## About

340

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Introduction

Professor in Computer Science and Operations Research at Université de Montreal, and Inria International Research Chair in Rennes, France.
Please do not ask me full text of publications (I do not have time to manage that); look for the links on my web page instead.

Additional affiliations

September 1990 - present

## Publications

Publications (340)

Based on data from real call centers, we develop, test, and compare forecasting methods to predict the waiting time of a call upon its arrival to the center, or more generally of a customer arriving to a service system. We are interested not only in estimating the expected waiting time, but also its probability distribution (or density), conditiona...

The generalized likelihood ratio (GLR) method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances. We put the GLR methods from previous work into a single framework, simplified regularity conditions to justify the unbiasedness of GLR, and relaxed some of those conditions that are d...

Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods include histograms and kernel density estimators. In this review paper, we are interested instead in the situat...

Reinforcement learning constantly deals with hard integrals, for example when computing expectations in policy evaluation and policy iteration. These integrals are rarely analytically solvable and typically esimated with the Monte Carlo method, which induces high variance in policy values and gradients. In this work, we propose to replace Monte Car...

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean in the sense that, for the best popular non-parametric density estimators, the mean integrated square error converges more slowly than at the canonical rate of O(1=n). When the sample is generated from a simulation model and we...

We study quasi-Monte Carlo (QMC) integration of smooth functions defined over the multi-dimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new construction-free median QMC rule which can exploit the smoothness and the weights of function spaces adaptively. For weighted Korobov spaces, we draw a sample of $r$ independent ge...

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the s-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets o...

We explore the use of Array-RQMC, a randomized quasi-Monte Carlo method designed for the simulation of Markov chains, to reduce the variance when simulating stochastic biological or chemical reaction networks with \(\tau \)-leaping. The task is to estimate the expectation of a function of molecule copy numbers at a given future time T by the sample...

Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods include histograms and kernel density estimators. In this review paper, we are interested instead in the situat...

We consider the problem of estimating the density of a random variable X that can be sampled
exactly by Monte Carlo (MC). We investigate the effectiveness of replacing MC by randomized
quasi Monte Carlo (RQMC) or by stratfieed sampling over the unit cube, to reduce the integrated
variance (IV) and the mean integrated square error (MISE) for kernel...

We study a solution approach for a staffing problem in multi-skill call centers. The objective is to find a minimal-cost staffing solution while meeting a target level for the quality of service to customers. We consider a common situation in which the arrival rates are unobserved random variables for which preliminary forecasts are available in a...

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the $s$-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets...

Monte Carlo (MC) methods use independent uniform random numbers to sample realizations of random variables and sample paths of stochastic processes, often to estimate high‐dimensional integrals that can represent mathematical expectations. Randomized quasi‐Monte Carlo (RQMC) methods replace the independent random numbers by dependent uniform random...

We explore the use of Array-RQMC, a randomized quasi-Monte Carlo method designed for the simulation of Markov chains, to reduce the variance when simulating stochastic biological or chemical reaction networks with $\tau$-leaping. We find that when the method is properly applied, variance reductions by factors in the thousands can be obtained. These...

We consider a multistage stochastic discrete program in which constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation. We study a sample average approximation (SAA) approach that uses nested sampling, in which at each stage, a number of scenarios are examined and a number of simulation r...

We propose a new unbiased stochastic gradient estimator for a family of stochastic models with uniform random numbers as inputs. By extending the generalized likelihood ratio (GLR) method, the proposed estimator applies to discontinuous sample performances with structural parameters without requiring that the tails of the density of the input rando...

We are interested in Monte Carlo simulations of discrete-time Markov chains on discrete and totally ordered state spaces. To improve simulation efficiency, we use a technique previously introduced in the context of quasi-Monte Carlo simulation of an array of N Markov chains. This method simulates the N copies of the chain simultaneously, reorders t...

This book presents the refereed proceedings of the 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Rennes, France, and organized by Inria, in July 2018. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings...

