 (1) ◽  
pp. 105-119 ◽  
Author(s):  
David Y. Burman ◽  
Donald R. Smith
Keyword(s):  
Asymptotic Analysis ◽  
Queueing System ◽  
Markov Modulated

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.

A NOTE ON INFINITE-SERVER MARKOV MODULATED AND SINGLE-SERVER RETRIAL QUEUES

2014 ◽  
Vol 31 (02) ◽  
pp. 1440003
Author(s):  
ZHE DUAN ◽  
MELIKE BAYKAL-GÜRSOY
Keyword(s):  
Queueing Systems ◽  
Retrial Queue ◽  
System Size ◽  
Retrial Queues ◽  
Stochastic Decomposition ◽  
Applied Probability ◽  
Single Server ◽  
The Matrix ◽  
Service Rates ◽  
Markov Modulated

We reconsider the M/M/∞ queue with two-state Markov modulated arrival and service processes and the single-server retrial queue analyzed in Keilson and Servi [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471]. Fuhrmann and Cooper type stochastic decomposition holds for the stationary occupancy distributions in both queues [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471; Baykal-Gürsoy, M and W Xiao (2004). Stochastic decomposition in M/M/∞ queues with Markov-modulated service rates. Queueing Systems, 48, 75–88]. The main contribution of the present paper is the derivation of the explicit form of the stationary system size distributions. Numerical examples are presented visually exhibiting the effect of various parameters on the stationary distributions.

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