Fairness Benchmarking of MACs

Transcription

1 Fairness Benchmarking of MACs Harmen R. van As, Günter Remsak, Jon Schuringa Vienna University of Technology, Austria vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

2 Goal and Content Goal: Finding an algorithm to determine the maximal individual node throughputs and at the same fulfilling bottleneck-link fairness Content: - Two definitions for bottleneck fairness - Corresponding fairness algorithms and examples - Two traffic scenarios vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

3 Local Fairness Definitions Flow rates on bottleneck are proportionally reduced by the total amount of offered traffic for that bottleneck link 2 Flow rates on bottleneck are proportionally reduced by the total number of connections on bottleneck link vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

4 Example 2 flows, link: f: 8 % i i+ f2: 4 % Definition : f: 8 * (/2) = 66.6% i i+ f2: 4 * (/2) = 33.3% Definition 2: f: 8 -> 5 -> 6% i i+ f2: 4 -> 5 -> 4% vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

5 Definitions Given: Number of nodes N Requested rate from node i to node j r i,j Calculated: Flow on link i f i Sum of all requested rates passing link i Number of demand flows passing link i nd i Remaining capacity on link i rc i Link capacity minus the sum of all allowed rates passing link i Allowed rate from node i to node j ar i,j Rate calculated by the algorithms vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

6 Algorithm for Fairness Definition Set: rc i =; // init remaining capacity Step : for all links: calculate flow on link i: f i Step 2: if ( rc i < f i ) // condition for a bottleneck take always the highest overloaded bottleneck: min(rc i /f i ) bottleneck link: indicated by index b else ar i,j = ar i,j + r i,j ; stop; Step 3: for all flows passing this bottleneck set: ar i,j =rc b /f b r i,j and r i,j = Step 4: calculate remaining capacities rc i of all links; goto Step ; vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

7 Set: rc i =; Algorithm for Fairness Definition 2 Step : for all links: calculate flow on link i: f i Step 2: if ( rc i < f i ) // condition for a bottleneck take always the highest overloaded bottleneck: min(rc i /nd i ) bottleneck link: indicated by index b else ar i,j = ar i,j + r i,j ; stop; Step 3: for all flows passing this bottleneck: if (rc b /nd b > r i,j ) ar i,j = r i,j ; nd b = nd b -; r i,j =; calculate remaining capacities rc i of all links; goto Step ; else ar i,j = rc b /nd b ; r i,j =; Step 4: calculate remaining capacities rc i of all links; goto Step ; vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

8 Example: Fairness Definition Bottleneck 2 Bottleneck 2 Source Sink 2 Rate.. Fair vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

9 Example: Fairness Definition 2 Bottleneck 2 2 Bottleneck Source Sink 2 Rate.. Fair vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

10 Throughput.8.7 Throughput Fairness Fairness 2 Bottleneck 2 2 Bottleneck 2 Source Node vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

11 Example: Fairness Definition 2 Bottleneck Bottleneck % 7 % 3 % 3 % 3 % 5 % 25 % 25 % 25 % 25 % Some bottlenecks can be resolved by resolving other bottlenecks vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

12 Scenario Uniform traffic Saturated sources 6 nodes vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

13 Number of Connections per Bottleneck Link Scenario 3 number of connections Ring link number of connections link Ring vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

14 Throughput per Node Scenario throughput throughput nodes Ring Ring throughput vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology nodes node Ring + Ring

15 Link Usage Scenario.2 usage Ring link usage Ring link vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

16 Throughput per Source/Destination Pair Scenario throughput Ring sources destinations vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

17 Throughput per Source/Destination Pair Scenario throughput Ring sources destinations vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

18 Scenario 2 Uniform traffic Saturated sources 6 nodes 4 8 vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

19 Number of Connections per Bottleneck Link Scenario 2 3 number of connections Ring link 4 8 number of connections Ring link vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

20 Throughput per Node Scenario throughput throughput throughput node node Ring Ring Ring + Ring vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology node

21 Link Usage Scenario 2.2 usage Ring link.2 8 usage Ring link vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

22 Throughput Comparison Cyclic Reservation MAC : IKNv (July 2) IKNv2 (Jan. 22).9.8 throughput Scenario Calculated IKNv2 IKNv Calculated: 7.93 IKNv2: 7.46 IKNv: 6.94 node vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology

23 Conclusion Two algorithms for solving the bottleneck problem have been shown The result is the optimum solution to this problem Both algorithms scale well Thus, both can be used to determine the fair bottleneck rates Theoretical benchmarking On-line scheduling vas_benmac_3 22 Institute of Communication Networks Vienna University of Technology