Dependence patterns for modeling simultaneous events Articles uri icon

publication date

  • October 2016

start page

  • 19

end page

  • 30

volume

  • 154

international standard serial number (ISSN)

  • 0951-8320

electronic international standard serial number (EISSN)

  • 1879-0836

abstract

  • In this paper we examine in detail some of the modeling capabilities of the stationary m-state BMAP, with simultaneous events up to size k, noted BMAP(m)(k). Specifically, we study the forms of the auto correlation functions of the inter-event times and event sizes. We provide a novel characterization of the functions which is suitable for analyzing the dependence patterns. In particular, this allows one to prove a geometrically decrease to zero of the functions and to identify four correlation patterns, when m=2. The case m >= 3 is illustrated via an extensive simulation study, from which it can be deduced that, as expected, richer structures can be obtained as m increases. In addition, the influence of the dependence patterns for both auto-correlation functions for the BMAP(2) (2) in the counting process has been explored through an empirical analysis. (C) 2016 Elsevier Ltd. All rights reserved.

keywords

  • Batch Markovian arrival process (BMAP); Dependent inter-event times; Dependent event arrivals size; Autocorrelation function; Markovian arrival process; Shocks; System; Failures; Repair; Maps