Application of point processes estimation to a Metro system

Metro systems are one of the most common transportation method in major cities. As a consequence, modeling and simulation of metro systems under different conditions are important to improve their performance. In this paper, we focus on the modeling of the arrival of passengers on a simple Metro line. In particular, we propose to estimate the parameters of two different point process models for the passenger arrival: a non-homogeneous Poisson process and a Hawkes-Phan process. We present preliminary numerical results based both on real data and data generated using a simulator developed by the authors jointly with MetroValparaiso, Chile.

[1]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[2]  G. Shedler,et al.  Simulation of Nonhomogeneous Poisson Processes by Thinning , 1979 .

[3]  D. Brillinger.  The Identification of Point Process Systems , 1975 .

[4]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[5]  A. Raftery,et al.  Detecting features in spatial point processes with clutter via model-based clustering , 1998 .

[6]  Roy L. Streit,et al.  Poisson Point Processes , 2010 .

[7]  Adrian Baddeley,et al.  Spatial Point Processes and their Applications , 2007 .

[8]  Victor Solo,et al.  Local likelihood estimation of time-variant Hawkes models , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[9]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[10]  A. Hawkes,et al.  A cluster process representation of a self-exciting process , 1974, Journal of Applied Probability.

[11]  A. Dassios,et al.  Exact Simulation of Hawkes Process with Exponentially Decaying Intensity , 2013 .

[12]  H. Akaike,et al.  On Linear Intensity Models for Mixed Doubly Stochastic Poisson and Self-exciting Point Processes , 1982 .

[13]  Y. Ogata.  Space-Time Point-Process Models for Earthquake Occurrences , 1998 .

[14]  R. Gnanadesikan,et al.  Probability plotting methods for the analysis of data. , 1968, Biometrika.

[15]  F. Schoenberg,et al.  Assessment of Point Process Models for Earthquake Forecasting , 2013, 1312.5934.

[16]  Jeffrey D. Scargle,et al.  An Introduction to the Theory of Point Processes, Vol. I: Elementary Theory and Methods , 2004, Technometrics.

[17]  A. Hawkes.  Spectra of some self-exciting and mutually exciting point processes , 1971 .

[18]  Erik A. Lewis,et al.  Self-exciting point process models of civilian deaths in Iraq , 2011, Security Journal.

[19]  E. S. Chornoboy,et al.  Maximum likelihood identification of neural point process systems , 1988, Biological Cybernetics.

[20]  Victor Solo,et al.  Maximum likelihood identification of Hawkes-Pham models with a guaranteed stability condition , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).