Power law characteristics and loss probability: finite buffer queueing systems

Author

Sharma, Shachi ; Karmeshu

Author_Institution

IBM Res. Lab., New Delhi, India

Volume

13

Issue

12

fYear

2009

fDate

12/1/2009 12:00:00 AM

Firstpage

971

Lastpage

973

Abstract

Analytical framework based on maximum Tsallis entropy is proposed for studying finite buffer queueing system when information about fractional moment of queue size and utilization is available. The framework enables us to obtain closed form expressions for queue length distribution and loss probability for generalized M/M/1/N system when input to the system possesses power law characteristics. It is shown that queue length distribution depicts power law as the number of units in the system becomes large. A new result for asymptotic loss probability exhibiting power law behavior is derived.

Keywords

information theory; probability; queueing theory; asymptotic loss probability; finite buffer queueing systems; generalized M/M/1/N system; maximum Tsallis entropy; queue length distribution; Analytical models; Brownian motion; Communication networks; Communication system traffic control; Complex networks; Entropy; IP networks; Size measurement; Telecommunication traffic; Traffic control; Queueing system, power law, Tsallis entropy, fractional moment, loss probability, utilization;

fLanguage

English

Journal_Title

Communications Letters, IEEE

Publisher

ieee

ISSN

1089-7798

Type

jour

DOI

10.1109/LCOMM.2009.12.091768

Filename

5353280