Fair Queueing

Fair Queueing Attempts to implement a scheduler that simultaneously serves all flows with a backlog at the same rate Not easy to implement Fair Queuing in a packet network FIFO Fair Queueing

Discussion of Fair Rate Allocation See class notes

Fair Scheduling Algorithms Fair Queueing (FQ), a.k.a as Processor Sharing (PS)  Objective: Achieve fair rate allocation Weighted Fair Queueing (WFQ), a.k.a. Generalized Processor Sharing (GPS)  Objective: Achieve weighted fair rate allocation Problem: How to realize a fair rate allocation when Traffic is transmitted in packet of variable size Transmission of a packet cannot be interrupted

Fair Queuing in packet networks Approach: Take a fluid-flow view of traffic View output link as a “pipe” with a given width Transmitted traffic flows like a fluid through the pipe  Scheduler can transmit traffic from multiple flows at the same time Scheduler controls the “output rate” for each flow  Output rates are set to satisfy “fairness” Result is a fluid flow schedule Approximate fluid-flow schedule by a packet-level scheduling algorithm

Fair Queuing (FQ): From fluid to packets Packet Size (bits) Packet inter-arrival time (ms) Rate (Kbps) Flow 1 1000 10 100 Flow 2 500 50 Flow 1 (f1 = 1) 100 Kbps Flow 2 (f2 = 1) Flow 1 (arrival traffic) 1 2 3 4 5 time Flow 2 (arrival traffic) 1 2 3 4 5 6 time Service in fluid flow system 10 20 30 40 50 60 70 80 time (ms) Slide from Ion Stoica

Fair Queueing (FQ): From fluid to packets (complete) Packet Size (bits) Packet inter-arrival time (ms) Rate (Kbps) Flow 1 1000 10 100 Flow 2 500 50 Flow 1 (f1 = 1) 100 Kbps Flow 2 (f2 = 1) Flow 1 (arrival traffic) 1 2 3 4 5 time Flow 2 (arrival traffic) 1 2 3 4 5 6 time 1 2 3 4 5 6 Service in fluid flow system time (ms) 10 20 30 40 50 60 70 80

Fair Scheduling (fluid flow) 5000 5000 Flow 1 Flow 2 4000 4000 3000 3000 2000 2000 1000 1000 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80

Fair Scheduling (fluid flow) 5000 5000 Flow 1 Flow 2 4000 4000 3000 3000 2000 2000 1000 1000 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80

Fair Scheduling (FQ) (fluid flow view) There are N flows At any time t, all backlogged flows are served at the same rate of: where B(t) is the set of backlogged flows at time t C is the capacity of the link The total rate guarantee to a flow j is:

Weighted Fair Scheduling (WFQ) (fluid flow view) There are N flows with weights f1 , f2 , …,fN The service given to two backlogged flows is proportional to their weights At any time t , the rate allocated to a backlogged flow i is: where B(t) is the set of backlogged flows at time t C is the capacity of the link The total rate guarantee to a flow is:

FQ/WFQ Scheduling for Packets (packet-level view) Packet-level implementation of FQ and WFQ tries to emulate the fluid-flow version Scheduling decision: Always select the packet that will finish next in the ideal fluid-flow FQ/WFQ system

WFQ scheduling (with place holder) Packet Size (bits) Packet inter-arrival time (ms) Rate (Kbps) Flow 1 1000 10 100 Flow 2 500 50 Flow 1 (f1 = 1) 100 Kbps Flow 2 (f2 = 1) Flow 1 (arrival traffic) 1 2 3 4 5 time Flow 2 (arrival traffic) 1 2 3 4 5 6 time 1 2 3 4 5 6 Service in fluid flow system time (ms) 10 20 30 40 50 60 70 80 Service in packet system 10 20 30 40 50 60 70 80 time (ms)

WFQ scheduling (complete) Packet Size (bits) Packet inter-arrival time (ms) Rate (Kbps) Flow 1 1000 10 100 Flow 2 500 50 Flow 1 (f1 = 1) 100 Kbps Flow 2 (f2 = 1) Flow 1 (arrival traffic) 1 2 3 4 5 time Flow 2 (arrival traffic) 1 2 3 4 5 6 time 1 2 3 4 5 6 Service in fluid flow system time (ms) 10 20 30 40 50 60 70 80 Service in packet system 1 2 1 3 2 3 4 4 5 5 6 10 20 30 40 50 60 70 80 time (ms) Slide from Ion Stoica

