Arrival rate approximation by nonnegative cubic splines

作     者：Alizadeh, Farid Eckstein, Jonathan Noyan, Nilay Rudolf, Gabor 

作者机构：Rutgers State Univ Sch Business Dept Management Sci & Informat Syst Piscataway NJ 08854 USA Rutgers State Univ RUTCOR Piscataway NJ 08854 USA Sabanci Univ Fac Engn & Nat Sci TR-34956 Istanbul Turkey 

出 版 物：《OPERATIONS RESEARCH》 (运筹学)

年 卷 期：2008年第56卷第1期

页      面：140-156页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：SIMULATING POISSON PROCESSES DATABASES ALGORITHM TRENDS 

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.