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.

The Use of the Fixed Points Method for Optimal Damping of Harmonically Forced Cantilever Beams

2011 ◽  
Author(s):  
Jimmy S. Issa
Keyword(s):  
Fixed Point ◽  
Objective Function ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Point Force ◽  
Cantilever Beams ◽  
Two Dimensional ◽  
Optimal Damping ◽  
Active Peak

The use of viscous dampers for vibration attenuation in harmonically forced cantilever beams is studied. The system considered is a cantilever beam with a point harmonic force applied at a given location and a viscous damper attached to it from one end, and grounded from the other. An assumed mode model of the system is derived using the first two transverse modes of the beam. For any given positions of the point force and damper, the optimal damping constant which minimizes the maximum of the frequency response function at the tip of the beam is determined analytically. It is shown that the objective function passes through a number of points independent of the damping constant. These inevitable points are used in the determination of the maximum allowable value of the objective function. As the locations of the point force and damper are varied separately from the fixed end of the beam to its tip, a two dimensional region plot is generated illustrating the different regions where each of these points is the highest. The optimal damping constant is determined analytically by forcing the frequency response function to pass horizontally through the highest fixed point which is referred to as the active peak. Four different damping ratios are determined and depending on the positions of the force and damper, the two dimensional map is consulted in the selection of the correct optimal damping ratio. The solution obtained is unique except when the active peak is the static fixed point. In this case, the solution is made unique by modifying the objective function to further enhance the solution at high frequencies.

scholarly journals Fixed point models of loss networks

1989 ◽  
Vol 31 (2) ◽  
pp. 204-218 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Fixed Point ◽  
Capacity Expansion ◽  
Dynamic Routing ◽  
Loss Networks ◽  
Simple Class ◽  
Definition Of

AbstractIn this paper we review a simple class of fixed point models for loss networks. We illustrate how these models can readily deal with heterogeneous call types and with simple dynamic routing strategies, and we outline some of the recent mathematical advances in the study of such models. We describe how fixed point models lead to a natural and tractable definition of the implied cost of carrying a call, and how this concept is related to issues of routing and capacity expansion in loss networks.

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.

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