Viability, the solution set, and fixed point approximation of hybrid systems

2004 ◽  
Author(s):  
G. Labinaz ◽  
M. Guay
Keyword(s):  
Fixed Point ◽  
Hybrid Systems ◽  
Solution Set ◽  
Point Approximation

Implied costs in loss networks

1989 ◽  
Vol 21 (3) ◽  
pp. 661-680 ◽  
Author(s):  
P. J. Hunt
Keyword(s):  
Fixed Point ◽  
Objective Function ◽  
Rate Of Change ◽  
Loss Networks ◽  
Point Approximation ◽  
Asymptotic Accuracy

Implied costs in loss networks are measures of the rate of change of an objective function with respect to the parameters of the network. This paper considers these costs and the costs predicted by the Erlang fixed-point approximation. We derive exact expressions for the implied costs and consider the asymptotic accuracy of the approximation. We show that the approximation is asymptotically valid in some cases but is not valid in one important limiting regime. We also show that a linearity approximation for the implied costs is asymptotically correct when taken over suitable subsets of links.

scholarly journals Erlang's Fixed-Point Approximation for Performance Analysis of HetNets

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Guozhi Song ◽  
Jigang Wu ◽  
John Schormans ◽  
Laurie Cuthbert
Keyword(s):  
Fixed Point ◽  
Performance Analysis ◽  
Heterogeneous Network ◽  
Multiple Access ◽  
Wireless Systems ◽  
Network System ◽  
Call Blocking ◽  
Analysis And Evaluation ◽  
Point Approximation ◽  
Call Dropping

We consider the analytic modelling of wireless systems with multiple access technologies in the perspective of teletraffic engineering and provide a framework for the performance analysis and evaluation of a wireless HetNet (heterogeneous network) system with both cellular and WLAN access technologies. In particular, an approach with Erlang's fixed-point approximation to calculate the new call blocking and handover call dropping probabilities in such systems is introduced. The model is versatile enough to cover not only cellular/WLAN HetNet systems but other wireless HetNets with difference access technologies in general.

Topological structure of solution sets for control problems governed by semilinear fractional impulsive evolution equations with nonlocal conditions

2020 ◽  
Vol 37 (4) ◽  
pp. 1089-1113
Author(s):  
Yi-rong Jiang ◽  
Qiong-fen Zhang ◽  
Qi-qing Song
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Control Problem ◽  
Mild Solution ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Nonlocal Conditions ◽  
Solution Set ◽  
Impulsive Evolution Equations

Abstract This article investigates the topological structural of the mild solution set for a control problem monitored by semilinear fractional impulsive evolution equations with nonlocal conditions. The $R_{\delta }$-property of the mild solution set is obtained by applying the measure of noncompactness and a fixed point theorem of condensing maps and a fixed point theorem of nonconvex valued maps. Then this result is applied to prove that the presented control problem has a reachable invariant set under nonlinear perturbations. The obtained results are also applied to characterize the approximate controllability of the presented control problem.

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