IIIT Hyderabad Publications
On an Exact Solution of Rate Matrix of QBD Process
Authors: Garimella Ramamurthy
Report no: IIIT/TR/2016/46
It is well known that there is a matrix geometric solution for the equilibrium probability vector of a Quasi-Birth-and-Death process. The computation of such vector involves a rate matrix which is the solution of a matrix quadratic equation. Traditionally rate matrix is computed by iterative procedure. In this research paper, we prove that when the number of states at each level is two, the rate matrix can be computed exactly by an algebraic formula. We generalize the result to arbitrary G/M/1-Type Markov processes
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Centre for Security, Theory and Algorithms
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