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Title: Modeling with the MAP counting process Authors:  Rosa Lillo - Universidad Carlos III de Madrid (Spain) [presenting]
Pepa Ramirez Cobo - Universidad de Cadiz (Spain)
Marcos Gonzalez - Universidad Carlos III de Madrid (Spain)
Abstract: It is known that Markovian arrival processes (MAPs) are very suitable processes for stochastic modeling, among other things because they allow dependent inter-arrival times. This property appears, for example, in the data relating to modern call centers, which are characterized by non-negligible dependence patterns and by significant changes in arrival rates throughout the day. Most of the previous statistical approaches for MAPs are based on the distribution of the inter-arrival times, but in many cases, it is more interesting and practical to take the counting process into account. For this reason, the inference of MAPs processes is approached from the perspective of the associated counting process, of which almost everything is unknown except for the closed-form expression of the counting process' covariance function. New properties concerning the correlation patterns and monotonicity shall be illustrated.