Digital nets are among the most successful methods to construct low-discrepancy point sets for quasi-Monte Carlo integration. Their quality is traditionally assessed by a measure called the t-value. A refinement computes the t-value of the projections over subsets of coordinates and takes a weighted average (or some other function) of these values....

Digital nets are among the most successful methods to construct low-discrepancy point sets for quasi-Monte Carlo integration. Their quality is traditionally assessed by a measure called the $t$-value. A refinement computes the $t$-value of the projections over subsets of coordinates and takes a weighted average (or some other function) of these val...

We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering, and computational statistics. The method uses independent trials starting from a single particle. We exploit th...

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular density estimators, the mean integrated square error converges slower than at the canonical rate of $\mathcal{O}(1/n)$. When the sample is generated from a simulation model and we have co...

Array-RQMC has been proposed as a way to effectively apply randomized quasi-Monte Carlo (RQMC) when simulating a Markov chain over a large number of steps to estimate an expected cost or reward. The method can be very effective when the state of the chain has low dimension. For pricing an Asian option under an ordinary geometric Brownian motion mod...

We extend a quasi-Monte Carlo scheme designed for coagulation to the simulation of the coagulation–fragmentation equation. A number N of particles is used to approximate the mass distribution. After time discretization, three-dimensional quasi-random points decide at every time step whether the particles are undergoing coagulation or fragmentation....

We study and compare various methods to generate a random variate or vector from the univariate or multivariate normal distribution truncated to some finite or semi-infinite region, with special attention to the situation where the regions are far in the tail. This is required in particular for certain applications in Bayesian statistics, such as t...

We consider the problem of estimating the density of a random variable $X$ that can be sampled exactly by Monte Carlo (MC) simulation. We investigate the effectiveness of replacing MC by randomized quasi Monte Carlo (RQMC) to reduce the integrated variance (IV) and the mean integrated square error (MISE) for histograms and kernel density estimators...

We survey basic ideas and results on randomized quasi-Monte Carlo (RQMC) methods, discuss their practical aspects, and give numerical illustrations. RQMC can improve accuracy compared with standard Monte Carlo (MC) when estimating an integral interpreted as a mathematical expectation. RQMC estimators are unbiased and their variance converges at a f...

We consider a network whose links have random capacities and in which a certain target amount of flow must be carried from some source nodes to some destination nodes. Each destination node has a fixed demand that must be satisfied and each source node has a given supply. We want to estimate the unreliability of the network, defined as the probabil...

We study the lattice structure of random number generators of the MIXMAX family, a class of matrix linear congruential generators that produces a vector of random numbers at each step. The design of these generators was inspired by Kolmogorov K-systems over the unit torus in the real space, for which the transition function is measure preserving an...

Random number generators were invented before there were symbols for writing numbers, and long before mechanical and electronic computers. All major civilizations through the ages found the urge to make random selections, for various reasons. Today, random number generators, particularly on computers, are an important (although often hidden) ingred...

The search neutrality debate is about whether search engines should or should not be allowed to uprank certain results among the organic content matching a query. This debate is related to that of network neutrality , which focuses on whether all bytes being transmitted through the Internet should be treated equally. In a recent paper, we have form...

We review the Array-RQMC method, its variants, sorting strategies, and convergence results. We are interested in the convergence rate of measures of discrepancy of the states at a given step of the chain, as a function of the sample size , and also the convergence rate of the variance of the sample average of a (cost) function of the state at a giv...

We examine the requirements and the available methods and software to provide (or imitate) uniform random numbers in parallel computing environments. In this context, for the great majority of applications, independent streams of random numbers are required, each being computed on a single processing element at a time. Sometimes, thousands or even...

We propose, develop, and compare new stochastic models for the daily arrival rate in a call center. Following standard practice, the day is divided into time periods of equal length (e.g., 15 or 30 minutes), the arrival rate is assumed random but constant in time in each period, and the arrivals are from a Poisson process, conditional on the rate....

The effective management of call centers is a challenging task, mainly because managers consistently face considerable uncertainty. One important source of this uncertainty is the call arrival rate, which is typically time-varying, stochastic, dependent across time periods and call types, and often affected by external events. The accurate modeling...

