Fluid queues driven by a birth and death process with alternating flow rates

P R Parthasarathy,K V Vijayashree,R B Lenin

doi:10.1155/s1024123x0420103x

P R Parthasarathy, K V Vijayashree + Show 1 more

Open Access

https://doi.org/10.1155/s1024123x0420103x

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Abstract

Fluid queue driven by a birth and death process (BDP) with only one negative effective input rate has been considered in the literature. As an alternative, here we consider a fluid queue in which the input is characterized by a BDP with alternating positive and negative flow rates on a finite state space. Also, the BDP has two alternating arrival rates and two alternating service rates. Explicit expression for the distribution function of the buffer occupancy is obtained. The case where the state space is infinite is also discussed. Graphs are presented to visualize the buffer content distribution.

Highlights

Recent measurements have revealed that in high-speed telecommunication networks, like the ATM-based broadband ISDN, traffic conditions exhibit long-range dependence and burstiness over a wide range of time scales
Fluid models driven by finite state Markov processes that modulate the input rate in the fluid buffer have been analyzed by many authors
Lenin and Parthasarathy [2] provide closed-form expressions for the eigenvalues and eigenvectors for fluid queues driven by an M/M/1/N queue

Summary

Introduction

Recent measurements have revealed that in high-speed telecommunication networks, like the ATM-based broadband ISDN, traffic conditions exhibit long-range dependence and burstiness over a wide range of time scales Fluid models characterize such a traffic as a continuous stream with a parameterized flow rate. Our aim is to obtain the stationary distribution function of the buffer occupancy for this fluid model which is modulated by a BDP with two alternating arrival rates and two alternating service rates. This modulating Markov process can be visualized as a simple case of a two-state Markov Modulated Poisson Process which is characterized. It may be helpful to think of credit as the energy which the server gathers during lean traffic period and consumes when the traffic is bursty

Model description

Finite state space

Infinite state space

Numerical illustrations