## Publication list Omar Aït-Hellal

Publication list Omar Aït-Hellal
Here you find my list of publications, and the links to postscript files (papers submitted to conferences, short versions). To obtain a copy of the original publication (or to give me some feedback), just send me an email.

### Redundancy

O. Ait-Hellal, E. Altman, Alain.Jean-Marie, Irina Kurkova, "On Loss Probabilities in Presence of Redundant Packets and Several Traffic Sources", Submitted to INFOC OMM'99.

The purpose of this paper is to study the effect of adding redundancy to an input stream on the losses that occur due to buffer overflow. We consider several sessions that generate trafic into a finite capacity queue. In most of the paper, the input trafic of each session is modeled by a Poisson input. We use multi-dimensional probability generating functions for solving the recursions introduced by Cidon, Khamisy and Sidi for computing the loss probabilities and derive analytical formulas. Using asymptotic analysis (for large n and small $\rho$), we obtain good approximations with very low complexity of computation and memory. Our analysis allows us to investigate when does adding redundancy decrease the loss probabilities. In many cases, adding capacity is seen to degrade the loss probabilities, which can be explained by the fact that the gain in adding redundancy is not sufficient to compensate the additional losses due to the fact that the trafic load is increased when redundancy is added. We show, however, that it is possible to decrease loss probabilities if a sufficiently large amount of redundancy is added. Indeed, we show that for an arbitrary stationary ergodic input process, if $\rho<1$ then redundancy can improve the performance and reduce loss probabilities to an arbitrarily small value. We compute the rate of additional redundancy required for the case Poisson input processes.

### Flow Control and Stability

O. Ait-Hellal, E. Altman, "Analysis of TCP-Vegas and TCP-Reno" IEEE International Conference on Communications (ICC'97) Montreal, 8-12 June 1997.

In this paper we use an analytic fluid approach in order to analyze the different features of both Vegas and Reno TCP versions. We then use simulations to confirm our analytic results. When the available 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 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.

O. Ait-Hellal, E. Altman, Problems in TCP-Vegas and TCP-Reno'', DNAC (De Nouvelles Architectures pour les Communications), UVSQ, Paris, 3-5 Décembre 1996.

This paper outlines some problems observed, by simulation in Reno and Vegas TCP versions. We describe the two protocols and give examples (obtained by simulation) where these problems can occur. The most serious problem causes in an erroneous estimation of the RTT, and can occur in both Vegas and Reno. Also, we show by an example that the technic which consists on retransmitting packets when we receive the first or second acknowledgment after retransmission can't work in many cases when the retransmission timer (coarse grain timeout) is not sufficiently large (very small as many papers suggested it for ATM networks).

Corrected TCP versions for REAL network simulator

TCP Tahoe, click tahoe.c to get the source.
TCP Reno, click reno.c to get the source.
TCP Vegas, click vegas.c to get the source.

Get also the indispensable file tcp.h
TCP versions for REAL network simulator 5.0

TCP Tahoe, click tahoe.c to get the source.
TCP Reno, click reno.c to get the source.
TCP Vegas, click vegas.c to get the source.
TCP New-Reno, click new_reno.c to get the source.

Get also the indispensable file tcp.h

O. Ait-Hellal, E. Altman, T. Basar, Rate based flow control with bandwidth information'', (invited paper) European Trans. on Telecom. , special issue on ABR, pp. 55-66, 1996. (invited paper) the proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 1996.

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.

O. Ait-Hellal, E. Altman, D. Elwadghiri and M. Erramdani, "Performance Evaluation of the Rate-Based Flow Control Mechanism for ABR Service", INRIA Research Report No. RR-3131. Second IFIP Workshop on Traffic Management and synthesis of ATM networks, Montreal, 24-26 Sept. 1997. To appear in Telecommunication systems, special issue.

In this paper we investigate the performances of the EFCI-based (Explicit Forward Congestion Indication) and ER-based (Explicit Rate) algorithms for the rate-based flow control of the ABR (available Bit Rate) traffic in an ATM network. We consider the case of two switches in tandem. We present several definitions of bottleneck, and provide conditions that determine whether the first, the second or both queues are bottleneck. We show that it is not necessarily the queue with the slowest transmission rate that is responsible'' for a bottleneck. We derive analytic formulas for the maximum queue length. 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 lengths under the approximating approach may largely underestimate the ones obtained in the real network.

O. Ait-Hellal, E. Altman, "Performance Evaluation of the Rate-Based Flow Control Mechanism for ABR Service: Generalization", IEEE INFOCOMM'99, New-York, Feb. 1999.

In this this work, we investigate the performances of the EFCI-based (Explicit Forward Congestion Indication) and ER-based (Explicit Rate) algorithms for the rate-based flow control of the ABR (Available Bit Rate) traffic in an ATM network. 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. We show that it is not necessarily the queue with the slowest transmission rate that is responsible'' for a bottleneck. We derive analytic formulas for the maximum queue length.

O. Ait-Hellal, "Stability Analysis of ABR Congestion Control Algorithms", Submitted.

In this paper, we investigate performances (stability, convergence ...) of the Fixed Point , ERAQLES and ERICA+ ABR congestion control algorithms. By using the stability theory of delayed differential equations, we get the stability conditions for each algorithm and examples where these algorithms are not stable are given. We propose parameters for which ERICA+ is always stable. We show that for a range of available bandwidths neither the Fixed Point nor ERAQLES algorithms are stable, whatever the other parameters are (round trip times, ...).