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Full-Text Articles in Physical Sciences and Mathematics
On Some Queue Length Controlled Stochastic Processes, Lev M. Abolnikov, Alexander M. Dukhovny, Jewgeni H. Dshalalow
On Some Queue Length Controlled Stochastic Processes, Lev M. Abolnikov, Alexander M. Dukhovny, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
The authors study the input, output and queueing processes in a general controlled single-server bulk queueing system. It is supposed that inter-arrival time, service time, batch size of arriving units and the capacity of the server depend on the queue length. The authors establish an ergodicity criterion for both the queueing process with continuous time parameter and the embedded process, study their transient and steady state behavior and prove ergodic theorems for some functionals of the input, output and queueing processes. The following results are obtained: Invariant probability measure of the embedded process, stationary distribution of the process with continuous …
Error Bounds For Two Even Degree Tridiagonal Splines, Gary W. Howell
Error Bounds For Two Even Degree Tridiagonal Splines, Gary W. Howell
Mathematics and System Engineering Faculty Publications
We study a C(¹) parabolic and a C(²) quartic spline which are determined by solution of a tridiagonal matrix and which interpolate subinterval midpoints. In contrast to the cubic C(²) spline, both of these algorithms converge to any continuous function as the length of the largest subinterval goes to zero, regardless of “mesh ratios”. For parabolic splines, this convergence property was discovered by Marsden [1974]. The quartic spline introduced here achieves this convergence by choosing the second derivative zero at the breakpoints. Many of Marsden’s bounds are substantially tightened here. We show that for functions of two or fewer coninuous …
A Theorem On Many Fixed Points For Nonlinear Operator, Yong Sun, Jingxian Sun
A Theorem On Many Fixed Points For Nonlinear Operator, Yong Sun, Jingxian Sun
Mathematics and System Engineering Faculty Publications
Multiple fixed points of weakly inward mappings are investigated by means of ordinary differential equations in abstract spaces.