### A matrix-algebraic solution to two $K_{m}$ servers in a loopA matrix-algebraic solution to two $K_{m}$ servers in a loop

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 Author van de Liefvoort, Appie ♦ Lipsky, Lester Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1986 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract An explicit steady-state solution is given for any queuing loop made up of two general servers, whose distribution functions have rational Laplace transforms. The solution is in matrix geometric form over a vector space that is itself a direct or Kronecker product of the internal state spaces of the two servers. The algebraic properties of relevant entities in this space are given in an appendix. The closed-form solution yields simple recursive relations that in turn lead to an efficient algorithm for calculating various performance measures such as queue length and throughput. A computational-complexity analysis shows that the algorithm requires at least an order of magnitude less computational effort than any previously reported algorithm. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1986-01-02 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 33 Issue Number 1 Page Count 17 Starting Page 207 Ending Page 223

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Source: ACM Digital Library