1. EECS122 – Lecture 5 Department of Electrical Engineering and Computer Sciences University of California Berkeley

2. EECS 122 - UCB2 TOCTOC: Network Performance Motivation Timing Diagrams Metrics Evaluation Techniques

3. EECS 122 - UCB3 PerformancePerformance: Motivation Understanding Network Behavior Improving Protocols Verifying Correctness of Implementation Detecting Faults Choosing Provider Feasibility of Applications Monitoring Service Level Agreements Billing

4. EECS 122 - UCB4 PerformancePerformance: Timing Sending one packet Illustration Examples Queuing Queuing example Store and forward S&F:Multiple packets Cut-Through Fluid View

5. EECS 122 - UCB5 P/R TimingTiming: One Packet P bits R bps T seconds Time T P/R = Transmission time T = Propagation time = L/speed = L(km)x(time/km) Time/km = 3.3  s in free space 4  s in copper 5  s in fiber Time/km = 3.3  s in free space 4  s in copper 5  s in fiber

6. EECS 122 - UCB6 TimingTiming: Illustration Each bit takes 1/R seconds to be transmitted The bits take T seconds to propagate Transmitter  Receiver Transmission Line Signal  One bit

7. EECS 122 - UCB7 TimingTiming: Examples P = 1KByte R = 1Gbps 100km, fiber T = 500  s P/R = 8  s P = 1KByte R = 100Mbps 1km, fiber T = 5  s P/R = 80  s T >> P/R T << P/R T P/R T

8. EECS 122 - UCB8 P/R TimingTiming: Queuing Link: P bits R bps T seconds Time T Q Q/R Q/R = queuing delay (load-dependent)

9. EECS 122 - UCB9 TimingTiming: Queuing Example Link: P bits R bps Q 1-kbit packets; R = 1Mbps1ms Time T(t) = Q/R + P/R for a packet that arrives at t 1ms Time t Let Tn = Q/R +P/R for packet n T1 = 1ms T2 = 1.5ms T3 = 2ms T4 = 1ms T5 = 1.5ms T6 = 1ms

10. EECS 122 - UCB10 TimingTiming: Store and Forward System: 10Mbps5Mbps100Mbps10Mbps

11. EECS 122 - UCB11 TimingTiming: S&F - Multiple System: 10Mbps5Mbps100Mbps10Mbps

12. EECS 122 - UCB12 TimingTiming: Cut-Through System: R1 = 10MbpsR2 = 10Mbps Header Start forwarding as soon as the header is received Note: What if R2 > R1?

13. EECS 122 - UCB13 TimingTiming: A Fluid View System: A(t); rate a(t)D(t); rate d(t) # bits in [0, t] X(t) Rate R a(t) d(t) X(t)

14. EECS 122 - UCB14 PerformancePerformance: Metrics Throughput Delay

15. EECS 122 - UCB15 MetricsMetrics: Throughput Definitions Example 1: Connection Example 2: Link Fluctuations Measurements

16. EECS 122 - UCB16 ThroughputThroughput: Definitions Roughly: throughput = bit rate (e.g., 120Kbits/second) More precisely: Throughput of a connection or of a link: total number of bits during some period [t, t + T] divided by T Bandwidth* of a link = link rate = bit rate of the transmitter *Note: misnomer, but common usage Utilization of a link = throughput of the link / link rate Bit rate units: 1Kbps = 10 3 bps, 1Mbps = 10 6 bps, 1Gbps = 10 9 bps [For memory: 1Kbytes = 2 10 bytes = 1,024 bytes; 1MBytes = 2 20 bytes] Some rates are expressed in packet per second (pps)  relevant when the bottleneck is the header processing

17. EECS 122 - UCB17 Connection: Send W bits (window size) Wait for ACKs Repeat Assume that the round-trip time is RTT seconds Throughput = W/RTT bps Numerical Example: W = 64KBytes = 512 kbits = 512x1,024 = 524,288 bits RTT = 200ms Throughput = W/T = 2.6Mbps ThroughputThroughput: Connection RTT K K Time Source Destination

18. EECS 122 - UCB18 ThroughputThroughput: Link 1Mbps link sends 1,000-bit packets Rate every  s Time t 1 0.5 Mbps Rate every 40 ms Utilization = 50%

19. EECS 122 - UCB19 ThroughputThroughput: Fluctuations Rate varies over time Throughput over last T seconds Time t max min mean

20. EECS 122 - UCB20 ThroughputThroughput: Measurements TCP: Keep track of number of bytes received Let R(t) = number of bits in [0, t] Throughput over last T seconds = [R(t) – R(t – T)]/T Link: Device has counter with number of bytes received; calculate as above

21. EECS 122 - UCB21 MetricsMetrics: Delay Definitions Illustration 1 Illustration 2 Little’s Result Measurements: Example 1 Measurements: Example 2

22. EECS 122 - UCB22 DelayDelay: Definitions Delay/Latency of bit (packet, file) from A to B The time required for bit (packet, file) to go from A to B Jitter: Variability in delay Round-Trip Time (RTT) Two-way delay from sender to receiver and back Bandwidth-Delay Product Product of bw and delay, indicates “storage” capacity of network

23. EECS 122 - UCB23 DelayDelay: Illustration 1 SD 1 2 Latest bit seen by time t at point 1at point 2 n Delay of bit n

24. EECS 122 - UCB24 DelayDelay: Illustration 2 SD 1 2 1 2 Packet arrival times at 1 Packet arrival times at 2 20 ms Max delay = 100 ms Min delay = 40 ms Jitter = 60 ms Max delay = 100 ms Min delay = 40 ms Jitter = 60 ms

25. EECS 122 - UCB25 SD 1 2 DelayDelay: Little’s Result N T S = area S = T(1) + … + T(N) = integral of X(t) T(N) T(N - 1) X(t) T(1) + … + T(N) N N T 1 X(t)dt = T S =. T  Average occupancy = (average delay)x(average arrival rate)

26. EECS 122 - UCB26 DelayDelay: Measurements 1 A Good Epoch

27. EECS 122 - UCB27 DelayDelay: Measurements 2 A Worse Epoch

28. EECS 122 - UCB28 PerformancePerformance: Evaluation Techniques Models + Analysis Models + Simulations Measurements

29. EECS 122 - UCB29 Example: M/M/1 Queue Arrivals are Poisson with rate Service times are exponentially distributed with mean 1/  Average delay per packet T = 1/(  –  ) = (1/  )/(1 –  ) where  = /  = utilization For instance, 1/  = 1ms and  = 80% => Q = 5ms EvaluationEvaluation: Analysis 

30. EECS 122 - UCB30 Model of traffic Model of routers, links, …. Simulation: Time Driven: X(n) = state at time n  X(n+1) = f(X(n), event at time n  ) Event Driven: Y(n) = state after event n E(n) = n-th event T(n) = time when event n occurs [Y(n+1), T(n+1)] = g(Y(n), T(n), E(n)] Key Step : Output analysis (estimates, confidence intervals….) EvaluationEvaluation: Simulation

31. EECS 122 - UCB31 Design Experiment Representative? Output Analysis EvaluationEvaluation: Measurements