1. Katz, Stoica F04 EECS 122: Introduction to Computer Networks Performance Modeling Computer Science Division Department of Electrical Engineering and Computer Sciences University of California, Berkeley Berkeley, CA 94720-1776

2. Katz, Stoica F04 2 Outline  Motivations  Timing diagrams  Metrics  Evaluation techniques

3. Katz, Stoica F04 3 Motivations  Understanding network behavior  Improving protocols  Verifying correctness of implementation  Detecting faults  Monitor service level agreements  Choosing provides  Billing

4. Katz, Stoica F04 4 Outline  Motivations  Timing diagrams  Metrics  Evaluation techniques

5. Katz, Stoica F04 5 Timing Diagrams  Sending one packet  Queueing  Switching -Store and forward -Cut-through  Fluid view

6. Katz, Stoica F04 6 Definitions  Link bandwidth (capacity): maximum rate (in bps) at which the sender can send data along the link  Propagation delay: time it takes the signal to travel from source to destination  Packet transmission time: time it takes the sender to transmit all bits of the packet  Queuing delay: time the packet need to wait before being transmitted because the queue was not empty when it arrived  Processing Time: time it takes a router/switch to process the packet header, manage memory, etc

7. Katz, Stoica F04 7 Sending One Packet R bits per second (bps) T seconds P bits Bandwidth: R bps Propagation delay: T sec time Transmission time = P/R T Propagation delay =T = Length/speed 1/speed = 3.3 usec in free space 4 usec in copper 5 usec in fiber

8. Katz, Stoica F04 8 Sending one Packet: Examples P = 1 Kbyte R = 1 Gbps 100 Km, fiber => T = 500 usec P/R = 8 usec T P/R time T P/R P = 1 Kbyte R = 100 Mbps 1 Km, fiber => T = 5 usec P/R = 80 usec T >> P/R T << P/R

9. Katz, Stoica F04 9 Queueing  The queue has Q bits when packet arrives  packet has to wait for the queue to drain before being transmitted P bits time P/R T Q bits Queueing delay = Q/R Capacity = R bps Propagation delay = T sec

10. Katz, Stoica F04 10 Queueing Example P = 1 Kbit; R = 1 Mbps  P/R = 1 ms Packet arrival Time (ms) Time Delay for packet that arrives at time t, d(t) = Q(t)/R + P/R Q(t) 1 Kb P bitsQ bits 0 0.5 1 77.5 0.5 Kb 1.5 Kb 2 Kb packet 1, d(0) = 1ms packet 2, d(0.5) = 1.5ms packet 3, d(1) = 2ms

11. Katz, Stoica F04 11 Switching: Store and Forward  A packet is stored (enqueued) before being forwarded (sent) Sender Receiver 10 Mbps 5 Mbps100 Mbps10 Mbps time

12. Katz, Stoica F04 12 Store and Forward: Multiple Packet Example Sender Receiver 10 Mbps 5 Mbps100 Mbps10 Mbps time

13. Katz, Stoica F04 13 Switching: Cut-Through  A packet starts being forwarded (sent) as soon as its header is received Sender Receiver R1 = 10 Mbps R2 = 10 Mbps time Header What happens if R2 > R1 ?

14. Katz, Stoica F04 14 Fluid Flow System  Packets are serviced bit-by-bit as they arrive a(t) e(t) Q(t) t Rate or Queue size Q(t) a(t) – arrival ratee(t) – departure rate Q(t) = queueing size at time t

15. Katz, Stoica F04 15 Outline  Motivations  Timing diagrams  Metrics Throughput Delay  Evaluation techniques

16. Katz, Stoica F04 16 Throughput  Throughput of a connection or link = total number of bits successfully transmitted during some period [t, t + T) divided by T  Link utilization = throughput of the link / link rate  Bit rate units: 1Kbps = 10 3 bps, 1Mbps = 10 6 bps, 1 Gbps = 10 9 bps [For memory: 1 Kbyte = 2 10 bytes = 1024 bytes] -Some rates are expressed in packets per second (pps)  relevant for routers/switches where the bottleneck is the header processing

17. Katz, Stoica F04 17 Example: Windows Based Flow Control  Connection: -Send W bits (window size) -Wait for ACKs -Repeat  Assume the round-trip- time is RTT seconds  Throughput = W/RTT bps  Numerical example: -W = 64 Kbytes -RTT = 200 ms -Throughput = W/T = 2.6 Mbps time Source Destination RTT

