Name
Abstract | ||
|---|---|---|
This paper studies the matrix R, which is the minimal nonnegative solution to a nonlinear matrix equation, raised in matrix analytic methods. Based on some partial orders defined on the transition matrix of Markov chains of GI/M/1 type, the monotonicity of the corresponding matrix R and its Perron--Frobenius eigenvalue is investigated. The results are useful in estimating tail probabilities of stationary distributions of Markov chains of GI/M/1 type and constructing upper bounds for the matrix R. Applications to the GI/MAP/1 queue are discussed as well. |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1137/S0895479897311214 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
frobenius eigenvalue,paper study,matrix r,matrix analytic methods,partial order,transition matrix,minimal nonnegative solution,corresponding matrix r,matrix analytic method,partial orders,markov chain,nonlinear matrix equation,queueing theory,stationary distribution,upper bound,eigenvalues,nonnegative matrix | Pascal matrix,Combinatorics,Mathematical optimization,Square root of a 2 by 2 matrix,Nonnegative matrix,Matrix function,Symmetric matrix,Matrix analytic method,Mathematics,Block matrix,Centrosymmetric matrix | Journal |
Volume | Issue | ISSN |
20 | 4 | 0895-4798 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Qi-Ming He | 1 | 230 | 34.21 |