Marcus theory - Revision history

80.109.22.231: /* Marcus theory */

2014-12-17T17:58:13Z

Marcus theory

← Older revision		Revision as of 19:58, 17 December 2014
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	~~'''Fairness measures''' or [[Metric (mathematics)\|metrics]] are used in [[network engineering]] to determine whether users or applications are receiving a fair share~~ of ~~system resources~~. ~~There are several mathematical and conceptual definitions of fairness.~~		The author is known by the name of Figures Lint. Minnesota is exactly where he's been residing for many years. One of the extremely best issues in the globe for me is to do aerobics and I've been doing it for quite a whilst. Hiring is his profession.<br><br>Look into my blog - [http://inspirationpedi.com/groups/useful-guidance-for-battling-your-yeast-infection/ inspirationpedi.com]
	~~__NOTOC__~~
	~~==TCP fairness==~~
	~~[[Congestion control]] mechanisms~~ for ~~new network transmission protocols or [[peer-to-peer]] applications must interact well with [[Transmission Control Protocol\|TCP]]~~. ~~TCP fairness requires that a new protocol receive no larger share~~ of the ~~network than a comparable TCP flow. This~~ is ~~important as TCP is the dominant transport protocol on the Internet,~~ and ~~if new protocols acquire unfair capacity they tend to cause problems such as [[congestion collapse]]. This was the case with the first versions of [[RealMedia\|RealMedia~~'~~s]] [[Streaming media\|streaming protocol]]:~~ it ~~was based on [[User Datagram Protocol\|UDP]] and was widely blocked at organizational firewalls until~~ a ~~TCP-based version was developed~~.~~{{Citation needed\|date=July 2007}}~~

	~~==Jain's fairness index==~~
	~~[[Raj Jain]]'s equation,~~

	~~:<math>\mathcal{J} (x_1, x_2, \dots, x_n) = \frac{( \sum_{i=1}^n x_i )^2}{n \cdot \sum_{i=1}^n {x_i}^2}</math>~~

	rates the fairness of a set of values where there are <math>n</math> users and <math>x_i</math> is the throughput for the <math>i</math>th connection. The result ranges from <math>\tfrac{1}{n}</math> (worst case) to 1 (best case), and it is ~~maximum when all users receive the same allocation~~. ~~This index is~~ <~~math~~>~~\tfrac{k}{n}~~<~~/math~~> ~~when <math>k</math> users equally share the resource, and the other <math>n~~-~~k</math> users receive zero allocation.~~

	This metric identifies underutilized channels and is not unduly sensitive to atypical network flow patterns.<ref>{{cite journal \|last1=Jain \|first1=R. \|last2=Chiu \|first2=D.M. \|last3=Hawe \|first3=W. \|year=1984 \|title=A Quantitative Measure of Fairness and Discrimination for Resource Allocation in Shared Computer Systems \|journal=DEC Research Report TR-301 \|url=http://~~www1~~.~~cse.wustl.edu~~/~~~jain~~/~~papers/ftp/fairness.pdf}}</ref>~~

	~~==Max~~-~~min fairness==~~
	~~{{main\|Max~~-~~min fairness}}~~
	Max-min fairness is said to be achieved by an allocation if and only if the allocation is feasible and an attempt to increase the allocation of any flow necessarily results in the decrease in the allocation of some other flow with an equal or smaller allocation. A max-min fair allocation is achieved when bandwidth is allocated equally and in infinitesimal increments to all flows until one is satisfied, then amongst the remainder of the flows and so on until all flows are satisfied or the bandwidth is exhausted.

	~~==Fairly shared spectrum efficiency==~~
	In [[packet radio]] [[wireless network]]s, ''The fairly shared spectrum efficiency'' (FSSE) can be used as a combined measure of fairness and [[system spectrum efficiency]]. The system spectral efficiency is the [[aggregate throughput]] in the network divided by the utilized [[radio bandwidth]] in hertz. The FSSE is the portion of the system spectral efficiency that is shared equally among all active users (with at least one backlogged data packet in queue or under transmission). In case of [[scheduling starvation]], the FSSE would be zero during certain time intervals. In case of equally shared resources, the FSSE would be equal to the system spectrum efficiency. To achieve [[max-min fairness]], the FSSE should be maximized.

