ECEN4533 Data Communications Lecture

1
ECEN4533 Data CommunicationsLecture 17 23
February 2009Dr. George Scheets

• Problems 2008 Exam 1, 1-3
• Exam 1 on 6 March, Lecture 22

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ECEN4533 Data CommunicationsLecture 18 25
February 2009Dr. George Scheets

• Read 11.1 11.3
• Problems
• 2008 Exam 1, page 4
• 2007 Exam 1, page 1 2
• Exam 1 on 6 March, Lecture 22

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ECEN4533 Data CommunicationsLecture 19 27
February 2009Dr. George Scheets

• Read 11.4
• Problems
• 2007 Exam 1, problems 3 4
• 2006 Exam 1, problem 1
• Exam 1 on 6 March, Lecture 22
• Design 1 ResultsHi 69, Low 24, Ave.
  56.67Standard Deviation 13.68

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Autocorrelation

• How alike is a waveform shifted version of
  itself?
• Given an arbitrary point on the waveform, how
  predictable is a point t seconds away?
• RX(t) 0?
• Not alike. Uncorrelated.
• RX(t) gt 0?
• Alike. Positively correlated.
• RX(t) lt 0?
• Opposite. Negatively correlated.

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255 point Noise Waveform(Low Pass Filtered White
Noise)
23 points
Volts
0
Time
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Autocorrelation Estimate of Low Pass Filtered
White Noise
Rxx
0
23
tau samples
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Autocorrelation in ATM Cell StreamEach cell slot
randomly On or Off (Empty)
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Autocorrelation in ATM Cell StreamOn Off
bursts average 20 cells
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Packet Switched StatMux
Router or Switch
100 Mbps Trunk
?? 1.54 Mbps Connections P(Access Line is
Active) 10
Trunk Bandwidth assigned based on average input
rates. Infinite Buffers? Can support 649
access lines. Negligible Buffering? Can
support 405 lines w/P(input gt 100 Mbps)
.0001
10
Statistical Multiplexed Packet Switch
Router or Switch
Trunk
Multiple Input Switch
Switch Memory
can be modeled by...
Trunk NIC
Queue
Server
11
Exponentially Distributed Inter-Arrival
Time(Not a good fit to real world traffic)
Bin Count
Time Between packet Arrivals (sec)
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Exponentially Distributed Packet Length(Not a
bad fit to real world traffic)
Bin Count
Bytes
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M/M/1 Queues

• Random, Uncorrelated, Packet Arrivals
• Exponentially Distributed IAT's
• Variable Length Packets
• Exponentially Distrubuted Packets
• Single Server
• Queue servicing 1 output trunk
• Multiple Input, Multiple Output Switch?
• Repeat analysis once per output trunk
• Base on input traffic exiting that trunk

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Classical M/M/1 Queuing Theory
Average Queue Size Dropped Packet Probability
0
100
Offered Load
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Finite Buffer Queuing Performance
Probability of dropped packets
Average Delay for delivered packets
0
100
Trunk Offered Load
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MegaMoron

• Low Working Bid 11,060.97
• Dustin Gaunder

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Little's Rule

• Under steady-state conditionsEK(t) ?
  ETEKq(t) ? ETqregardless of PDF's
  involved.

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M/M/a Queues

• Random, Uncorrelated, Packet Arrivals
• Exponentially Distributed IAT's
• Variable Length Packets
• Exponentially Distrubuted Packets
• Multiple Servers ( a)
• Queue servicing "a" output trunks
• Trunks same speed, same load
• M/M/1 versus equal speed M/M/a
• Less time is spent in M/M/1 system
• Want big trunks to minimize delay thru switch