EECS 122: Introduction to Computer Networks Performance Modeling

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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

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Outline

• Motivations
• Timing diagrams
• Metrics
• Evaluation techniques

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Motivations

• Understanding network behavior
• Improving protocols
• Verifying correctness of implementation
• Detecting faults
• Monitor service level agreements
• Choosing provides
• Billing

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Outline

• Motivations
• Timing diagrams
• Metrics
• Evaluation techniques

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Timing Diagrams

• Sending one packet
• Queueing
• Switching
• Store and forward
• Cut-through
• Fluid view

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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

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Sending One Packet
R bits per second (bps)
Bandwidth R bps Propagation delay T sec
T seconds
P bits
T
Transmission time P/R
time
Propagation delay T Length/speed
1/speed 3.3 usec in free space
4 usec in copper 5 usec in
fiber
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Sending one Packet Examples
P 1 Kbyte R 1 Gbps 100 Km, fiber gt T
500 usec P/R 8 usec
T gtgt P/R
T
P/R
time
T ltlt P/R
T
P 1 Kbyte R 100 Mbps 1 Km, fiber gt T
5 usec P/R 80 usec
P/R
time
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Queueing

• The queue has Q bits when packet arrives ? packet
  has to wait for the queue to drain before being
  transmitted

Capacity R bps Propagation delay T sec
P bits
Q bits
Queueing delay Q/R
T
P/R
time
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Queueing Example
P bits
Q bits
P 1 Kbit R 1 Mbps ? P/R 1 ms
Time (ms)
Packet arrival
0
0.5
1
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7.5
Delay for packet that arrives at time t, d(t)
Q(t)/R P/R
Q(t)
1 Kb
Time
packet 1, d(0) 1ms
packet 2, d(0.5) 1.5ms
packet 3, d(1) 2ms
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Switching Store and Forward

• A packet is stored (enqueued) before being
  forwarded (sent)

5 Mbps
100 Mbps
10 Mbps
10 Mbps
Receiver
Sender
time
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Store and Forward Multiple Packet Example
5 Mbps
100 Mbps
10 Mbps
10 Mbps
Receiver
Sender
time
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Switching Cut-Through

• A packet starts being forwarded (sent) as soon as
  its header is received

R2 10 Mbps
R1 10 Mbps
Receiver
Sender
Header
time
What happens if R2 gt R1 ?
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Fluid Flow System

• Packets are serviced bit-by-bit as they arrive

Q(t) queueing size at time t
a(t) arrival rate
e(t) departure rate
Q(t)
Rate or Queue size
a(t)
t
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Outline

• Motivations
• Timing diagrams
• Metrics
• Throughput
• Delay
• Evaluation techniques

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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 103bps, 1Mbps 106bps, 1
  Gbps 109bps For memory 1 Kbyte 210 bytes
  1024 bytes
• Some rates are expressed in packets per second
  (pps) ? relevant for routers/switches where the
  bottleneck is the header processing

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Example Windows Based Flow Control
Source
Destination

• 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
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Throughput Fluctuations

• Throughput may vary over time

Throughput
max
mean
min
Time
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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

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Delay Illustration 1
1
2
Sender
Receiver
Latest bit seen by time t
at point 2
at point 1
Delay
time
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Delay Illustration 2
1
2
Sender
Receiver
Packet arrival times at 1
1
2
Packet arrival times at 2
Delay
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Littles 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?

d(i) delay of packet i
a(t) arrival rate
system

• 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?

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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
time
T
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S area
time
T
Average occupancy S/T
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S(N)
S area
time
T
S S(1) S(2) S(N) P(d(1) d(2)
d(N))
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S(N)
S area
time
T
S/T (P(d(1) d(2) d(N)))/T
((PN)/T) ((d(1) d(2) d(N))/N)
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Littles Theorem
1
2
Latest bit seen by time t
Sender
Receiver
S(N)
a(i)
S(N-1)
d(N-1)
x(t)
S area
time
T
Average occupancy (average arrival rate) x
(average delay)
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Outline

• Motivations
• Timing diagrams
• Metrics
• Evaluation techniques

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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

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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

s
a
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Simulation

• Model of traffic
• Model of routers, links
• Simulation
• Time driven
• X(t) state at time t
• X(t1) 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(n1), T(n1) g(Y(n), T(n), E(n))
• Output analysis estimates, confidence intervals

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Evaluation Putting Everything Together
Abstraction
Reality
Model
Plausibility
Derivation
Tractability
Prediction
Hypothesis
Conclusion
Realism

• 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)