Models Motivation Timing Diagrams Metrics Evaluation Techniques TOC Models 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 Timing Sending one packet Illustration Examples Queuing Queuing example Store and forward S F Multiple packets Cut Through Fluid View TOC Models Timing One Packet R bps P bits T seconds T P R Time 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 TOC Models Timing One Packet 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 Examples T P R T P 1KByte R 1Gbps 100km fiber T 500 s P R 8 s P R T T P R TOC Models Timing Examples P R P 1KByte R 100Mbps 1km fiber T 5 s P R 80 s Queuing Link P bits R bps Q T seconds Q R Q R queuing delay load dependent T P R Time TOC Models Timing Queuing Queuing Example P bits Link R bps 1 kbit packets R 1Mbps Q 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 TOC Models Timing Queuing Example T5 1 5ms T6 1ms Store and Forward System 10Mbps 5Mbps 100Mbps TOC Models Timing Store and Forward 10Mbps S F Multiple System 10Mbps 5Mbps TOC Models Timing S F Multiple 100Mbps 10Mbps Cut Through System R1 10Mbps Header Note What if R2 R1 TOC Models Timing Cut Through R2 10Mbps Start forwarding as soon as the header is received A Fluid View System A t rate a t bits in 0 t a t d t X t TOC Models Timing Fluid View X t Rate R D t rate d t bits in 0 t Metrics Throughput Delay TOC Models Metrics Throughput Definitions Example 1 Connection Example 2 Link Fluctuations Measurements TOC Models Metrics Throughput 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 103bps 1Mbps 106bps 1Gbps 109bps For memory 1Kbytes 210 bytes 1 024 bytes 1MBytes 220 bytes Some rates are expressed in packet per second pps relevant when the bottleneck is the header processing TOC Models Metrics Throughput Definitions Connection 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 Source K RTT K RTT TOC Models Metrics Throughput Connection Destination Time Link Mbps 1Mbps link sends 1 000 bit packets Rate every s 1 Rate every 40 ms 0 5 Utilization 50 TOC Models Metrics Throughput Link Time t Fluctuations Rate varies over time Throughput over last T seconds max mean min Time t TOC Models Metrics Throughput Fluctuations 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 Delay Definitions Illustration 1 Illustration 2 Little s Result Measurements Example 1 Measurements Example 2 TOC Models Metrics Delay Definitions Delay Latency of bit packet file from A to B Jitter Variability in delay Round Trip Time RTT The time required for bit packet file to go from A to B 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 Illustration 1 2 1 S D Latest bit seen by time t at point 1 at point 2 n Delay of bit n TOC Models Metrics Delay Illustration 1 Illustration 2 1 2 S D Packet arrival times at 1 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 Little s Result N 1 S T N T N 1 2 D X t S area S T 1 T N integral of X t 1 X t dt S T 1 T N N T T N T T Average occupancy average delay x average arrival rate TOC Models Metrics Delay Little s Result Measurements 1 A Good Epoch TOC Models Metrics Delay Measurements 1 Measurements 2 A Worse Epoch TOC Models Metrics Delay Measurements 2 Evaluation Techniques Models Analysis Models Simulations Measurements TOC Models Evaluation Analysis 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 TOC Models Evaluation Analysis Simulation 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 TOC Models Evaluation Simulation Measurements Design Experiment Representative Output Analysis TOC Models Evaluation Measurements
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