Models. One Packet. Timing. Illustration. Examples UCB. Models EECS 122. P bits. Motivation Timing Diagrams Metrics Evaluation Techniques

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1 Motivation iming iagrams Metrics Evaluation echniques Motivation Understanding Network Behavior Improving Protocols Verifying Correctness of Implementation etecting Faults Choosing Provider Feasibility of Applications Monitoring ervice Level Agreements Billing OC OC Motivation iming ending one packet Illustration Examples Queuing Queuing example tore and forward &F:Multiple packets Cut-hrough Fluid View OC iming One Packet = ransmission time seconds = Propagation time = L/speed = L(km)x(time/km) /km = 3.3µs in free space 4 µs in copper 5 µs in fiber OC iming One Packet Illustration Examples ransmitter ignal ransmission Line One bit Each bit takes 1/R seconds to be transmitted he bits take seconds to propagate Receiver << >> P = 1KByte R = 1Gbps 100km, fiber = 500µs = 8µs P = 1KByte R = 100Mbps 1km, fiber = 5µs = 80µs OC iming Illustration OC iming Examples

2 Queuing Q seconds Queuing Example 1-kbit packets; R = 1Mbps Q 1ms Q/R (t) = Q/R + for a packet that arrives at t Q/R = queuing delay (load-dependent) OC iming Queuing 1ms Let n = Q/R + for packet n 1 = 1ms 2 = 1.5ms 3 = 2ms 4 = 1ms OC iming Queuing Example 5 = 1.5ms 6 = 1ms t tore and Forward &F - Multiple 10Mbps 5Mbps 100Mbps 10Mbps 10Mbps 5Mbps 100Mbps 10Mbps OC iming tore and Forward OC iming &F Multiple Cut-hrough R1 = 10Mbps R2 = 10Mbps A Fluid View Rate R A(t); rate a(t) (t); rate d(t) # bits in [0, t] # bits in [0, t] Header tart forwarding as soon as the header is received a(t) d(t) Note: What if R2 > R1? OC iming Cut-hrough OC iming Fluid View

3 Metrics hroughput hroughput elay efinitions Example 1: Connection Example 2: Link Fluctuations Measurements OC Metrics OC Metrics hroughput efinitions Roughly: throughput = bit rate (e.g., 120Kbits/second) More precisely: hroughput of a connection or of a link: total number of bits during some period [t, t + ] divided by 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] ome rates are expressed in packet per second (pps) relevant when the bottleneck is the header processing Connection Connection: end W bits (window size) Wait for ACKs Repeat Assume that the round-trip time is R seconds hroughput = W/R bps Numerical Example: W = 64KBytes = 512 kbits = 512x1,024 = 524,288 bits R = 200ms hroughput = W/ = 2.6Mbps ource R R K K estination OC Metrics hroughput efinitions OC Metrics hroughput Connection Link 1Mbps link sends 1,000-bit packets Fluctuations Rate varies over time Mbps 1 Rate every µs hroughput over last seconds Rate every 40 ms max 0.5 mean Utilization = 50% min OC Metrics hroughput Link t OC Metrics hroughput Fluctuations t

4 Measurements CP: Keep track of number of bytes received Let R(t) = number of bits in [0, t] hroughput over last seconds = [R(t) R(t )]/ evice has counter with number of bytes received; calculate as above elay efinitions Illustration 1 Illustration 2 Little s Result Measurements: Example 1 Measurements: Example 2 OC Metrics hroughput Measurements OC Metrics elay efinitions elay/latency of bit (packet, file) from A to B he time required for bit (packet, file) to go from A to B Jitter: Variability in delay Round-rip (R) wo-way delay from sender to receiver and back Bandwidth-elay Product Product of bw and delay, indicates storage capacity of network Illustration 1 n Latest bit seen by time t at point 1 at point 2 elay of bit n OC Metrics elay efinitions OC Metrics elay Illustration 1 Illustration Packet arrival times at 1 Packet arrival times at 2 Max delay = 100 ms Min delay = 40 ms Jitter = 60 ms OC Metrics elay Illustration 2 20 ms N Little s Result = area (N) (N - 1) = (1) + + (N) = integral of 1 (1) + + (N) N dt = =. N Average occupancy = (average delay)x(average arrival rate) OC Metrics elay Little s Result

5 Measurements 1 Measurements 2 A Good Epoch A Worse Epoch OC Metrics elay Measurements 1 OC Metrics elay Measurements 2 Evaluation echniques + Analysis + imulations Measurements Analysis Example: M/M/1 Queue λ µ Arrivals are Poisson with rate λ ervice times are exponentially distributed with mean 1/µ Average delay per packet = 1/(µ λ) = (1/µ)/(1 ρ) where ρ = λ/µ = utilization For instance, 1/µ = 1ms and ρ = 80% => Q = 5ms OC Evaluation OC Evaluation Analysis imulation Model of traffic Model of routers, links,. imulation: riven: X(n) = state at time nε X(n+1) = f(x(n), event at time nε) Event riven: Y(n) = state after event n E(n) = n-th event (n) = time when event n occurs [Y(n+1), (n+1)] = g(y(n), (n), E(n)] Key tep: Output analysis (estimates, confidence intervals.) Measurements esign Experiment Representative? Output Analysis OC Evaluation imulation OC Evaluation Measurements