Arrival Rate Approximation by Nonnegative Cubic Splines

Farid Alizadeh (), Jonathan Eckstein (), Nilay Noyan () and Gábor Rudolf ()
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Farid Alizadeh: Department of Management Science and Information Systems, Business School and RUTCOR, Rutgers University, Piscataway, New Jersey 08854
Jonathan Eckstein: Department of Management Science and Information Systems, Business School and RUTCOR, Rutgers University, Piscataway, New Jersey 08854
Nilay Noyan: Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, Tuzla, 34956 Istanbul, Turkey
Gábor Rudolf: RUTCOR, Rutgers University, Piscataway, New Jersey 08854

Operations Research, 2008, vol. 56, issue 1, 140-156

Abstract: 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.

Keywords: nonlinear programming; applications; probability; statistics; nonparametric (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:56:y:2008:i:1:p:140-156

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