Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
A Numerically E cient Method for the MAP/D/1/K Queue via Rational Approximations
 

Summary: A Numerically E cient Method for the
MAP/D/1/K Queue via Rational Approximations
Nail Akar1
Computer Science Telecommunications, University of Missouri-Kansas City,
5100 Rockhill Road, Kansas City, MO 64110
Erdal Ar kan
Electrical and Electronics Eng. Dept., Bilkent University, 06533 Ankara, Turkey
Abstract
The Markovian Arrival Process (MAP), which contains the Markov Modulated
Poisson Process (MMPP) and the Phase-Type (PH) renewal processes as special
cases, is a convenient tra c model for use in the performance analysis of Asyn-
chronous Transfer Mode (ATM) networks. In ATM networks, packets are of xed
length and the bu ering memory in switching nodes is limited to a nite num-
ber K of cells. These motivate us to study the MAP/D/1/K queue. We present
an algorithm to compute the stationary virtual waiting time distribution for the
MAP/D/1/K queue via rational approximations for the deterministic service time
distribution in transform domain. These approximations include the well-known
Erlang distributions and the Pade approximations that we propose. Using these
approximations, the solution for the queueing system is shown to reduce to the
solution of a linear di erential equation with suitable boundary conditions. The

  

Source: Akar, Nail - Department of Electrical and Electronics Engineering, Bilkent University

 

Collections: Engineering