ON A MULTI-COMPARTMENT STORAGE MODEL
Abstract
In this thesis, a multi-compartment storage system with one-way flow is studied, which is defined as follows. Let {(X(,n),T(,n))n (GREATERTHEQ) 0} be a Markov renewal process with 0 = T(,0) < T(,1) < ... a.s., and let {X(,n)} take values in a set (L-HOOK EQ) {0,1,2,...}. The imbedded Markov chain {X(,n)} is assumed to be positive recurrent, aperiodic with stationary distribution (pi). For a K-compartment model, define for every i (ELEM) an i.i.d. non-negative vector sequence {V(,n)(i)} = {(V(,n)('(0))(i),V(,n)('(1))(i),...,V(,n)('(K))(i))} independent of {(X(,n),T(,n))} and of {V(,n)(j)} for j (NOT=) i. Also assume for all (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) If at time T(,n), X(,n) = i and V(,n)('(l))(i) > 0, then there is a demand of size V(,n)('(l))(i) upon compartment l, which is tranferred to compartment l + 1, if that much material is available in compartment l at that time. In the above situation, l = 0 is treated as an input into the system via compartment 1, while l = K is treated as an output from the system, taking material from compartment K. For the imbedded, discrete time version of the model, we assume for all l, 0 (LESSTHEQ) l (LESSTHEQ) k, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) exists and is finite. Conditions based on (E(,(pi))V('(0)),E(,(pi))V('(1)),...,E(,(pi))V('(K))) are then obtained under which the levels of certain compartments coverge in distribution to finite random variables, and the levels of the other compartments become finite as discrete time n (--->) (INFIN). For the continuous time version of the model, we restrict ourselves to the two-compartment model. Assume the random variables V(,n)('(i))(j) have finite first and second moments for all j (ELEM) and for i = 0,1,2, and E(,(pi))V('(i)) is finite for i = 0,1,2. Then we obtain the bivariate limit distributions as time t (--->) (INFIN) for the levels of the two compartments, when each level is suitably normalized, for the nine different cases that emerge according to the relationships of E(,(pi))V('(0)), E(,(pi))V('(1)), and E(,(pi))V('(2)) to one another.
Degree
Ph.D.
Subject Area
Statistics
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