Computer Networks (Graduate level)

1
Computer Networks(Graduate level)
Lecture 3 Performance Evaluation

• University of Tehran
• Dept. of EE and Computer Engineering
• By
• Dr. Nasser Yazdani

2
Outline

• Strategy
• Performance factors
• Queuing Theory

3
Strategies

• Circuit switching carry bit streams
• Connection oriented.
• original telephone network
• Dedicated resource.
• Packet switching store-and-forward messages
• Connectionless (IP) or connection oriented (ATM)
• Internet
• Shared resource.
• Packet switching is the focus of computer
  Networks.

4
Packet Switching
R2
Source
Destination
R1
R3
R4

• Its the method used by the Internet.
• Each packet is individually routed
  packet-by-packet, using the routers local
  routing table.
• The routers maintain no per-flow state.
• Different packets may take different paths.
• Several packets may arrive for the same output
  link at the same time, therefore a packet switch
  has buffers.

5
Packet SwitchingSimple router model
Link 1, ingress
Link 1, egress
Choose Egress
Link 2
Link 2, ingress
Link 2, egress
Choose Egress
R1
Link 1
Link 3
Link 3, ingress
Link 3, egress
Choose Egress
Link 4
Link 4, ingress
Link 4, egress
Choose Egress
6
Multiplexing (resource sharing)

• Time-Division Multiplexing (TDM)
• Frequency-Division Multiplexing (FDM)

7
Statistical Multiplexing

• On-demand time-division
• Schedule link on a per-packet basis
• Packets from different sources interleaved on
  link
• scheduling
• fairness, quality of service
• Buffer packets that are contending for the link
• Buffer (queue) overflow is called congestion

8
Statistical MultiplexingBasic idea
One flow
Two flows
rate
rate
Average rate
time
Many flows
rate
time
Average rates of 1, 2, 10, 100, 1000 flows.

• Network traffic is bursty.i.e. the rate changes
  frequently.
• Peaks from independent flowsgenerally occur at
  different times.
• Conclusion The more flows we have, the smoother
  the traffic.

time
9
Packet Switches

• A node in a packet switching network

Node
incoming links
outgoing links
Memory
10
Packet SwitchingStatistical Multiplexing
Packets for one output
Queue Length X(t)
Dropped packets
1
Data
Hdr
R
X(t)
B
R
2
Data
Hdr
Link rate, R
R
Packet buffer
N
Data
Hdr
Time

• Because the buffer absorbs temporary bursts, the
  egress link need not operate at rate (NxR).
• But the buffer has finite size, B, so losses will
  occur.

11
Statistical Multiplexing
A
Rate
C
C
A
time
B
Rate
C
C
B
time
12
Statistical Multiplexing Gain
AB
Rate
2C
R lt 2C
A
R
B
time
Statistical multiplexing gain 2C/R Other
definitions of SMG The ratio of rates that give
rise to a particular queue occupancy, or
particular loss probability.
13
Why does the Internet usepacket switching?

• Efficient use of expensive links
• The links are assumed to be expensive and scarce.
  
• Packet switching allows many, bursty flows to
  share the same link efficiently.
• Circuit switching is rarely used for data
  networks, ... because of very inefficient use of
  the links - Gallager
• Resilience to failure of links routers
• For high reliability, ... the Internet was to
  be a datagram subnet, so if some lines and
  routers were destroyed, messages could be ...
  rerouted - Tanenbaum

14
Some Definitions

• Packet length, P, is the length of a packet in
  bits.
• Link length, L, is the length of a link in
  meters.
• Data rate, R, is the rate at which bits can be
  sent, in bits/second, or b/s.1
• Propagation delay, PROP, is the time for one bit
  to travel along a link of length, L. PROP
  L/c.
• Transmission time, TRANSP, is the time to
  transmit a packet of length P. TRANSP P/R.
• Latency is the time from when the first bit
  begins transmission, until the last bit has been
  received. On a link Latency PROP TRANSP.

1. Note that a kilobit/second, kb/s, is 1000
bits/second, not 1024 bits/second.
15
Packet Switching
R2
Source
Destination
R1
R3
R4
16
Packet Switching vs. Message switching
Breaking message into packets allows parallel
transmission across all links, reducing end to
end latency. It also prevents a link from being
hogged for a long time by one message.
17
Performance Metrics

• Bandwidth (throughput)
• data transmitted per time unit
• link versus end-to-end
• notation
• KB 210 bytes
• Mbps 106 bits per second
• Latency (delay)
• time to send message from point A to point B
• one-way versus round-trip time (RTT)
• components
• Latency Propagation Transmit Queuing
• Queuing time can be a dominant factor

18
Latency (Queuing Delay)
The egress link might not be free, packets may be
queued in a buffer. If the network is busy,
packets might have to wait a long time.
TRANSP1
Host A
Q2
TRANSP2
How can we determine the queuing delay?
R1
PROP1
TRANSP3
R2
PROP2
TRANSP4
R3
PROP3
Host B
PROP4
19
Queues and Queuing Delay

• To understand the performance of a packet
  switched network, we can think of it as a series
  of queues interconnected by links.
• For given link rates and lengths, the only
  variable is the queuing delay.
• If we can understand the queuing delay, we can
  understand how the network performs.

