Fixed Point Approximation for Multirate Multihop Loss Networks With State-Dependent Routing

2004 ◽  
Vol 12 (2) ◽  
pp. 361-374 ◽  
Author(s):  
M. Liu ◽  
J.S. Baras
Keyword(s):  
Fixed Point ◽  
Loss Networks ◽  
Point Approximation ◽  
State Dependent

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.

Implied costs in loss networks

1989 ◽  
Vol 21 (03) ◽  
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 A reduced load approximation accounting for link interactions in a loss network

2003 ◽  
Vol 7 (4) ◽  
pp. 229-248 ◽  
Author(s):  
M. R. Thompson ◽  
P. K. Pollett
Keyword(s):  
Fixed Point ◽  
Network Performance ◽  
Accurate Determination ◽  
Telecommunications Networks ◽  
Reasonable Time ◽  
Loss Networks ◽  
Point Approximation ◽  
Exact Determination ◽  
Reduced Load Approximation

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimen- sioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation that improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

scholarly journals About the Existence Results of Fractional Neutral Integrodifferential Inclusions with State-Dependent Delay in Fréchet Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Selvaraj Suganya ◽  
Dumitru Baleanu ◽  
Siva Selvarasu ◽  
Mani Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Semigroup Theory ◽  
Existence Results ◽  
Fréchet Spaces ◽  
State Dependent ◽  
Nonlinear Alternative ◽  
State Dependent Delay ◽  
Multivalued Contractions

A recent nonlinear alternative for multivalued contractions in Fréchet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral integrodifferential inclusions (FNIDI) with state-dependent delay (SDD). An example is described to represent the hypothesis.

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