18. Katz, Stoica F04 18 Throughput: Fluctuations  Throughput may vary over time max min mean Throughput Time

19. Katz, Stoica F04 19 Delay  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 bandwidth and delay  “storage” capacity of network

20. Katz, Stoica F04 20 Delay: Illustration 1 at point 2 at point 1 Latest bit seen by time t Delay SenderReceiver 12 time

21. Katz, Stoica F04 21 Delay: Illustration 2 SenderReceiver 12 2 1 Packet arrival times at 1 Packet arrival times at 2 Delay

22. Katz, Stoica F04 22 Little’s Theorem  Assume a system (e.g., a queue) at which packets arrive at rate a(t)  Let d(i) be the delay of packet i, i.e., time packet i spends in the system  What is the average number of packets in the system? system a(t) – arrival rate d(i) = delay of packet i  Intuition: -Assume arrival rate is a = 1 packet per second and the delay of each packet is s = 5 seconds -What is the average number of packets in the system?

23. Katz, Stoica F04 23 Little’s Theorem Latest bit seen by time t SenderReceiver 12 time x(t) d(i) = delay of packet i x(t) = number of packets in transit (in the system) at time t T What is the system occupancy, i.e., average number of packets in transit between 1 and 2 ?

24. Katz, Stoica F04 24 Little’s Theorem Latest bit seen by time t SenderReceiver 12 time x(t) T Average occupancy = S/T d(i) = delay of packet i x(t) = number of packets in transit (in the system) at time t S= area

25. Katz, Stoica F04 25 Little’s Theorem Latest bit seen by time t SenderReceiver 12 time x(t) S(N) P d(N-1) S(N-1) T S = S(1) + S(2) + … + S(N) = P*(d(1) + d(2) + … + d(N)) d(i) = delay of packet i x(t) = number of packets in transit (in the system) at time t S= area

26. Katz, Stoica F04 26 Average occupancy Average arrival time Average delay Little’s Theorem Latest bit seen by time t SenderReceiver 12 time x(t) S(N) P d(N-1) S(N-1) T S/T = (P*(d(1) + d(2) + … + d(N)))/T = ((P*N)/T) * ((d(1) + d(2) + … + d(N))/N) d(i) = delay of packet i x(t) = number of packets in transit (in the system) at time t S= area

27. Katz, Stoica F04 27 Little’s Theorem Latest bit seen by time t SenderReceiver 12 time x(t) S(N) Average occupancy = (average arrival rate) x (average delay) S= area a(i) d(N-1) S(N-1) T d(i) = delay of packet i x(t) = number of packets in transit (in the system) at time t

28. Katz, Stoica F04 28 Outline  Motivations  Timing diagrams  Metrics  Evaluation techniques

29. Katz, Stoica F04 29 Evaluation Techniques  Measurements -gather data from a real network -e.g., ping www.berkeley.edu -realistic, specific  Simulations: run a program that pretends to be a real network -e.g., NS network simulator, Nachos OS simulator  Models, analysis -write some equations from which we can derive conclusions -general, may not be realistic  Usually use combination of methods

30. Katz, Stoica F04 30 Analysis  Example: M/M/1 Queue  Arrivals are Poisson with rate a  Service times are exponentially distributed with mean 1/s -s - rate at which packets depart from a full queue  Average delay per packet: T = 1/(s – a) = (1/a)/(1 – u), where u = a/s = utilization Numerical example, 1/a = 1ms; u = 80%  Q = 5ms a s

31. Katz, Stoica F04 31 Simulation  Model of traffic  Model of routers, links  Simulation: -Time driven: X(t) = state at time t X(t+1) = f(X(t), event at time t) -Event driven: E(n) = n-th event Y(n) = state after event n T(n) = time when even n occurs [Y(n+1), T(n+1)] = g(Y(n), T(n), E(n))  Output analysis: estimates, confidence intervals

32. Katz, Stoica F04 32 Evaluation: Putting Everything Together  Usually favor plausibility, tractability over realism -Better to have a few realistic conclusions than none (could not derive) or many conclusions that no one believes (not plausible) RealityModel HypothesisConclusion Abstraction Plausibility DerivationTractability Realism Prediction