Title: a Deenition of Generalized Fairness and Its Support in Switch Algorithms. Source: Distribution: Atm Forum Technical Working Group Members (af-tm)

In this contribution we give a general de nition of fairness and show how this can achieve various fairness de nitions such as those mentioned in the ATM Forum TM Speci cations We discuss how a pricing policy can be mapped to general fairness The general fairness can be achieved by calculating the ExcessFairshare for each VC We show how a switch algorithm can be modi ed to support the general fairness by using the ExcessFairshare We use ERICA as an example switch algorithm and show how it can be modi ed to achieve the general fairness Simulations results are presented to demonstrate that the modi ed switch algorithm achieves general fairness Source Bobby Vandalore Sonia Fahmy Raj Jain Rohit Goyal Mukul Goyal The Ohio State University Department of Computer and Information Science Columbus OH Contact Phone Fax E mail fvandalor jaing cis ohio state edu This work done in this contribution is sponsored by NASA Lewis Research Center Date February Distribution ATM Forum Technical Working Group Members AF TM Notice This contribution has been prepared to assist the ATM Forum It is o ered to the Forum as a basis for discussion and is not a binding proposal on the part of any of the contributing organizations The statements are subject to change in form and content after further study Speci cally the contributors reserve the right to add to amend or modify the statements contained herein Introduction In ABR available bit rate service the users specify MCR minimum cell rate during connection set up The ABR service gives guarantee that the ACR allowed cell rate is never less than MCR When MCR is zero for all sources the available bandwidth can be allocated equally among the competing sources This allocation achieves max min fairness When MCRs are non zero other de nitions of fairness allocate the excess bandwidth which is available ABR capacity less the sum of MCRs equally among sources or proportional to MCRs or proportional to a predetermined weight assigned for di erent sources In the real world the users prefer to get a service which re ects the amount they are paying The pricing policy requirements can be realized by mapping appropriately the weights associated with the sources We show how a switch schemes can support non zero MCRs and achieve the generalized fairness As an example we show how the ERICA switch scheme can be modi ed to support generalized fairness The modi ed scheme is tested using simulations on various con gurations The simulations test the performance of the modi ed algorithm using di erent weights using a simple con gurations with transient sources a link bottleneck con guration and a source bottlenecked con guration The simulations show that the scheme realizes various fairness de nitions in ATM TM speci cations which are special cases of the generalized fairness Section discusses the general fairness de nition and shows how the various other de nitions of fairness can be realized using this general de nition Section shows how a switch scheme can achieve general fairness Section shows as an example how ERICA is modi ed to support general fairness Section explains the simulation con gurations and the parameters values used and section gives the simulation results General Fairness De nition De ne the following parameters A Total available bandwidth for all ABR connections on a given link U Sum of bandwidth of underloaded connections which are bottlenecked elsewhere B A U excess bandwidth to be shared by connections bottlenecked on this link Na Number of active connections Nu Number of active connections bottlenecked elsewhere n Na Nu number of active connections bottlenecked on this link M Sum of MCRs of active connections within bottlenecked on this link B i Generalized Fair Allocation for connection i MCR i MCR of connection i w i preassigned weight associated with the connection i The generalized fair allocation is de ned as follows B i MCR i w i B M Pn j w j Note that this de nition of fairness is di erent from the weighted allocation given as an example fairness criterion in ATM TM speci cations In the above de nition only the excess bandwidth is allocated proportional to weights This above de nition ensures the allocation is at least MCR Mapping TM Fairness to Generalized Fairness Here we show how the di erent fairness criteria mentioned in ATM TM speci cation can be realized based on the above fairness Max Min In this case MCRs are zero and the bandwidth is shared equally B i B n This is a special case of generalized fairness with MCR i and w i c where c is a constant MCR plus equal share The excess bandwith is shared equally B i MCR i B M n by assigning equal weights we achieve the above fairness Proportional to MCR The allocation is proportional to its MCR B i B MCR i M M B M MCR i M MCR i B M MCR i M By assigning w i MCR i we can achieve the above fairness Relationship to Pricing Charging Policies Consider a very small interval T of time The charge C that a customer pays for using a network during this interval is a function of the number of bits W that the network transported successfully C f W R Where R W T is the average rate It is reasonable to assume that f is a non decreasing function of W That is those sending more bits do not pay less The function f should also be a non increasing function of time T or equivalently a non decreasing function of rate R For economy of scale it is important that the cost per bit does not increase as the number of bits goes up That is C W is a non decreasing function of W Mathematically we have three requirements C W C R C W dW One simple function that satis es all these requirements is C c wW rR Here c is the xed cost per connection w is the cost per bit and r is the cost per Mbps In general c w and r can take any non negative value In the presence of MCR the above discussion can be generalized to C f W R L Where L is the MCR All arguments given above for R apply to L also except that the customers requesting larger L possibly pay more One possible function is C c wW rR mL where m is dollars per Mbps of MCR In e ect the customer pays r m dollars per Mbps upto L and then pays only r dollars per Mbps for all the extra bandwidth he she gets over and above L Consider two users with MCRs L and L Suppose their allocated rates are R and R and thus they transmit W and W bits respectively Their costs are C c wW rR mL C c wW rR mL Cost per bit C W should be a decreasing function of bits W Thus if W W C W C W c W w rR W mL W c W w rR W mL W Since Ri Wi T we have c R T w r T mL R T c R T w r T mL R T