Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue

Authors:
Bara Kim;Jeongsim Kim;Jerim Kim
Affiliations:
Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul, Republic of Korea 136-701;Department of Mathematics Education, Chungbuk National University, Chungbuk, Republic of Korea 361-763;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul, Republic of Korea 136-701
Venue:
Queueing Systems: Theory and Applications
Year:
2010

Citing 6
Cited 2

A survey on retrial queues

Queueing Systems: Theory and Applications
A survey of retrial queues

Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications
Modeling and analysis of stochastic systems

Modeling and analysis of stochastic systems
Tail asymptotics for the queue length in an M/G/1 retrial queue

Queueing Systems: Theory and Applications
Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

Queueing Systems: Theory and Applications
Accessible bibliography on retrial queues

Mathematical and Computer Modelling: An International Journal

Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

Queueing Systems: Theory and Applications
Tail asymptotics of the queue size distribution in the M/M/m retrial queue

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a MAP/G/1 retrial queue where the service time distribution has a finite exponential moment. We derive matrix differential equations for the vector probability generating functions of the stationary queue size distributions. Using these equations, Perron---Frobenius theory, and the Karamata Tauberian theorem, we obtain the tail asymptotics of the queue size distribution. The main result on light-tailed asymptotics is an extension of the result in Kim et al. (J. Appl. Probab. 44:1111---1118, 2007) on the M/G/1 retrial queue.