Title: Performance analysis of an internet router using the Markovian quasi birth and death process

Authors: Abhilash Vollala; Malla Reddy Perati

Addresses: Department of Mathematics, Kakatiya University, Hanamkonda, 506009, India ' Department of Mathematics, Kakatiya University, Hanamkonda, 506009, India

Abstract: In networking, network nodes play a crucial role, and their performance analysis has greater significance for providing high-quality service. Here, an asynchronous network node with self-similar input traffic is modelled as a single server queuing system with a finite buffer, where the input process is the Markov modulated Poisson process (MMPP), and the service follows an exponential distribution. It is intended to study the behaviour at arbitrary times, which is carried out by using continuous-time Markov chain and a finite quasi birth and death process (QBD). The transient state probability vector of the transition rate matrix is obtained, which, in turn, gives performance metrics. Queuing behaviour is studied through performance metrics, namely blocking probability and mean waiting time (MWT) at arbitrary times, and comparisons are made between steady and transient cases.

Keywords: network node; queuing system; continuous time Markov chain; Markov modulated Poisson process; self-similar traffic; exponential distribution; state probability vector; transition rate matrix.

DOI: 10.1504/IJCSM.2023.134554

International Journal of Computing Science and Mathematics, 2023 Vol.18 No.3, pp.214 - 223

Accepted: 07 Mar 2023
Published online: 27 Oct 2023 *

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