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A Note on the Dependence Structure of the Two-State Markovian Arrival Process

Published online by Cambridge University Press:  04 February 2016

Pepa Ramírez-Cobo*
Affiliation:
University of Seville
Emilio Carrizosa*
Affiliation:
University of Seville
*
Postal address: Institute of Mathematics, University of Seville, Avda. Reina Mercedes s/n, 41012 Seville, Spain. Email address: jrcobo@us.es
∗∗ Postal address: Department of Statistics and Operations Research, University of Seville, Avda. Reina Mercedes s/n, 41012 Seville, Spain. Email address: ecarrizosa@us.es
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Abstract

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The Markovian arrival process generalizes the Poisson process by allowing for dependent and nonexponential interarrival times. We study the autocorrelation function of the two-state Markovian arrival process. Our findings show that the correlation structure of such a process has a very specific pattern, namely, it always converges geometrically to zero. Moreover, the signs of the autocorrelation coefficients are either constant or alternating.

Type
Research Article
Copyright
© Applied Probability Trust 

References

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