ABSTRACT
We use the standard notation for the Markovian arrival process (MAP) and assume fa miliari ty with the classical properties and examples as t reated in the surveys of Lucantoni (1991) and Neuts ( 1992) . The discussion is organized around three major themes:
• The mathematical descriptors of qualitative behavior of the lIIAP. • The computat ional problems of MAPs with many phases.