This chapter covers the basic design principles and methods for uniform random number generators used in simulation. We also briefly mention the connections between these methods and those used to construct highly-uniform point sets for quasi-Monte Carlo integration. The emphasis is on the methods based on linear recurrences modulo a large integer,...

Traditionally, both researchers and practitioners rely on standard Erlang queueing models to analyze call center operations. Going beyond such simple models has strong implications, as is evidenced by theoretical advances in the recent literature. However, there is very little empirical research to support that body of theoretical work. In this pap...

Gerber and Chopin combine SMC with RQMC to accelerate convergence. They apply RQMC as in the array-RQMC method discussed below, for which convergence rate theory remains thin despite impressive empirical performance. Their proof of o(N −1/2) convergence rate is a remarkable contribution. Array-RQMC simulates an array of N dependent realizations of...

We introduce a new software tool and library named Lattice Builder, written in C++, that implements a variety of construction algorithms for good rank-1 lattice rules. It supports exhaustive and random searches, as well as component-by-component (CBC) and random CBC constructions, for any number of points, and for various measures of (non)uniformit...

In spite of its tremendous economic significance, the problem of sales staff schedule optimization for retail stores has received relatively scant attention. Current approaches typically attempt to minimize payroll costs by closely fitting a staffing curve derived from exogenous sales forecasts, oblivious to the ability of additional staff to (some...

The call center managers at Hydro-Québec (HQ) need to deliver both low operating costs and high service quality. Their task is especially difficult because they need to handle a large workforce (more than 500 employees) while satisfying an incoming demand that is typically both time-varying and uncertain. The current techniques for determining the...

We study call routing policies for call centers with multiple call types and multiple agent groups. We introduce new weight-based routing policies where each pair (call type, agent group) is given a matching priority deﬁned as an aﬃne combination of the longest waiting time for that call type and the longest idle time or the number of idle agents i...

We propose an adaptive parameterized method to approximate the zero-variance change of measure for the evaluation of static network reliability models, with links subject to failures. The method uses two rough approximations of the unreliability function, conditional on the states of any subset of links being fixed. One of these approximations, bas...

We study static network reliability models in which the component failures are not independent. To model the dependence and also to develop effiective simulation methods that estimate the system unreliability, we extend the static model into an auxiliary dynamic model where the components fail at random time, according to a Marshall-Olkin multivari...

When a customer searches for a keyword at a classified ads website, at an online retailer, or at a search engine (SE), the platform has exponentially many choices in how to sort the output to the query. The two extremes are (a) to consider a ranking based on relevance only, which attracts more customers in the long run because of perceived quality,...

We propose a two-stage stochastic version of the classical economic dispatch problem with alternating-current power flow constraints, a nonconvex optimization formulation that is central to power transmission and distribution over an electricity grid. ...

In a static network reliability model, one typically assumes that the failures of the components of the network are independent. This simplifying assumption makes it possible to estimate the network reliability efficiently via specialized Monte Carlo algorithms. Hence, a natural question to consider is whether this independence assumption can be re...

The cross-entropy method is a versatile heuristic tool for solving difficult estimation and optimization problems, based on Kullback–Leibler (or cross-entropy) minimization. As an optimization method it unifies many existing population-based optimization heuristics. In this chapter we show how the cross-entropy method can be applied to a diverse ra...

Grand challenges are significant themes that can bring together researchers to bring significant change to a field. In 2012 a new initiative to restart the debate on major grand challenges for modeling and simulation (M&S) began. Leading researchers have presented M&S Grand Challenges in areas such as ubiquitous simulation, high performance computi...

The effect on multiskill call-center performance of pooling dependent call types is investigated. For this purpose, a copula-based modeling approach is used to provide multivariate models that take into account the call types’ asymmetric dependence structures found in empirical data. Then, the realistic input models of the call-type-dependent arriv...

We propose an approach to characterize the behavior of classes using dynamic coupling distributions. To this end, we propose a general framework for modeling execution possibilities of a program by defining a probabilistic model over the inputs that drive the program. Because specifying inputs determines a particular execution, this model defines i...