CprE 458/558: Real-Time Systems (G. Manimaran)1 CprE 458/558: Real-Time Systems Real-Time Networks – WAN Packet Scheduling

CprE 458/558: Real-Time Systems (G. Manimaran)2 Scheduler Ensuring bandwidth (and delay), and buffer guarantees to connections Determining the service order among packets from different connections Scheduling algorithm has an associated admission control that is used during channel setup

CprE 458/558: Real-Time Systems (G. Manimaran)3 Scheduler requirements Fairness – achieving fairness among competing flows Performance bounds for the guaranteed flows Efficiency -- schedulability Protection – guarantees of well-behaving flows are protected from ill-behaving flows Flexibility – accommodating a diverse mix of traffic class and rates Ease of implementation – high speed implementation

CprE 458/558: Real-Time Systems (G. Manimaran)4 Fairness and Max-Min Fairness Fairness –Providing equal share of the resource to all the flows –The notion of fairness is obvious if all the flows demand equal share of the resource –Typically different flows exhibit varying resource demands. The notion of Max-min fairness is employed in such situations

CprE 458/558: Real-Time Systems (G. Manimaran)5 Max-Min Fairness Basic Idea: A fair share allocates –a source with a small demand what it wants, and evenly distributes unused resources to the big sources Formally, max-min fair share allocation is defined as: –Resources are allocated in order of increasing demands –No source gets a resource share larger than its demands –Sources with unsatisfied demands get an equal share of the resource

CprE 458/558: Real-Time Systems (G. Manimaran)6 Max-Min Fairness: Example Max-Min Scheduler Four incoming flows with their corresponding demands 10 Output Link The max-min fairness allocation proceeds in several rounds

CprE 458/558: Real-Time Systems (G. Manimaran)7 Max-Min Fairness: Example (1) Round #1: Tentatively divide the resource (output bandwidth) into four equal portions of size 10 / 4 = 2.5 Allocation = [2.5, 2.5, 2.5, 2.5] Round #2: Deduct the excess resource allocation and redistribute equally among others

CprE 458/558: Real-Time Systems (G. Manimaran)8 Max-Min Fairness: Example (2) Source 1’s demand is only 2.0 so deduct ( = 0.5) and distribute the remaining amount of (0.5 / 3 = 0.167) to each of the rest three Allocation = [2.0, 2.67, 2.67, 2.67] Source 2’s demand is only 2.6 so deduct ( = 0.07) and distribute the remaining amount of (0.07 / 2) to each of the rest two Final Allocation = [2.0, 2.6, 2.7, 2.7]

CprE 458/558: Real-Time Systems (G. Manimaran)9 Working of the example [2.5, 2.5, 2.5, 2.5] [2.0, 2.67, 2.67, 2.67] [2.0, 2.6, 2.7, 2.7] Flow 1 has excess = 0.5 add (0.5 / 3) to each of the rest Flow 2 has excess = 0.07 add (0.07 / 2) to each of the rest

CprE 458/558: Real-Time Systems (G. Manimaran)10 Max-Min Fairness: Example Max-Min Fairness Resource Allocation 2 / / / / 5 Four incoming flows with their max-min resource (bandwidth) allocations / demands 10 Output Link

CprE 458/558: Real-Time Systems (G. Manimaran)11 Weighted Max-Min Fairness A max-min weighted fairness share is as follows –Resources are allocated in order of increasing demand, normalized by the weight –No source gets a resource share larger than its demand –Sources with unsatisfied demands get resource shares in proportion to their weights

CprE 458/558: Real-Time Systems (G. Manimaran)12 Weighted Max-Min Fairness: Example Max-Min Scheduler Four incoming flows with their corresponding demands 16 Output Link W1 = 2.5 W2 = 4 W3 = 0.5 W4 = 1.0 The normalized weights are: [5, 8, 1, 2] Now pretend as if the number of flows are ( ) = 16 instead of just 4

CprE 458/558: Real-Time Systems (G. Manimaran)13 Working of the example Divide the capacity into 16 equal parts –Flow 1’s share (capacity / 16) * 5 = (16 / 16) * 5 = 5 Assign each flow an amount equal to its corresponding normalized weight If there is excess allocation deduct it and redistribute it for the rest in a weighted manner

CprE 458/558: Real-Time Systems (G. Manimaran)14 Working of the example [5, 8, 1, 2] [4, 2, 3.33, 6.66] Flow 1 has excess = 1 Flow 2 has excess = 6 We have to distribute excess “7” units among flows 3 and 4 Their weights are 1 and 2 respectively Therefore, flow 3 will get an additional share of (7/3) * 1 and flow 4 will get an additional share of (7/3) * 2

CprE 458/558: Real-Time Systems (G. Manimaran)15 Working of the example [5, 8, 1, 2] [4, 2, 3.33, 6.66] Flow 1 has excess = 1 Flow 2 has excess = 6 Flow 4 has excess = 2.66 allocate it to flow 3 Final Allocation [4, 2, 6, 4]

CprE 458/558: Real-Time Systems (G. Manimaran)16 General Processor Sharing (GPS) or Fluid Flow Model for achieving Max-min Fairness GPS Resource Allocation (Ideal, but Not practical) 5 5 Two incoming flows with their resource demands 10 Output Link 0510 The schedule (ideal, but not realizable in networks)

CprE 458/558: Real-Time Systems (G. Manimaran)17 Max-Min fairness Approximation Packetized GPS (Max-Min Fairness Approximation) 5 5 Two incoming flows with their resource demands 10 Output Link 5 units of time 0510 The schedule

CprE 458/558: Real-Time Systems (G. Manimaran)18 A Simple Round Robin Scheduler Round Robin Scheduler Four incoming flows Output Link 0 The schedule Cannot achieve max-min fairness Need to handle weighted flows Need to handle variable length packets

CprE 458/558: Real-Time Systems (G. Manimaran)19 Weighted Round Robin Scheduler Round Robin Scheduler Four incoming flows with their corresponding weights Output Link 0 Normalized weights are as follows: [2, 3, 1, 1] Cannot achieve max-min fairness Need to handle variable length packets