Arrival rate approximation by nonnegative cubic splines
成果类型：
Article
署名作者：
Alizadeh, Farid; Eckstein, Jonathan; Noyan, Nilay; Rudolf, Gabor
署名单位：
Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick; Sabanci University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1070.0443
发表日期：
2008
页码：
140-156
关键词：
摘要：
We describe an optimization method to approximate the arrival-rate function of a nonhomogeneous Poisson process based on observed arrival data. We estimate the function by cubic splines, using an optimization model based on the maximum-likelihood principle. A critical feature of the model is that the splines are constrained to be nonnegative everywhere. We enforce these constraints by using a characterization of nonnegative polynomials by positive semidefinite matrices. We also describe versions of our model that allow for periodic arrival-rate functions and input data of limited time precision. We formulate the estimation problem as a convex nonlinear program, and solve it with standard nonlinear optimization packages. We present numerical results using both an actual record of e-mail arrivals over a period of 60 weeks, and artificially generated data sets. We also present a cross-validation procedure for determining an appropriate number of spline knots to model a set of arrival observations.