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ECE 466 - Computer Networks II Problem Set #8 : Fair Scheduling 1. Consider an arrival scenario from two flows to a WFQ scheduler, with arrival times and packet sizes given as follows: Packet label Arrival time Packet Size 1a 1 1 Flow 1 1b 1c 2 3 1 2 1d 11 2 2a 0 3 Flow 2 2b 2c 5 9 2 2 • Assume that the transmission rate is (C = 1), i.e., it takes one time unit to transmit a packet of size 1, two time units to transmit a packet of size 2, etc.. • Assume the two flows have weights such that φ1 = 1/3 and φ2 = 2/3. (a) Show the value of the system virtual time for t ≤ 13. (b) Devise the transmission schedule of a fluid-flow WFQ scheduler. Provide the departure times of all packets. (Refer to individual packets using the labels given in the table). (c) Devise a transmission schedule of a packet-level WFQ scheduler. Provide the departure times of all packets. (Refer to individual packets using the labels given in the table). Solutions: The example is straight out the Parekh/Gallager paper. Note that we need to select a values for φ1 and φ2 . Here we select φ1 = 1/3 and φ2 = 2/3. 1 22 21 20 Virtual time: V(t) 19 Slope = 3 18 17 16 Slope = 3/2 15 14 13 Slope = 3 12 11 10 Slope = 1 9 8 7 Slope = 3 6 5 4 Slope = 1 3 2 1 Slope = 3/2 0 Backlogged Flows B(t) 1 2 2 3 1,2 4 5 1 6 7 1,2 8 9 10 1 Figure 1: Virtual Time for Problem 3. 2 2 11 12 1 13 packet size 1c 1d 2 Arrivals from Flow 1 1a 1b 1 2 1 0 3 4 5 6 7 8 9 10 11 12 13 14 time 10 11 12 13 14 time 13 14 time packet size 2a 2b 2c 2 Arrivals from Flow 2 1 0 Fluid-flow WFQ schedule 1 2 3 4 5 6 1a 2a 0 1 2 3 2a 0 1 4 1a 2 8 9 1c 1b 2a Packet-level WFQ schedule 7 3 5 1b 4 1c 2b 6 7 2b 5 6 8 2c 9 1c 7 8 10 1d 11 2c 9 10 12 1d 11 12 13 14 time Figure 2: Arrival Scenario for Problem 3. 2. Consider a service discipline NFQ (Not Fair Queueing) which services packets according to the priority index (j) (j) (j) Fk = V (ak ) + Lk /φj NFQ is inferior to packetized WFQ in emulating the fluid-flow WFQ and satisfying the weighted fairness property in the definition of fluid-flow WFQ. (a) Describe in words why NFQ is inferior to WFQ: what property (or properties) should it possess that it does not? (b) Construct a numerical example with two flows to illustrate WFQ’s superiority to NFQ. Solution: • (a) The “max” in WFQ’s definition of virtual finishing time, in essence queues a particular session’s traffic behind itself. Since NFQ does not have the max, a session can send an arbitrarily large amount of traffic at a particular time and receive the same priority index for all of this traffic, potentially starving out other users. In other words, NFQ lacks fairness and protection from misbehaving users. (b) As a simple example, consider two sessions with φ1 = φ2 , C = 1, fixed sized packets, and an empty queue at t = 0. If session 1 sends 10 packets at t = 0, all receive the same priority index of 1 under NFQ, while the indexes are 1, 2, · · · , 10 under WFQ. If session 2 sends 1 packet at t = 1, that packet has priority index 2 and will be serviced last under NFQ while it will be serviced 2nd or 3rd under WFQ. 3 3. Consider two flows. The first with packets of size 2 and 2 arriving at times 3 and 5, and the second with packets of size 1, and 3 arriving at times 0 and 2. Further, let φ1 = 2φ2 . (a) Sketch the arrival and departure functions, for the fluid-flow WFQ and for packetized WFQ for C = 1. (b) Sketch the virtual time V (t) (Set V (0) = 0). (c) Provide the departure times of the packets under fluid-flow WFQ and packetized WFQ. Solution: (a) The arrival and departure functions are sketched in the figure (In the figure, the curve labeled GPS refers to fluid-flow GPS, and the curve labeled WFQ is for packetized WFQ). A[0,t] 4 GPS 3 A[0,t] 4 WFQ 3 2 GPS 2 WFQ 1 1 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 (b) The system virtual time is shown in the figure. V(t) 4 3 2 1 t 1 (c) 2 3 Packet number arrival times fluid-flow WFQ packetized WFQ 4 5 6 Session 1 1 2 3 5 6 9 7 9 4 7 8 Session 2 1 2 0 2 1 9 1 5 9 8 9