First passage analysis of a 'square wave' filtered Poisson process

N Kordzakhia*, R. E. Melchers, A. Novikov

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review


    Because of their relatively simple properties, Poisson pulse models are convenient for load modelling. This paper considers the first passage analysis of a train of intermittent load applications each composed of overlapping component rectangular ('square wave') filtered Poisson pulses. The pulses have exponentially distributed inter-arrival times, exponential durations and Gausssian pulse heights. By carefully considering the start and stop of individual pulses over a given time period and applying the Wald's identity to the relevant random walks the Laplace transformation of first passage time is derived and by this, an extended version of the standard (negative exponential) form of probability of exceedence incorporating the average duration of pulses is obtained.

    It is shown that in the limit as pulse duration becomes negligible, the standard first passage solution for Poisson spike processes is recovered. A comparison with Monte Carlo simulation runs for both the generalized result and the spike result is made for different threshold levels.

    Original languageEnglish
    Title of host publicationApplications of statistics and probability, vols 1 and 2
    EditorsRE Melchers, MG Stewart
    Place of PublicationLondon
    PublisherA. A. Balkema
    Number of pages9
    ISBN (Print)9058090868
    Publication statusPublished - 2000
    Event8th International Conference on Applications of Statistics and Probability (ICASP 8) - SYDNEY, Australia
    Duration: 12 Dec 199915 Dec 1999


    Conference8th International Conference on Applications of Statistics and Probability (ICASP 8)




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