A Mathematical Model of Shifted Gamma Distribution for Internet Traffic Packet Delay over a Next Generation Core Internetwork

Abstract

Broadband  Internet  traffic  is transported over the  next generation  core internetworks, which are composed of several IP/MPLS/GE network sections and transport  multi-services. In practice, IP packet delay is normally  measured  in  each  separated  network  section but  not  over  a  whole  internetwork.  It  is  proved  in  the paper  that  packet  delay  distribution  of  Internet  traffic component  in  core  network  sections  can  be approximately  expressed  as  a  shifted  gamma distribution.  Moreover  a  new  explicit  mathematical model  based  on  shifted  gamma  distribution  has  also been proposed to compose delay distribution of Internet traffic  packet  transported  over  a  core  internetwork from  component  ones  in  each  network  section.  It  is resulted from this model that Internet packet delay over an  internetwork  inherits  distribution  properties  from that  over  component  networks.  Other  properties  and parameters  relationship  of  the  model  such  as  additive property of shape and location parameters, the relation between  distribution  lower  moments  and  parameters, the dependence  of distribution  on parameters variation are also exposed in the paper. The proposed model of IP packet  delay  distributions  has  a  certain  scientific significance  and  plays  an  important  role  in  practical performance analysis, network  planning, designing and traffic engineering for improving the quality of service