Seminarium  i matematisk statistik fredagen den 22 september
13.50-14.25  i MH227



David Perry, Department of Statistics, The University of Haifa, Israel



A Mountain Process with State Dependent Input and Output and a
Correlated Dam


Abstract

We consider a single machine, subject to breakdown, that produces items
to inventory. While the machine is working (an ON period) there is a net
flow, with general deterministic production rate, into the buffer. As a
result, the production rate minus the demand rate, generate a certain
deterministic increase rate which is state dependent. There are two
different types of OFF periods. One is the repair operation initiated
after a breakdown; the second is a preventive maintenance operation. The
length of an OFF period depends on the preceding ON period. During the
OFF periods there is a deterministic outflow (whose release rule is
general but state dependent), generated by the demand rate. The buffer
content process can then be described as a fluid model called the
mountain process. The main tool employed in determining its steady state
low exploits an equivalence relationship between the mountain process
and a special dam process with general release rule whose jumps are also
state dependent. This study is a continuation and generalization of a
previous work (Perry and Posner, 2000) in which both the production rate
and the demand rate are assumed to be constant.