Packet-level Implementation of WFQ Problems to deal with: The finishing time of a packet in the fluid-flow system may depend on arrivals after a packet has been selected packet-level version of WFQ cannot be 100% accurate Once started, packet transmission cannot be preemtped Implementation: When a packet arrives, it is assigned a “virtual finishing time” This is the finishing time in the fluid flow system if the set of backlogged flows does not change after packet arrival Orders packets in increasing order of virtual finishing times Compute virtual finishing time with the help of a system virtual time

Rate of system virtual time B(t) : the set of backlogged flows at time t The rate allocated to a backlogged flow i at time t is or : service that a backlogged flow with weight 1 receives in GPS Rate of Rate of system virtual time

WFQ: System Virtual Time WFQ uses a System Virtual Time which tracks the progress of GPS system Suppose the times when the set B(t) changes are Let Bl be the set of backlogged flows in time interval Then we have When fewer flows are active, virtual time moves faster

WFQ: Implementation Virtual finish time of k-th packet from flow j ajk is the arrival time and Lkj is thesize of the k-th packet from flow j Packets are sorted and transmitted in the order of virtual finishing times Virtual time needs to be computed only at arrival time of packets must keep track of the busy set Bl

WFQ Example (packet level) Flow 1 (arrival traffic) 1 2 3 4 5 time Flow 2 (arrival traffic) 1 2 3 4 5 6 time 5000 Virtual time V(t) 4000 Time t 10 20 30 40 50 60 70 80 V(t) (x 100) Fn1 (x 100) Fn2 (x 100) 3000 2000 actual transmission order 1 2 1 3 2 3 4 4 5 5 6 1000 10 20 30 40 50 60 70 80 time t time (ms) 10 20 30 40 50 60 70 80

WFQ Example (packet level) Flow 1 (arrival traffic) 1 2 3 4 5 time Flow 2 (arrival traffic) 1 2 3 4 5 6 time 5000 Virtual time V(t) 4000 Time t 10 20 30 40 50 60 70 80 V(t) (x 100) 25 35 45 Fn1 (x 100) Fn2 (x 100) 3000 2000 actual transmission order 1 2 1 3 2 3 4 4 5 5 6 1000 10 20 30 40 50 60 70 80 time t time (ms) 10 20 30 40 50 60 70 80

Worst-Case Fair Fair Queueing (WF2Q)

WFQ and WF2Q … … 12 flows, all packets have size 1, C = 1: Flow 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Flow 1 f1 = 0.5 time Flow 2 f2 = 0.05 time … … Flow 11 f11 = 0.05 time fluid flow system 20 2 6 4 21

WFQ and WF2Q … … … … 12 flows, all packets have size 1, C = 1: Flow 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Flow 1 f1 = 0.5 time Flow 2 f2 = 0.05 time … … Flow 11 f11 = 0.05 time Flow 1 fluid flow system Flow 2 … … Flow 11 20 2 6 4 21

WFQ transmission order WFQ and WF2Q 12 flows, all packets have size 1, C = 1: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Flow 1 f1 = 0.5 time Flow 2 f2 = 0.05 time … … Flow 11 f11 = 0.05 time WFQ transmission order time 10 20 21

Worst-Case Fair Fair Queueing Issue: While WFQ never falls behind the fluid-flow schedule by more than one packet size, it can run ahead of the fluid-flow schedule by an arbitrary amount. WF2Q Scheduling: Only considers packets for transmission that have already started transmission in the fluid-flow system Of these, it selects the packet with the smallest finishing time (in the fluid-flow system) WF2Q Properties: Like WFQ, WF2Q never falls behind the fluid-flow schedule by more than one packet size ( same end-to-end delay bounds as WFQ) Unlike WFQ, it never runs ahead of the fluid-flow schedule by more than one packet size

WFQ and WF2Q … … 12 flows, all packets have size 1, C = 1: Flow 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Flow 1 f1 = 0.5 time Flow 2 f2 = 0.05 time … … Flow 11 f11 = 0.05 time WFQ transmission order WF2Q transmission order time 10 20 21

WFQ and WF2Q … … 12 flows, all packets have size 1, C = 1: Flow 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Flow 1 f1 = 0.5 time Flow 2 f2 = 0.05 time … … Flow 11 f11 = 0.05 time WFQ transmission order WF2Q transmission order time 10 20 21