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Transient solutions of some multiserver queueing systems with finite spaces
Author(s) -
Chaudhry M.L.,
Zhao Y.Q.
Publication year - 1999
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.1999.tb00149.x
Subject(s) - eigenvalues and eigenvectors , queueing theory , markov chain , computation , transient (computer programming) , mathematics , stochastic matrix , matrix (chemical analysis) , layered queueing network , algebra over a field , computer science , pure mathematics , algorithm , physics , statistics , materials science , quantum mechanics , composite material , operating system
Abstract The purpose of this paper is to provide explicit transient solutions for the multiserver queueing system Geom ( n )/ Geom ( n )/ c / N + c . The method proposed here can also be used for obtaining transient solutions of Markov chains having the transition matrix of Hesselberg type. To support this, we also consider a more complex model such as GI / M / c / N + c . In our analysis, we use eigenvalues and generalized eigenvectors of transition probability matrices. Since we use the Jordan canonical form from linear algebra, the method is good even if the eigenvalues are repeated. Numerical procedures for computations involved in various examples are also provided.