Veronique Inghelbrecht

An Analytical Approach to Obtain the Interdeparture Time Characteristics in a Multistage VoIP Network

In this paper, we investigate the evolution of the interarrival and interdeparture times between voice packets when they are proceeding through a number of network nodes. We model the arrival process in a node as the superposition of a single tagged stream and an independent background process that aggregates the remaining traffic sources. Because we assume that the load of a single voice stream is very low compared to the load of the aggregate traffic, we can represent the tagged voice packets as markers (packets with size zero). We will establish an expression for the probability generating function (pgf) of the interdeparture time of the voice packets after one stage and use this interdeparture-time pgf as the pgf of the interarrival time of the voice packets in the next stage, in order to assess the evolution of the interarrival-time characteristics throughout the network.

Analytic study of the interdeparture time characteristics in a multistage network

In this paper, we will investigate the evolution of the interarrival and interdeparture times between voice packets when they are proceeding through a number of network nodes. But, instead of separately specifying the characteristics of each individual source, we will model the arrival process in a node as the superposition of a single tagged stream and an independent background process that aggregates the remaining traffic sources. Because we assume that the load of a single voice stream is very low compared to the load of the aggregate traffic, we can represent the tagged voice packets as markers (packets with size zero). At the entrance of each network node we thus have the tagged traffic stream, namely the markers, and the background stream. The tagged marker stream is characterized by the consecutive interarrival times between the markers, which are assumed to be identically distributed. The background arrival process, on the other hand, is described on a slot-per-slot basis according to a general i.i.d. process. First, we will establish an expression for the probability generating function (pgf) of the interdeparture time of the voice packets after one stage. We will use this interdeparture-time pgf as the pgf of the interarrival time of the voice packets in the next stage, in order to assess the evolution of the interarrival-time characteristics throughout the network. Also, we will calculate the joint pgf of the interdeparture times between 3 successive voice packets (in case two successive interarrival times may be dependent of each other). To end this paper, we will present some numerical results and draw some conclusions.

Buffer contents and cell delay in a rate adaptation buffer with Markovian arrivals

Abstract This paper investigates the performance of a rate adaptation buffer in the case that the arriving cell stream is generated by an on/off-source, where both the on-periods and the off-periods are geometrically distributed. The ratio between the input rate and the output rate takes an arbitrary integer value greater than one. Under the assumption of an infinite storage capacity, exact explicit expressions are obtained for the mean values and the tail distributions of the buffer contents and the cell delay. Furthermore, an approximation is derived for the cell loss ratio in a finite-capacity buffer. Some numerical results are presented and discussed. Scope and purpose In communication networks a rate adaptation buffer is used at the interface between two consecutive links, when the speed of the incoming link exceeds the speed of the outgoing link, in order to avoid excessive loss of information. So far, only few papers in the literature have investigated the buffer dimensioning of a rate adapter. All of these papers assume an uncorrelated arrival process on the incoming link and/or small differences between the input and the output rates, assumptions which in practice may not always be realistic. The present paper therefore presents and analyzes a discrete-time queueing model for a rate adaptation buffer which both accounts for the presence of correlation in the arrival stream and allows (possibly) large input/output ratios.

Rate adapters with bursty arrivals and rational rate reduction: queueing analysis

Abstract In ATM-based communication networks, the transmission links that interconnect the network nodes do not necessarily operate at the same transmission speeds. If the speed of the incoming link in a node exceeds the speed of the outgoing link, a rate adaptation buffer must be provided in order to avoid frequent cell loss. This paper presents an analytical queueing analysis of a rate adaptation buffer in the case where the cell arrival stream on the incoming link is modeled as an interrupted Bernoulli process and the ratio of the arrival rate versus the transmission rate can take any rational value. Based on a generating-functions approach, an expression for the probability generating function of the buffer contents is derived. From this result, closed-form formulas for several performance measures are obtained. The results are illustrated by some numerical examples.