We develop stochastic models of time-dependent arrivals, with focus on the application to call centers. Our models reproduce three essential features of call center arrivals observed in recent empirical studies: a variance larger than the mean for the number of arrivals in any given time interval, a time-varying arrival intensity over the course of a day, and nonzero correlation between the arrival counts in different periods within the same day. For each of the new models, we characterize the joint distribution of the vector of arrival counts, with particular focus on characterizing how the new models are more flexible than standard or previously proposed models. We report empirical results from a study on arrival data from a real-life call center, including the essential features of the arrival process, the goodness of fit of the estimated models, and the sensitivity of various simulated performance measures of the call center to the choice of arrival process model.

Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The huge-period generators proposed so far are not quite optimal in this respect. In this article, we propose new generators of that form with better equidistribution and "bit-mixing" properties for equivalent period length and speed. The state of our new generators evolves in a more chaotic way than for the Mersenne twister. We illustrate how this can reduce the impact of persistent dependencies among successive output values, which can be observed in certain parts of the period of gigantic generators such as the Mersenne twister.

This is a review article on lattice methods for multiple integration over the unit hypercube, with a variance-reduction viewpoint. It also contains some new results and ideas. The aim is to examine the basic principles supporting these methods and how they can be used effectively for the simulation models that are typically encountered in the area of management science. These models can usually be reformulated as integration problems over the unit hypercube with a large (sometimes infinite) number of dimensions. We examine selection criteria for the lattice rules and suggest criteria which take into account the quality of the projections of the lattices over selected low-dimensional subspaces. The criteria are strongly related to those used for selecting linear congruential and multiple recursive random number generators. Numerical examples illustrate the effectiveness of the approach.simulation, variance reduction, quasi-Monte Carlo, low discrepancy, lattice rules

No abstract

Multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variance-reduction purposes, and for making independent replications. A portable set of software utilities is described for uniform randomnumber generation. It provides for multiple generators (streams) running simultaneously, and each generator (stream) has its sequence of numbers partitioned into many long disjoint contiguous substreams. The basic underlying generator for this implementation is a combined multiple recursive generator with period length of approximately 2 191 , proposed in a previous paper. A C++ interface is described here. Portable implementations are available in C, C++, and Java via the On-line Companion to this paper on the Operations Research website.This report is an expanded version of the article by L' Ecuyer et al. (2001).

In this paper we present an efficient way to combine two or more Multiplicative Linear Congruential Generators (MLCGs) and propose several new generators. The individual MLCGs, making up the proposed combined generators, satisfy stringent theoretical criteria for the quality of the sequence they produce (based on the Spectral Test) and are easy to implement in a portable way. The proposed simple combination method is new and produces a generator whose period is the least common multiple of the individual periods. Each proposed generator has been submitted to a comprehensive battery of statistical tests. We also describe portable implementations, using 16-bit or 32-bit integer arithmetic. The proposed generators have most of the beneficial properties of MLCGs. For example, each generator can be split into many independent generators and it is easy to skip a long subsequence of numbers without doing the work of generating them all.

Combining parallel multiple recursive sequences provides an efficient way of implementing random number generators with long periods and good structural properties. Such generators are statistically more robust than simple linear congruential generators that fit into a computer word. We made extensive computer searches for good parameter sets, with respect to the spectral test, for combined multiple recursive generators of different sizes. We also compare different implementations and give a specific code in C that is faster than previous implementations of similar generators.

Abstract. We study an iterative cutting-plane algorithm on an integer program, for minimizing the staffing costs of a multiskill call center subject to service-level requirements which are estimated by simulation. We solve a sample average version of the problem, where the service-levels are expressed as functions of the staffing for a fixed sequence of random numbers driving the simulation.An optimal solution of this sample problem is also an optimal solution to the original problem when the sample size is large enough. Several difficulties are encountered when solving the sample problem, especially for large problem instances, and we propose practical heuristics to deal with these difficulties. We report numerical experiments with examples of different sizes. The largest example corresponds to a real-life call center with 65 types of calls and 89 types of agents (skill groups).