Arrival rate approximation by nonnegative cubic splines

Alizadeh, Farid and Noyan, Nilay and Eckstein, Jonathan and Rudolf, Gabor (2008) Arrival rate approximation by nonnegative cubic splines. Operations Research, 56 (1). 140- 156. ISSN 00030-364X

This is the latest version of this item.

[img]PDF - Registered users only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader

Official URL: http://or.journal.informs.org/cgi/content/abstract/56/1/140


We describe an optimization method to approximate the arrival rate function of a non-homogeneous 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 everywhere nonnegative. 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 sixty 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.

Item Type:Article
Subjects:T Technology > T Technology (General)
Q Science > Q Science (General)
ID Code:9646
Deposited By:Nilay Noyan
Deposited On:26 Oct 2008 18:52
Last Modified:20 Oct 2011 16:34

Available Versions of this Item

Repository Staff Only: item control page