Real eigenvalues of certain tridiagonal matrix polynomials, with queueing applications

DOI10.1016/S0024-3795(01)00462-1zbMath0997.15007MaRDI QIDQ1347935

Winfried K. Grassmann

Publication date: 15 May 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: http://www.mathematicsweb.org/pub/8/4/48/173/27/33/abstract.html

zbMATH Keywords

queueingSturm sequencesreal eigenvaluesmirrored processesquasi birth-death processestridiagonal matrix polynomials

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Eigenvalues, singular values, and eigenvectors (15A18) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Matrices over function rings in one or more variables (15A54)

Related Items (11)

Transient solutions for multi-server queues with finite buffers ⋮ Asymptotics for the late arrivals problem ⋮ A continuous-time queueing model with class clustering and global FCFS service discipline ⋮ The continuous spectrum for theM/M/cqueue ⋮ Explicit formula for positive integer powers of \(k\)-tridiagonal Toeplitz matrices ⋮ Finding equilibrium probabilities of QBD processes by spectral methods when eigenvalues vanish ⋮ Symbolic algorithms for the inverses of general \(k\)-tridiagonal matrices ⋮ A primer of Perron--Frobenius theory for matrix polynomials ⋮ On the inverses of general tridiagonal matrices ⋮ A note on simple eigenvalues of matrix polynomials in queueing models with Erlang distribu\-tions ⋮ q-SERIES IN MARKOV CHAINS WITH BINOMIAL TRANSITIONS

Cites Work

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• Spectral theory for the differential equations of simple birth and death processes
• An analytical solution for a tandem queue with blocking

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