Package jline.api.mam

Class Mam_is_renewal_map

java.lang.Object
jline.api.mam.Mam_is_renewal_map
public final class Mam_is_renewal_map extends Object
True if a process (D0, D1) is a renewal process.

A renewal process embedded as a MAP has D1 = t * alpha (rank one): the phase entered after an event does not depend on the phase the process was in at that event, so successive interevent times are independent and the process is fully described by its marginal.

The test is on the algebraic structure alone, so it holds equally for a MAP, a matrix-exponential (ME) and a rational arrival process (RAP): an ME renewal stream satisfies it, a correlated MAP or RAP does not. That is what makes it the right guard in front of any closed form that reads only the marginal (a PH pair (pie, D0), a mean and an SCV), because such a form is exact for a renewal input and silently discards the correlation otherwise.

Mirrors MATLAB mam_is_renewal_map.m and python _is_renewal_map in the MAM handler.

  • Method Details

    • mam_is_renewal_map

      public static boolean mam_is_renewal_map(Matrix D0, Matrix D1)