Models. Motivation Timing Diagrams Metrics Evaluation Techniques. TOC Models

Transcription

1 Models Motivation Timing Diagrams Metrics Evaluation Techniques TOC Models

2 Motivation Understanding Network Behavior Improving Protocols Verifying Correctness of Implementation Detecting Faults Choosing Provider Feasibility of Applications Monitoring Service Level Agreements Billing TOC Models Motivation

3 Timing Sending one packet Illustration Examples Queuing Queuing example Store and forward S&F:Multiple packets Cut-Through Fluid View TOC Models Timing

4 One Packet P bits R bps T seconds T Time P/R P/R = Transmission time T = Propagation time = L/speed = L(km)x(time/km) Time/km = 3.3µs in free space 4 µs in copper 5 µs in fiber TOC Models Timing One Packet

5 Illustration Transmission Line Transmitter Receiver Signal One bit Each bit takes 1/R seconds to be transmitted The bits take T seconds to propagate TOC Models Timing Illustration

6 Examples T >> P/R T P = 1KByte R = 1Gbps 100km, fiber T = 500µs P/R = 8µs T << P/R T P/R P/R P = 1KByte R = 100Mbps 1km, fiber T = 5µs P/R = 80µs TOC Models Timing Examples

7 Queuing Link: P bits Q R bps T seconds Q/R Q/R = queuing delay (load-dependent) T P/R Time TOC Models Timing Queuing

8 Queuing Example R bps Link: P bits Q 1-kbit packets; R = 1Mbps 1ms 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 TOC Models Timing Queuing Example

9 Store and Forward System: 10Mbps 5Mbps 100Mbps 10Mbps TOC Models Timing Store and Forward

10 S&F - Multiple System: 10Mbps 5Mbps 100Mbps 10Mbps TOC Models Timing S&F Multiple

11 Cut-Through System: R1 = 10Mbps R2 = 10Mbps Header Start forwarding as soon as the header is received Note: What if R2 > R1? TOC Models Timing Cut-Through

12 A Fluid View System: Rate R A(t); rate a(t) X(t) D(t); rate d(t) # bits in [0, t] # bits in [0, t] a(t) d(t) X(t) TOC Models Timing Fluid View

13 Metrics Throughput Delay TOC Models Metrics

14 Throughput Definitions Example 1: Connection Example 2: Link Fluctuations Measurements TOC Models Metrics Throughput

15 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 TOC Models Metrics Throughput Definitions

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

17 Link 1Mbps link sends 1,000-bit packets Mbps Rate every µs 1 Rate every 40 ms 0.5 Utilization = 50% TOC Models Metrics Throughput Link Time t

18 Fluctuations Rate varies over time Throughput over last T seconds mean max min Time t TOC Models Metrics Throughput Fluctuations

19 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 TOC Models Metrics Throughput Measurements

20 Delay Definitions Illustration 1 Illustration 2 Little s Result Measurements: Example 1 Measurements: Example 2 TOC Models Metrics Delay

21 Definitions Delay/Latency of bit (packet, file) from A to B Jitter: The time required for bit (packet, file) to go from A to B 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 TOC Models Metrics Delay Definitions

22 Illustration 1 S 1 2 D Latest bit seen by time t n at point 1 at point 2 Delay of bit n TOC Models Metrics Delay Illustration 1

23 Illustration 2 S 1 2 D 1 Packet arrival times at 1 20 ms 2 Packet arrival times at 2 Max delay = 100 ms Min delay = 40 ms Jitter = 60 ms TOC Models Metrics Delay Illustration 2

24 N S Little s Result 1 2 D X(t) T(N) T(N - 1) S = area S = T(1) + + T(N) = integral of X(t) 1 T(1) + + T(N) N X(t)dt = S =. T T N T T Average occupancy = (average delay)x(average arrival rate) TOC Models Metrics Delay Little s Result

25 Measurements 1 A Good Epoch TOC Models Metrics Delay Measurements 1

26 Measurements 2 A Worse Epoch TOC Models Metrics Delay Measurements 2

27 Evaluation Techniques Models + Analysis Models + Simulations Measurements TOC Models Evaluation

28 Analysis Example: M/M/1 Queue λ µ Arrivals are Poisson with rate λ Service times are exponentially distributed with mean 1/µ Average delay per packet T = 1/(µ λ) = (1/µ)/(1 ρ) where ρ = λ/µ = utilization For instance, 1/µ = 1ms and ρ = 80% => Q = 5ms TOC Models Evaluation Analysis

29 Simulation Model of traffic Model of routers, links,. Simulation: Time Driven: X(n) = state at time nε X(n+1) = f(x(n), event at time nε) 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.) TOC Models Evaluation Simulation

30 Measurements Design Experiment Representative? Output Analysis TOC Models Evaluation Measurements