| Summary: | 碩士 === 國立中山大學 === 應用數學研究所 === 84 === This thesis is divided into the following two parts. Part 1.We
give some characterizations of the geometric distribution by
the equality of distributions or the coincidence of
expectations of total service times of two models in Khalil and
Dimitrov (1994), where a single-server queueing system with an
unreliable server is considered.These results can be viewed as
a kind of memoryless property of the geometric distribution.
Part 2.A point process {A(t),t= 0,1,2,...} is said to be a
mixed geometric renewal process of type 0 if and only if there
exist a set \Theta\subset (0,1) and a probability measure \mu
on {\cal B}(\Theta), such that given \alpha\in{\Theta} , the
inter-arrival times are i.i.d. with the common mass function
P_{\alpha}(X=x) ={\alpha}^{x}(1-{\alpha}), x=0,1,2,.... In this
work, we will study some properties of such kind of of
processes.
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