20
Queues and Queuing Delay
Cross traffic causes congestion and variable
queuing delay.
21
A router queue
Model of router queue
Buffer
Server
A(t), l
D(t)
m
Q(t)
22
A router queue (cont)

• Usually buffer size if fine
• State of the system depends on
• Packet arrival process, (Poisson, deterministic,
  etc)
• Packet length distribution
• The service discipline (FCFS, LCFS, priority,
  etc)
• of Server, service process

23
A simple deterministic model

• Service discipline is FIFO
• Buffer can finite of infinite
• Properties of A(t), D(t)
• A(t), D(t) are non-decreasing
• A(t) gt D(t)

24
A simple deterministic modelbytes or fluid
Cumulative number of bits that arrived up until
time t.
A(t)
A(t)
Cumulative number of bits
D(t)
Q(t)
m
Service process
m
time
D(t)

• Properties of A(t), D(t)
• A(t), D(t) are non-decreasing
• A(t) gt D(t)

Cumulative number of departed bits up until time
t.
25
Simple deterministic model
Cumulative number of bits
d(t)
A(t)
Q(t)
D(t)
time

• Queue occupancy Q(t) A(t) - D(t).
• Queuing delay, d(t), is the time spent in the
  queue by a bit that arrived at time t, and if the
  queue is served first-come-first-served (FCFS or
  FIFO)

26
Example
Cumulative number of bits
Q(t)
Example Every second, a train of 100 bits arrive
at rate 1000b/s. The maximum departure rate is
500b/s.What is the average queue occupancy?
d(t)
A(t)
100
D(t)
time
0.1s
0.2s
1.0s
27
Queues with Random Arrival Processes

1. Usually, arrival processes are complicated, so we
   often model them as random processes.
2. The study of queues with random arrival processes
   is called Queueing Theory.
3. Queues with random arrival processes have some
   interesting properties. Well consider some here.

28
Properties of queues

• Time evolution of queues.
• Examples
• Burstiness increases delay
• Determinism minimizes delay
• Littles Result.
• The M/M/1 queue.

29
Time evolution of a queuePackets
Model of FIFO router queue
A(t), l
D(t)
m
Q(t)
Packet Arrivals
time
Departures
Q(t)
30
Burstiness increases delay

• Example 1 Periodic arrivals
• 1 packet arrives every 1 second
• 1 packet can depart every 1 second
• Depending on when we sample the queue, it will
  contain 0 or 1 packets.
• Example 2
• N packets arrive together every N seconds (same
  rate)
• 1 packet departs every second
• Queue might contain 0,1, , N packets.
• Both the average queue occupancy and the variance
  have increased.
• In general, burstiness increases queue occupancy
  (which increases queuing delay).

31
Determinism minimizes delay

• Example 3 Random arrivals
• Packets arrive randomly on average, 1 packet
  arrives per second.
• Exactly 1 packet can depart every 1 second.
• Depending on when we sample the queue, it will
  contain 0, 1, 2, packets depending on the
  distribution of the arrivals.
• In general, determinism minimizes delay. i.e.
  random arrival processes lead to larger delay
  than simple periodic arrival processes.

32
Littles Result
33
The Poisson process

• Arrival process is Poisson
• Queuing system is M/M/1, Poisson arrival,
  Exponential service,
• with 1 server.
• Arrival process is momeryless or arrival of
  packets are
• independent of each others
• Prob. of one arrival in ?t is ? ?t o(?t)

34
The Poisson process (cont)

• Poisson process is a probability distribution
  function.
• Sp(k) 1 for all k0, 1,
• How many arrivals in t second? It is the expected
  value
• Skp(k) ?t
• What is interarrival time, r, between two arrival
• f(r) ?e-?r
• This is the same the service time.
• f(r) µe- µr

35
The Poisson process

• Why use the Poisson process?
• It is the continuous time equivalent of a series
  of coin tosses.
• It is known to model well systems in which a
  large number of independent events are aggregated
  together. e.g.
• Arrival of new phone calls to a telephone switch
• Decay of nuclear particles
• Shot noise in an electrical circuit
• It makes the math easy.
• Be warned
• Network traffic is very bursty!
• Packet arrivals are not Poisson.
• But it models quite well the arrival of new flows.

36
An M/M/1 queue

• A(t) is a Poisson process with rate l, and the
  time to serve each packet is exponentially
  distributed with rate m, then
• We assume the system is in steady state, or
  stationary, with none time varying values.
• Pn is the probability that there are n customer
  in the queue including the one in the service.
• ? l/m , ration of load on capacity, is
  utilization or traffic intensity.

37
An M/M/1 queue (cont)
l
l
l
l
l
l
.
n1
n
n-1
2
1
0
m
m
m
m
m
m
m

• Prob. that the system move from state n-1 to n is
  l , with no departure, and probability that it
  moves from state n to n-1 is m. In order the
  system to be in stationary state the probability
  of departure and moving state should be equal.
• (l m)Pn lPn-1 mPn1

38
An M/M/1 queue (cont)
l
l
l
l
l
.
n1
n
n-1
2
1
0
m
m
m
m
m
m

• Considering the rate of interring and leaving the
  surface gives us .
• Pn mPn1 gt Pn1 rPn gt Pn rnP0
• What is the value of P0?
• SnPn 1 gt P0Snrn 1 gt P0 1 r
• Pn (1 r) rn

39
An M/M/1 queue
Model of FIFO router queue
A(t), l
D(t)
m

• If A(t) is a Poisson process with rate l, and the
  time to serve each packet is exponentially
  distributed with rate m, then

40
Next Lecture LANs

• How to share the wire
• How to extend to multiple segments
• Assigned reading
• MB76 ETHERNET Distributed Packet Switching for
  Local Area Networks
• B88 Measured Capacity of an Ethernet Myths
  and Reality
• Chap. 2 of book (Recommended!)