WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 14, 2015
On a Two-Variable Functional Equation Arising from Databases
Authors: , ,
Abstract: Functional equations offer a tool for narrowing the models used to describe many phenomena. Recently, a certain class of functional equations stems when obtaining the generating functions of queueing systems distributions. This paper has been motivated by an issue considered by L. Flatto and S. Hahn in [SIAM Journal on Applied Mathematics 44(5), (1984), 1041–1053]. The functional equation obtained there has been converted into a set of conditions on the two-unknowns, which in turn lead to the determination of the main unknown. Another motivation of solving such functional equation comes from the fact that the underlying queueing system has applications in the inventory control of database systems. Unfortunately that solution seems to be a bit too general with many technical assumptions. In this paper we introduce a solution using boundary value problem approach. Our solution is validated, obtained by assuming full symmetry on the system under study, and by the reduction to a Riemann-Hilbert boundary value problem.
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Keywords: Queueing systems, Functional equations, Boundary value problems, Inventory control of database systems
Pages: 265-270
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 14, 2015, Art. #25