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For the \nfirst time, this paper proves the persistent conjecture that - \nin two dimensions - the respective sets, MAP(2) and MEP(2), are \nindeed identical with respect to the stationary behavior. \nFurthermore, this equivalence extends to acyclic MAPs, i.e., \nAMAP(2), so that AMAP(2) MAP(2) MEP(2). For higher orders, \nthese equivalences do not hold. The second-order equivalence is \nestablished via a novel canonical form for the (correlated) \nprocesses. An explicit moment/correlation-matching procedure to \nconstruct the canonical form from the first three moments of the \ninterarrival time distribution and the lag-1 correlation \ncoefficient shows how these compact processes may conveniently \nserve as input models for arrival/service processes in \napplications. (C) 2007 Elsevier B.V. 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