A multivariate Markovian arrival process framework for modeling emergency call counts

M. González, R. E. Lillo, P. Ramírez-Cobo, L. Senade

We analyze a real dataset of multivariate count observations of emergency telephone calls classified into five priority categories. The data exhibit both intra- and inter-component dependence, motivating the use of flexible stochastic models. We propose a five-dimensional extension of the Markovian Arrival Process (MAP) as a suitable framework for modeling such data. The model builds on the two-state Markov Modulated Poisson Process and its multivariate construction via the Marshall–Olkin distribution.

We also address the problem of statistical inference, as only count data are observed and neither the likelihood function nor the joint moments admit closed-form expressions. To overcome this, we adopt an Approximate Bayesian Computation (ABC) approach, initialized through a method-of-moments estimation. The proposed model and inference procedure are validated on real data, showing their ability to capture the dependence structure of emergency call counts.

Keywords: Markov-modulated Poisson process, Counting processes, Marshall-Olkin exponential distribution, correlated count data, Approximate Bayesian computation

GT Procesos Estocásticos y sus Aplicaciones III
September 3, 2026  9:00 AM
Aula 26

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