Traffic%20Modeling%20and%20Performance%20Analysis%20in%20Telecommunication%20Networks

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Module 2.0 Modeling of Network Components
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Queueing theory

• Basics

? average number of packets
1/? mean service time per packet s
arriving per second p/s ? average
number of packets being ? service time for
a given packet s served per second
p/s ? traffic intensity ?²
variance on service time s²
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Queueing theory

• Classification Kendalls notation
• A / B / m - q.d. - N

A packet interarrival time distribution
function B service time distribution
function m number of queues q.d.
queue discipline (FIFO, priority) N
buffer size
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Queueing theory

• Performance indicators
• N average number of packets in
  the system
• T average time a packet spends
  in the system
• W average time a packet spends
  in the queue
• PB blocking probability
• ? throughput

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Inside a Router
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Component models

• Router

?interface A
B
?interface B
A
C
?interface C
?routing
?interface D
D

• routing time independent from packet size
• Routing rate is the packet forwarding rate and
  includes queueing-in time, processing, and
  queueing-out time. This is usually done by
  manipulating pointers.
• Model as M/M/1

7
Component models

• Switch

?interface A
B
?interface B
A
C
?interface C
?switching
?interface D
D

• switching time proportional to packet size.
• In ATM, packet is fixed so it is M/D/1
• In our 3Com Superstack III, even if you fix the
  packet size, model as M/M/1. The switch uses
  store and forward, and not cut-through. Packet
  is completely stored before it gets forwarded
  similar to a router. Thus, processing is
  variable.

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Component models

• Client/Server

?processing

• time to process a packet is variable and it
  depends on CPU utilization, tasks, other
  interrupts, etc.
• ?processing is the average packet processing
  rate from Application to Interface. This needs
  to be truly measured. It is not the advertised
  one. For simplicity, assume the CPU utilization
  is 100.
• Model as M/M/1

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Component models

• Interface serial line

propagation delay
?line speed

• time to place packet on line proportional to
  packet size
• Model as M/D/1

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Component models

• Simplifications
• packets (requests) arrive according to a poisson
  process (exponential interarrival times)
• infinite buffer size
• independent queues (just add delays induced in
  the different queues encountered on the path)

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Exercise

• Three 2 Mbps full-duplex links are connected to a
  Cisco 4700 router (?routing 40000 p/s).
  Measurements show the following traffic load
• All packets have a length of 5000 bit. What
  is the average delay for a packet travelling from
  A to B. What is the major cause of this delay ?

incoming outgoing connection A
300 p/s 200 p/s connection B 100 p/s
300 p/s connection C 200 p/s 100 p/s