Alain Jean-Marie

Markov-modulated Markov chains and the covarion process of molecular evolution.

The covarion (or site specific rate variation, SSRV) process of biological sequence evolution is a process by which the evolutionary rate of a nucleotide/amino acid/codon position can change in time. In this paper, we introduce time-continuous, space-discrete, Markov-modulated Markov chains as a model for representing SSRV processes, generalizing existing theory to any model of rate change. We propose a fast algorithm for diagonalizing the generator matrix of relevant Markov-modulated Markov processes. This algorithm makes phylogeny likelihood calculation tractable even for a large number of rate classes and a large number of states, so that SSRV models become applicable to amino acid or codon sequence datasets. Using this algorithm, we investigate the accuracy of the discrete approximation to the Gamma distribution of evolutionary rates, widely used in molecular phylogeny. We show that a relatively large number of classes is required to achieve accurate approximation of the exact likelihood when the number of analyzed sequences exceeds 20, both under the SSRV and among site rate variation (ASRV) models.

Dynamic configuration of RED parameters [random early detection]

Our work focuses on an adaptive approach to RED, namely ARED (adaptive RED) that performs a constant tuning of RED parameters according to the traffic load. ARED requires no hypothesis on the type of traffic, which diminishes its dependency on the scenario parameters such as the bandwidth, the round-trip time and the number of active connections. Our goal is to find a simple extension to ARED in order to improve the predictability of performance measures like queueing delay and delay jitter without sacrificing the loss rate. To achieve this goal, we propose a new algorithm that sets the RED parameters and evaluate it by extensive simulations. Our results show that compared to the original ARED, our algorithm can stabilize the queue size, keep it away from buffer overflow and underflow, and achieves a more predictable average queue size without substantially increasing the loss rate.

Open-loop video distribution with support of VCR Functionality

Scalable video distribution schemes have been studied for quite some time. For very popular videos, open-loop broadcast schemes have been devised that partition each video into segments and periodically broadcast each segment on a different channel. Open-loop schemes provide excellent scalability as the number of channels required is independent of the number of clients. However, open-loop schemes typically do not support VCR functions. We will show for open-loop video distribution how, by adjusting the rate at which the segments are transmitted, one can provide VCR functionality. We consider deterministic and probabilistic support of VCR functions: depending on the segment rates chosen, the VCR functions are supported either 100% of the time or with very high probability. For the case of probabilistic support of PLAY and Fast-forward (FF) only, we model the reception process as a semi-Markov accumulation process. We are able to calculate a lower bound on the probability of successfully executing FF actions.

The interaction of forward error correction and active queue management

This paper studies the interaction of a forward error correction (FEC) code with queue management schemes like Drop Tail (DT) and RED. Since RED spreads randomly packet drops, it reduces consecutive losses. This property makes RED compatible a priori with the use of FEC at the packet level. We show, through simulations, that FEC combined with RED may indeed be more efficient than FEC combined with DT. This however depends on several parameters like the burstiness of the background traffic, the FEC block size and the amount of redundancy in a FEC block. We conclude generally that using FEC is more efficient with RED than with DT when the loss rate is small, a relatively important amount of redundancy and at most a moderate FEC block size is used. We complement these observations with a simple model, which is able to capture the tradeoff between the locality and the frequency of losses.

Scheduling Services in a Queuing System with Impatience and Setup Costs

We consider a single-server queue in discrete time, in which customers must be served before some limit sojourn time of geometrical distribution. A customer who is not served before this limit leaves the system: it is impatient. The service of customers, the loss due to impatience and the holding of customers in the queue induce costs. The purpose is to decide when to serve the customers so as to minimize them. We use a Markov decision process with infinite horizon and discounted cost. We establish the structural properties of the stochastic dynamic programming operator and we deduce that the optimal policy is of threshold type. In addition, we are able to compute explicitly the optimal value of this threshold in terms of the parameters of problem.

Data replication optimisation in grid delivery network

In this paper, we examine the data replication problem in a particular Grid Delivery Network (GDN) which is a system that provides video services, among which is Video On Demand (VOD). In this system, the data are divided into fixed size blocks which must be replicated on hosts to decrease the total download time. We propose a probabilistic model to optimise the average download time of requests based on the hosts availability and the document size distribution. The objective function induced by this model is a non-linear integer problem. It can be solved in real values by Lagrangian optimisation. We prove that in a particular case, this problem can be reduced to a knapsack problem. We propose approximation algorithms and validate them using simulations with varying characteristics.

Guaranteed Download Time in a Distributed Video on Demand System

The paper deals with the study of the optimisation of the distribution of the download time from a particular Video on Demand System.xa0xa0This VOD system is based on Grid Delivery Network which is an hybrid architecture based on P2P and Grid Computing concepts. In this system, the data arexa0xa0shrunk into fixed size blocks which mustxa0xa0be replicated on hosts toxa0xa0decrease the total download time. We propose an optimal replication factor to optimise the average download time. We showed that the allocation methods are directly correlatedxa0xa0with the variance ofresponse waiting time.xa0xa0xa0We analyse different heuristics to solve these two problems in practice, and validate them through simulation. With our methods, we can guarantee a pre-established waiting response time with an error of approximatively 10 %.

Performance Evaluation of Networks: New Problems and Challenges

The purpose of this talk is to give an introduction to the domain of Performance Evaluation of Networks, its methods and its practical results. The short tour will begin with the classical results and finish with some of the principal challenges faced by the theory today. n nThe concern about mathematically predicting the performance of communication systems is not new: the beginning of the theory is traditionally associated with the work of A.E. Erlang (1917) on the blocking probability for telephone trunk lines. The family of stochastic models used by him and his followers eventually led to Queuing Theory, a wealth of formulas and methods for computing throughputs, waiting times, occupation levels of resources and other performance measures.