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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.)
