TITLE:  On Recurrence and Transience in Heavy-Tailed Generalized Semi-Markov Processes

SPEAKER:  Peter J. Haas, IBM Research

ABSTRACT:

The generalized semi-Markov process (GSMP) is the usual model for the underlying stochastic process of a complex discrete-event system. It is important to understand fundamental behavioral properties of the GSMP model, such as the conditions under which the states of a GSMP are recurrent. For example, recurrence is necessary for the validity of steady-state simulation output analysis methods such as the regenerative method, spectral method, and the method of batch means. We review some sufficient conditions for recurrence in irreducible finite-state GSMPs. These conditions include requirements on the "clocks" that govern the occurrence times of state transitions. For example, each clock-setting distribution must have finite mean. We then show that, in contrast to ordinary semi-Markov processes, an
irreducible finite-state GSMP can have transient states in the presence of multiple clock-setting distributions with heavy tails. (Joint work with Peter Glynn.)