4005-741-01 Advanced Computer Networks
Module 3. Monte Carlo Simulation
Lecture Notes

Example: Network Failure Probability

Given a (connected) network topology, given the probability of link failure, assuming each link fails independently with the same probability, what is the probability of network failure, that is, a disconnected network?

• Network topology input file: net1
  • Nodes represented as integers, starting at 0
  • Bidirectional links represented as pairs of nodes

    0       1
    1       2
    2       3
    3       4
    4       5
    5       0
    1       4
    2       5
    

• Class Network [source code]

• Class Connectivity01 [source code]

• Class Connectivity02 [source code]

• Example

  $ java Connectivity02 net1 0.05 0.05 19 1000000 793876
  Link fail prob = 0.050000
  Net fail count = 5936
  Trials = 1000000
  Net fail prob = 0.005936
  Link fail prob = 0.100000
  Net fail count = 27518
  Trials = 1000000
  Net fail prob = 0.027518
  Link fail prob = 0.150000
  Net fail count = 68176
  Trials = 1000000
  Net fail prob = 0.068176
  Link fail prob = 0.200000
  Net fail count = 130526
  Trials = 1000000
  Net fail prob = 0.130526
  Link fail prob = 0.250000
  Net fail count = 210640
  Trials = 1000000
  Net fail prob = 0.210640
  Link fail prob = 0.300000
  Net fail count = 306616
  Trials = 1000000
  Net fail prob = 0.306616
  Link fail prob = 0.350000
  Net fail count = 411385
  Trials = 1000000
  Net fail prob = 0.411385
  Link fail prob = 0.400000
  Net fail count = 519923
  Trials = 1000000
  Net fail prob = 0.519923
  Link fail prob = 0.450000
  Net fail count = 626212
  Trials = 1000000
  Net fail prob = 0.626212
  Link fail prob = 0.500000
  Net fail count = 722450
  Trials = 1000000
  Net fail prob = 0.722450
  Link fail prob = 0.550000
  Net fail count = 805729
  Trials = 1000000
  Net fail prob = 0.805729
  Link fail prob = 0.600000
  Net fail count = 873694
  Trials = 1000000
  Net fail prob = 0.873694
  Link fail prob = 0.650000
  Net fail count = 924411
  Trials = 1000000
  Net fail prob = 0.924411
  Link fail prob = 0.700000
  Net fail count = 959381
  Trials = 1000000
  Net fail prob = 0.959381
  Link fail prob = 0.750000
  Net fail count = 981551
  Trials = 1000000
  Net fail prob = 0.981551
  Link fail prob = 0.800000
  Net fail count = 993048
  Trials = 1000000
  Net fail prob = 0.993048
  Link fail prob = 0.850000
  Net fail count = 998167
  Trials = 1000000
  Net fail prob = 0.998167
  Link fail prob = 0.900000
  Net fail count = 999713
  Trials = 1000000
  Net fail prob = 0.999713
  Link fail prob = 0.950000
  Net fail count = 999988
  Trials = 1000000
  Net fail prob = 0.999988
  

  

Radio Power Concepts

• Transmit and receive power
  • P_t = Transmit (TX) power
  • P_r = Receive (RX) power

• Path loss
  • L = Path loss factor
  • P_r = P_t / L

• Antenna gain
  • G_t = TX antenna gain
  • G_r = RX antenna gain
  • An isotropic antenna radiates power in all 3-D directions equally
  • A directional antenna radiates more power in some 3-D directions than others
  • Antenna gain (in a certain direction) = actual power radiated / power radiated by an isotropic antenna

• Propagation model
  • Expresses path loss L as a function of transmitter-receiver distance d, L(d)

• The ground reflection (two-ray) propagation model
  • From Theodore S. Rappaport, Wireless Communications: Principles and Practice, 2nd Edition (Prentice Hall, 2002), pages 124-125
  • Received signal consists of the sum of two components:
    • Direct signal from transmit antenna straight to receive antenna
    • Reflected signal from transmit antenna, bounces off the ground, then to receive antenna
  • Received power:
    • P_r = P_t G_t G_r h_t² h_r² / d⁴
  • Path loss:
    • L(d) = d⁴ / (G_t G_r h_t² h_r²)
  • Where:
    • L = Path loss
    • d = TX-RX distance (m)
    • G_t = TX antenna gain
    • G_r = RX antenna gain
    • h_t = TX antenna height (m)
    • h_r = RX antenna height (m)

• Receiver sensitivity
  • S = The minimum RX power required to reliably receive the transmitted signal
  • That is, P_r ≥ S
  • Setting P_r = S and solving for d gives d_max, the maximum TX-RX distance
  • d_max = (P_t G_t G_r h_t² h_r² / S)^1/4

Example: Sensor Network Lifetime

• Class SensorNet01 [source code]

• Class SensorNet02 [source code]

• Class SensorNet03 [source code]

Advanced Computer Networks • 4005-741-01 • Fall Quarter 2009

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Alan Kaminsky • Department of Computer Science • Rochester Institute of Technology • 4486 + 2220 = 6706

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Copyright © 2009 Alan Kaminsky. All rights reserved. Last updated 23-Oct-2009. Please send comments to ark­@­cs.rit.edu.