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A queueing model to study the occurrence and duration of ozone exceedances in Mexico City

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  • Juan Martin Barrios
  • Eliane R. Rodrigues

Abstract

It is well known that long-term exposure to high levels of pollution is hazardous to human health. Therefore, it is important to study and understand the behavior of pollutants in general. In this work, we study the occurrence of a pollutant concentration's surpassing a given threshold (an exceedance) as well as the length of time that the concentration stays above it. A general N ( t )/ D /1 queueing model is considered to jointly analyze those problems. A non-homogeneous Poisson process is used to model the arrivals of clusters of exceedances. Geometric and generalized negative binomial distributions are used to model the amount of time (cluster size) that the pollutant concentration stays above the threshold. A mixture model is also used for the cluster size distribution. The rate function of the non-homogeneous Poisson process is assumed to be of either the Weibull or the Musa-Okumoto type. The selection of the model that best fits the data is performed using the Bayes discrimination method and the sum of absolute differences as well as using a graphical criterion. Results are applied to the daily maximum ozone measurements provided by the monitoring network of the Metropolitan Area of Mexico City.

Suggested Citation

  • Juan Martin Barrios & Eliane R. Rodrigues, 2015. "A queueing model to study the occurrence and duration of ozone exceedances in Mexico City," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(1), pages 214-230, January.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:1:p:214-230
    DOI: 10.1080/02664763.2014.939613
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    References listed on IDEAS

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    1. Lucas W. Davis, 2008. "The Effect of Driving Restrictions on Air Quality in Mexico City," Journal of Political Economy, University of Chicago Press, vol. 116(1), pages 38-81, February.
    2. Omosigho, S. E. & Worthington, D. J., 1985. "The single server queue with inhomogeneous arrival rate and discrete service time distribution," European Journal of Operational Research, Elsevier, vol. 22(3), pages 397-407, December.
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