	~~FSSE is useful especially when analyzing advanced [[radio resource management]] (RRM) schemes,~~ for ~~example [[channel adaptive scheduling]], for cellular networks with [[best~~-effort]] packet data service. In such system it may be tempting to optimize the spectrum efficiency (i.e. the throughput). However, that might result in scheduling starvation of "expensive" users at far distance from the access point, whenever another active user is closer to the same or an adjacent access point. Thus the users would experience unstable service, perhaps resulting in a reduced number of happy customers. Optimizing the FSSE results in a compromise between fairness (especially avoiding scheduling starvation) and achieving high spectral efficiency.

	If the cost of each user is known, in terms of consumed resources per transferred information bit, the FSSE measure may be redefined to reflect [[proportional fairness]]. In a proportional fair system, this "proportionally fair shared spectrum efficiency" (or "fairly shared radio resource cost") is maximized. This policy is less fair since "expensive" users are given lower throughput than others, but still scheduling starvation is avoided.

	~~==See also==~~
	* [[Income inequality metrics]]
	* [[Gini coefficient]]
	* [[Lorenz curve]]

	~~==Notes==~~
	~~{{reflist}}~~

	~~== Further reading ==~~
	* Almeida, A.; Casetti, C.; Oueslati, S.; Avratchenkov, K. & Johansson, M. [http://euronf.enst.fr/archive/127/jra21_deliverable_final.pdf#page=6 A Taxonomy of Congestion Control (in deliverable No: D.WP.JR.2.1.1)] EuroNGI, 2004
	* {{Cite journal \|last1=Mo \|first1=J. \|last2=Walrand \|first2=J. \|year=2000 \|title=Fair End-to-~~End Window~~-~~Based Congestion Control \|journal=IEEE~~/~~ACM Transactions on Networking \|volume=8 \|pages=556–567 \|url=http://fleece~~.~~ucsd.edu/~tjavidi/ECE257A/MoWalrand.pdf \|doi=10.1109/90.879343 }}~~

	~~{{DEFAULTSORT:Fairness Measure}}~~
	~~[[Category:Routing algorithms]~~]

en>BD2412: Fixing links to disambiguation pages using AWB

2013-12-24T20:48:35Z

Fixing links to disambiguation pages using AWB

← Older revision		Revision as of 22:48, 24 December 2013
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	~~Hello~~. ~~Let me introduce~~ the ~~writer~~. ~~Her name~~ is ~~Emilia Shroyer but~~ it's ~~not~~ the ~~most feminine name out~~ there. The ~~thing she adores most is physique developing~~ and ~~now she~~ is ~~trying to earn money with it~~. ~~Puerto Rico~~ is ~~where he's been residing for many years~~ and ~~he will by no means transfer~~. ~~Bookkeeping~~ is ~~her day job now~~.<br><br>~~Have~~ a ~~look~~ at ~~my web blog~~ - [http://~~www~~.~~youporn~~-~~nederlandse~~.~~com~~/~~user~~/~~CMidgett at home std testing~~]		'''Fairness measures''' or [[Metric (mathematics)\|metrics]] are used in [[network engineering]] to determine whether users or applications are receiving a fair share of system resources. There are several mathematical and conceptual definitions of fairness.
			__NOTOC__
			==TCP fairness==
			[[Congestion control]] mechanisms for new network transmission protocols or [[peer-to-peer]] applications must interact well with [[Transmission Control Protocol\|TCP]]. TCP fairness requires that a new protocol receive no larger share of the network than a comparable TCP flow. This is important as TCP is the dominant transport protocol on the Internet, and if new protocols acquire unfair capacity they tend to cause problems such as [[congestion collapse]]. This was the case with the first versions of [[RealMedia\|RealMedia's]] [[Streaming media\|streaming protocol]]: it was based on [[User Datagram Protocol\|UDP]] and was widely blocked at organizational firewalls until a TCP-based version was developed.{{Citation needed\|date=July 2007}}

			==Jain's fairness index==
			[[Raj Jain]]'s equation,

			:<math>\mathcal{J} (x_1, x_2, \dots, x_n) = \frac{( \sum_{i=1}^n x_i )^2}{n \cdot \sum_{i=1}^n {x_i}^2}</math>

			rates the fairness of a set of values where there are <math>n</math> users and <math>x_i</math> is the throughput for the <math>i</math>th connection. The result ranges from <math>\tfrac{1}{n}</math> (worst case) to 1 (best case), and it is maximum when all users receive the same allocation. This index is <math>\tfrac{k}{n}</math> when <math>k</math> users equally share the resource, and the other <math>n-k</math> users receive zero allocation.

