• O. Ait-Hellal, E. Altman, ``Stability of ABR congestion control using the theory of delayed differential equations'',  International Journal of Systems Science, Vol. 34, Numbers 10-11, 15 August- 15 September 2003, pp. 575-584.Abstract Download(.pdf)

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Ait-Hellal, E. Altman, ``Stability of ABR congestion control using the theory of delayed differential equations'', International Journal of Systems Science, Vol. 34, Numbers 10-11, 15 August- 15 September 2003, pp. 575-584.

In this paper, we investigate the stability of the Fixed Point, ERAQLES, and ERICA ABR congestion algorithms. By using the stabiitlity theory of delayed differential equations, we get the stability conditions for each algorithm and examples whee these algorithms fail to be stable are given. We show that for a range of control parameters, meither the fixed point nor ERAQLES algorithms are stable, whatever the network parameters are (round trip times, etc...).

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P. Dube, O. Ait-Hellal, E. Altman, "On Loss Probabilities in Presence of Redundant Packets with Random Drop”, in Performance Evaluation 53, pp. 147-167, 2003.

The purpose of this paper is to study the loss probabilities of messages in an M/M/1/K queueing system where in addition to losses due to buffer overflow there are also random losses in the incoming and outgoing links. We focus on the influence of adding redundant packets to the messages (as in error correction coding, e.g. Reed–Solomon code, etc.). In the first part we use multi-dimensional probability generating functions for solving the recursions which generalize those introduced by Cidon et al. [IEEE Trans. Inform. Theory 39 (1) (1993) 98] for computing the loss probabilities and derive analytical formulae for a special case. In the second part of the paper we use combinatorial arguments and Ballot theorem results to alternatively obtain the loss probabilities. The analytical results allow us to investigate when does adding redundancy decrease the loss probabilities.

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O. Ait-Hellal, L. Yamamoto, L. Kuty, G. Leduc, ``Layered multicast using a TCP friendly algorithm'', Research report, University of Liege, Belgium, 2000.

The heterogeneity of receivers is a crucial problem in multicast delivery; different routes may experience different network conditions. When using a source based protocol, the session performance is often imposed by the less successful elements of the network (e.g. slow receivers or congested paths). To tackle this problem, the more convenient and elegant way is to divide the stream into many layers, and give the ability to the receivers to choose the number of layers they can subscribe to, with reasonable loss rate. In this context, many receiver-based adaptation schemes have been proposed. However, most of them do not achieve fairness, mainly between different sessions and towards TCP. Others require complex coordination mechanisms. In this paper, we present a simple and flexible algorithm for layered multicast, in which the receivers adapt the number of layers they receive to the network conditions. We show that the algorithm achieves intra-sessions and inter-session fairness as well as fairness towards TCP, without requiring any coordination among receivers.}

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Cycle-Based TCP-Friendly algorithm

Several TCP-Friendly algorithms have been recently proposed to support multimedia applications. These algorithms try to mimic the congestion control behavior of TCP. However, the oscillatory (bursty) nature of TCP traffic widely known to be unsuitable for many real time applications. This behavior often results in annoying QoS oscillations for the users. In the present paper we describe a new TCP-Friendly algorithm based on the TCP cycle estimation. We show through simulations that the proposed algorithm is able to smooth the oscillations while keeping fairness towards TCP. We also present a refinement for the parameters of Mathis' formula, which takes the round trip time variation into account.

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O. Ait-Hellal, E. Altman, ``Analysis of TCP-Vegas and TCP-Reno'', Telecommunication Systems 2000.

In this paper we use an analytic fluid model approach in order to anlyze the different features of both Vegas and Reno TCP versions. We then use simulations to confirm our analytic results. When the availbale bandwidth is high, indeed Vegas can retransmit less than one-fifth as much data as Reno does, so that the higher the available bandwidth is, the more efficient Vegas is. However, under heavy congestion (or small buffer size) Vegas behaves like Reno and does not manage to make efficient use of its new mechanism for congestion detection. The analytic results that we obtain are the evolution of the window size, round trip times and their averages, and the average throughput. .

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Performance evaluation of the rate-based flow control mechanism for ABR service

In this paper we investigate the performance of the EFCI-based (Explicit Forward Congestion Indication) and ER-Based (Explicit Rate; EPRCA in perticular) algorithms for the rate-based flow control of the ABR (Available Bit Rate) traffic in ATM networks. We consider the case of multiple switches in tandem. We present several definitions of a bottleneck, and provide conditions that determine which queue is the bottleneck in the chain. We show that is is not necessarilly the queue with the slowest transmission rate that is the "responsible" for a bottleneck. We derive analytic formulas for the maximum queue lenght. We compare our results to those obtained by approximating a network by a simpler one, containing only the bottleneck switch. We show that the maximum queue lenghts under the approximating approach may largely underestimate the ones obtained in the real network. Keywords: ATM, Available Bit Rate, bottleneck, closed-loop congestion control, differential equations, fluid approximations.

