Arrival rate approximation by nonnegative cubic splines

Farid Alizadeh, Jonathan Eckstein, N. Noyan, G. Rudolf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We describe an optimization method to approximate the arrival rate of data such as e-mail messages, website visits, changes to databases, and changes to websites mirrored by other servers. We model these arrival rates as non-homogeneous Poisson process based on observed arrival data. We estimate the arrival function by cubic splines using the maximum likelihood principle. A critical feature of the model is that the splines are constrained to be everywhere nonnegative. We formulate this constraint 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 precision. We formulate the estimation problem as a convex program related to semidefinite programming and solve it with a standard nonlinear optimization package called KNITRO. 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.

Original languageEnglish (US)
Title of host publication2005 IEEE International Conference on Electro Information Technology
StatePublished - Dec 1 2005
Event2005 IEEE International Conference on Electro Information Technology - Lincoln, NE, United States
Duration: May 22 2005May 25 2005

Publication series

Name2005 IEEE International Conference on Electro Information Technology
Volume2005

Other

Other2005 IEEE International Conference on Electro Information Technology
CountryUnited States
CityLincoln, NE
Period5/22/055/25/05

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Keywords

  • Database update frequency
  • E-mail arrival rate
  • Nonhomogeneous poisson process
  • Semidefinite programming
  • Spline approximation

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