			This metric identifies underutilized channels and is not unduly sensitive to atypical network flow patterns.<ref>{{cite journal \|last1=Jain \|first1=R. \|last2=Chiu \|first2=D.M. \|last3=Hawe \|first3=W. \|year=1984 \|title=A Quantitative Measure of Fairness and Discrimination for Resource Allocation in Shared Computer Systems \|journal=DEC Research Report TR-301 \|url=http://www1.cse.wustl.edu/~jain/papers/ftp/fairness.pdf}}</ref>

			==Max-min fairness==
			{{main\|Max-min fairness}}
			Max-min fairness is said to be achieved by an allocation if and only if the allocation is feasible and an attempt to increase the allocation of any flow necessarily results in the decrease in the allocation of some other flow with an equal or smaller allocation. A max-min fair allocation is achieved when bandwidth is allocated equally and in infinitesimal increments to all flows until one is satisfied, then amongst the remainder of the flows and so on until all flows are satisfied or the bandwidth is exhausted.

			==Fairly shared spectrum efficiency==
			In [[packet radio]] [[wireless network]]s, ''The fairly shared spectrum efficiency'' (FSSE) can be used as a combined measure of fairness and [[system spectrum efficiency]]. The system spectral efficiency is the [[aggregate throughput]] in the network divided by the utilized [[radio bandwidth]] in hertz. The FSSE is the portion of the system spectral efficiency that is shared equally among all active users (with at least one backlogged data packet in queue or under transmission). In case of [[scheduling starvation]], the FSSE would be zero during certain time intervals. In case of equally shared resources, the FSSE would be equal to the system spectrum efficiency. To achieve [[max-min fairness]], the FSSE should be maximized.

			FSSE is useful especially when analyzing advanced [[radio resource management]] (RRM) schemes, for example [[channel adaptive scheduling]], for cellular networks with [[best-effort]] packet data service. In such system it may be tempting to optimize the spectrum efficiency (i.e. the throughput). However, that might result in scheduling starvation of "expensive" users at far distance from the access point, whenever another active user is closer to the same or an adjacent access point. Thus the users would experience unstable service, perhaps resulting in a reduced number of happy customers. Optimizing the FSSE results in a compromise between fairness (especially avoiding scheduling starvation) and achieving high spectral efficiency.

			If the cost of each user is known, in terms of consumed resources per transferred information bit, the FSSE measure may be redefined to reflect [[proportional fairness]]. In a proportional fair system, this "proportionally fair shared spectrum efficiency" (or "fairly shared radio resource cost") is maximized. This policy is less fair since "expensive" users are given lower throughput than others, but still scheduling starvation is avoided.

			==See also==
			* [[Income inequality metrics]]
			* [[Gini coefficient]]
			* [[Lorenz curve]]

			==Notes==
			{{reflist}}

			== Further reading ==
			* Almeida, A.; Casetti, C.; Oueslati, S.; Avratchenkov, K. & Johansson, M. [http://euronf.enst.fr/archive/127/jra21_deliverable_final.pdf#page=6 A Taxonomy of Congestion Control (in deliverable No: D.WP.JR.2.1.1)] EuroNGI, 2004
			* {{Cite journal \|last1=Mo \|first1=J. \|last2=Walrand \|first2=J. \|year=2000 \|title=Fair End-to-End Window-Based Congestion Control \|journal=IEEE/ACM Transactions on Networking \|volume=8 \|pages=556–567 \|url=http://fleece.ucsd.edu/~tjavidi/ECE257A/MoWalrand.pdf \|doi=10.1109/90.879343 }}

			{{DEFAULTSORT:Fairness Measure}}
			[[Category:Routing algorithms]]

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Hello. Let me introduce the writer. Her name is Emilia Shroyer but it's not the most feminine name out there. The thing she adores most is physique developing and now she is trying to earn money with it. Puerto Rico is where he's been residing for many years and he will by no means transfer. Bookkeeping is her day job now.<br><br>Have a look at my web blog - [http://www.youporn-nederlandse.com/user/CMidgett at home std testing]