Exploring correctness and accuracy of solutions to matrix polynomial equations in queues

Spectral expansion and matrix analytic methods are important solution mechanisms for matrix polynomial equations. These equations are encountered in the steady-state analysis of Markov chains with a semi-finite or finite two dimensional lattice of states, which describe a significant class of finite and infinite queues. We prove that the limited size of the eigenspectrum of the matrix geometric representation used in matrix analytic solution mechanisms confines its applicability to systems with a number of eigenvalues less than or equal to the dimension of the matrices used to form the solution. As well as proving this limitation, we relate our experience of a practical queue with generalized exponential traffic whose steady state cannot be represented using one or two rate matrices. We also provide an explanation for the numerical issues creating difficulty in finding matrix geometric solutions for finite queues. While we have not found a solution to these numerical issues,...

• Type: Conference
• Year: 2006
• Where: QEST
• Authors: David Thornley, Harf Zatschler
• Keywords: Matrix, Matrix Analytic Methods, QEST 2006, Quantitative Evaluation Of Systems, Spectral Expansion