Title: Delay behaviour of internet router under self-similar traffic via rational approximations

Authors: D. Mallikarjuna Reddy; Rajaiah Dasari; Malla Reddy Perati; M. Krishna Reddy

Addresses: Department of Statistics, Kakatiya University, Warangal, Andhra Pradesh, 506-009, India ' Department of Mathematics, Kakatiya University, Warangal, Andhra Pradesh, 506-009, India ' Department of Mathematics, Kakatiya University, Warangal, Andhra Pradesh, 506-009, India ' Department of Statistics, Osmania University, Hyderabad, Andhra Pradesh, 500-007, India

Abstract: It has been reported that local area and wide area network traffic exhibit self-similarity and causes degradation of router performance. Therefore, it is crucial for appropriate design of the router. In this paper, first, the router with self-similar input traffic is modelled as MAP/G/1 queuing system and the same is investigated numerically with MMPP/D/1 queuing system. Rational approximations are made from the power series of an irrational function so as to determine its inverse transform thereby to compute virtual waiting time distribution. Numerical results, namely waiting time distribution and mean waiting time against traffic intensity are computed. The analysis presented in this paper is useful in dimensioning the router.

Keywords: internet routers; self-similarity; delay behaviour; rational approximations; power series; router design; local area networks; LANs; wide area networks; WANs; modelling; queuing systems; waiting time; traffic intensity.

DOI: 10.1504/IJCNDS.2015.067654

International Journal of Communication Networks and Distributed Systems, 2015 Vol.14 No.2, pp.134 - 144

Received: 08 Aug 2013
Accepted: 15 May 2014
Published online: 31 Mar 2015 *

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