Invariant subspaces of matrices with applications
Invariant subspaces of matrices with applications
Rational iterative methods for the matrix sign function
SIAM Journal on Matrix Analysis and Applications
Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I
Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I
The solution of quasi birth and death processes arising from multiple access computer systems
The solution of quasi birth and death processes arising from multiple access computer systems
A new paradigm in teletraffic analysis of communication networks
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 3
Approximation models of feed-forward G/G/1/N queueing networks with correlated arrivals
Performance Evaluation
Capacity of multiservice WCDMA networks with variable GoS
Wireless Networks
Journal of Computational and Applied Mathematics
A simple algorithm for the rate matrices of level-dependent QBD processes
Proceedings of the 5th International Conference on Queueing Theory and Network Applications
Identifying Good Nursing Levels: A Queuing Approach
Operations Research
Journal of Network and Computer Applications
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In this paper, we present a novel algorithmic approach, the hybrid matrix geometric/invariant subspace method, for finding the stationary probability distribution of the finite QBD process which arises in performance analysis of computer and communication systems. Assuming that the QBD state space is defined in two dimensions with m phases and K+1 levels, the solution vector for level k, \pi_k, 0 \leq k \leq K is shown to be in a modified matrix geometric form \pi_k = v_1 R_1^k + v_2 R_2^{K-k} where R_1 and R_2 are certain solutions to two nonlinear matrix equations and v_1 and v_2 are vectors to be determined using the boundary conditions. We show that the matrix geometric factors R_1 and R_2 can simultaneously be obtained independently of K via finding the sign function of a real matrix by an iterative algorithm with quadratic convergence rates. The time complexity of obtaining the coefficient vectors v_1 and v_2 is shown to be O(m^3 \log_2 K) which indicates that the contribution of the number of levels on the overall algorithm is minimal. Besides the numerical efficiency, the proposed method is numerically stable and in the limiting case of K \rightarrow \infty, it is shown to yield the well-known matrix geometric solution \pi_k = \pi_0 R_1^k for the infinite QBD chain.