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On loss probabilities in presence of redundant packets with random drop Parijat Dube, Omar Ait-Hellal, and Eitan Altman

The purpose of this paper is to study the loss probabilities of messages in an M/M/1/K queueing system where in addition to losses due to buffer overflow there are also random losses in the incoming and outgoing links. We focus on the influence of adding redundant packets to the messages (as in error correction coding, e.g. Reed–Solomon code, etc.). In the first part we use multi-dimensional probability generating functions for solving the recursions which generalize those introduced by Cidon et al. [IEEE Trans. Inform. Theory 39 (1) (1993) 98] for computing the loss probabilities and derive analytical formulae for a special case. In the second part of the paper we use combinatorial arguments and Ballot theorem results to alternatively obtain the loss probabilities. The analytical results allow us to investigate when does adding redundancy decrease the loss probabilities.

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P. Dube, O. Ait-Hellal, E. Altman, "On Loss Probabilities in Presence of Redundant Packets with Random Drop” , in Performance Evaluation 53, pp. 147-167, 2003. PaperID:96i-38d

Rate based flow control with bandwidth information

Omar Ait-Hellal : INRIA B.P. 93, 06902 Sophia Antipolis Cedex, France
Eitan Altman : INRIA B.P. 93, 06902 Sophia Antipolis Cedex, France
Tamer Basar : Coordinated Science Lab, UIUC, Urbana, IL 61801/USA

The ATM Forum has chosen the rate-based approach for flow control of ABR traffic in ATM, and has specified the behavior of the source and destination, as well as the manner in which feedback information should be conveyed back to the source. The decision on the precise control mechanism, however, has been left to the designer of the switches. We propose in this paper a reactive control scheme that is based only on information on the available bandwidth. We analyze its< stability, and test its performance by simulations in the presence of other higher priority CBR or VBR traffic.

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Rate Based Flow Control with Bandwidth Information (1997)

The ATM Forum has chosen the rate-based approach for AEow control of ABR (Available Bit Rate) traOEc in ATM. It is based on a reactive approach whereby the transmission rate of ABR sources can be adapted to the available bandwidth at a bottleneck link. The ATM forum has speciøed the behavior of the source and destination, as well as the manner in which feedback information (on the available bandwidth and on the congestion state of the network) should be conveyed back to the source.

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A robust identification algorithm for traffic models in telecommunications.

There has been a growing interest in MA, AR and ARMA models of traffic in telecommunications networks in recent years. Such models allow not only to identify the characteristics and understand the behavior of traffic, but also allow for (i) the queueing performance analysis and (ii) optimization and control issues. The goal of this paper is to propose a new robust identification approach for the parameters of AR stochastic processes, and use these for analyzing telecommunication traffic data.

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Performance of TCP/IP: the case of two Controlled Sources.

In order to control the AEow in TCP/IP protocol, each TCP source uses a transmission window which indicates the number of packets that may be transmitted by the source but not yet acknowledged by the destination. We consider the Tahoe algorithm [7] developed by Van Jacobson for the adjustment of the window size and the computations of time-out values. This paper analyses the synchronization and coupling that occur between several controlled sources using this algorithm. We restrict to two controlled sources for simplicity of presentation.

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Performance Evaluation of Congestion Phenomena in the Rate Based Flow Control Mechanism for ABR.

In this paper we investigate the performances of the EFCI-based (Explicit Forward Congestion Indication) and ER-based (Explicit Rate; EPRCA in particular) algorithms for the rate-based flow control ofthe ABR (Available Bit Rate) traffic in an ATM network. We consider the case of multiple switches in tandem. We present several definitions of abottleneck, and provide conditions that determine which queue is the bottleneck. We show that it is not necessarily the queue with the slowest trans-mission rate that is "responsible" for a bottleneck. We derive analytic formulas for the maximum queue length. We compare our results to thoseobtained by approximating a network by a simpler one, containing only the bottleneck switch. We show that the maximum queue lengths under the ap-proximating approach may largely underestimate the ones obtained in the real network.

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O. Ait-Hellal, G. Leduc, ``TCP Vegas-Like algorithm for layered multicast transmission''

Layered multicast is probably the most elegant solution to tackle the heterogeneity problem in multicast delivery of real-time multimedia streams. However, the multiple join experiments carried out by different receivers in order to detect the available bandwidth make it hard to achieve fairness. In the present paper, we present a simple protocol, inspired from TCP-Vegas, that reduces considerably the unnecessary join experiments while achieving intra-session and inter-session fairness as well as being TCP-Friendly.

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