Dependence patterns for modeling simultaneous events

作者：Rodriguez Joanna^*; Lino Rosa E; Ramirez Cobo Pepa

来源：Reliability Engineering & System Safety, 2016, 154: 19-30.

DOI：10.1016/j.ress.2016.05.008

• Batch Markovian arrival process (BMAP)
• Dependent inter-event times
• Dependent event arrivals size
• Autocorrelation function

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.

• 出版日期2016-10