We consider two model variants of a production-inventory system.
The system is characterized by a producing machine which is
susceptible to failure following which it must be repaired to
make it operative again. The machine's production can also
be stopped deliberately because of stocking capacity limitations.
During ON periods the input into the buffer is continuous and
uniform (until a threshold is reached), whereas during OFF periods
the output from the buffer is a compound Poisson process. We
are interested in computing the equilibrium content level process
under the assumption that full backlogging is allowed. In the
first model, variant OFF periods are independent of the demand
process, and in the second variant, they are determined and
controlled in accordance with a certain level crossing stopping
rule.
Nonadiabatic transition probabilities in the presence of strong dissipation at an avoided-level crossing point