Limiting distribution functions of a dam content process with alternating poisson inputs

Abstract

This thesis is to obtain the limiting distribution of a dam content process. It will be pursued under the restriction that input processes are composed of two different continuous stochastic processes, each occurring alternately in a stationary Poisson process and being mutually independent and identically distributed random variables. It is known that the limiting distribution of a finite dam is difficult to solve, while it is not hard for a infinite dam. There, the limiting distribution of the infinite dam was first analyzed. For instance, by use of overflow concept the finite dam can be managed under the framework of the infinite dam. In addition, such finite dam was studied under the restriction of lower bound at which water release is to be stopped in consideration of purposes such as hydro-elec tric power generation and environmental conservation, etc... In order to compute the limiting distribution of the infinite dam the integrodifferential equations of the time dependent content distribution were derived first by application of M/G/l queueing process. Then, Laplace-Stieltjes transform technique was applied to get the limiting distribution of the infinite dam. Under the further restriction that the expected input process is less than the expected output(release) process, the limiting distribution of the infinite dam was solved and applied to find that of the finite dam with nonegative lower bound. Finally, given input processes, some examples were treated to illustrate the limiting distribution computation for dams with various cases of release rate and lower bound.