Network blocking probability by dhawal sharma
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Transcript of Network blocking probability by dhawal sharma
etwork Blocking Probability
1By – Dhawal G. Sharma
Outline A brief history of communication Telephone Network Blocking Network Blocking Probability End to End Blocking Probability
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a brief history of communication…
Pigeon Delivery
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Voice Messaging
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Primitive Telephone
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Dialer Telephone
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Type-500 Telephone
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DTMF Telephone
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Cordless Telephone
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Wireless Telephony
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Voice Devices
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Enhancements
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Desktop PCs
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Multimedia Cellular Phones
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Laptops
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Satellite Telephony
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Touch Telephony
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elephone T Network
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Hierarchy
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The Focus
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Centralised N/W
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De-centralised N/W
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Advantage of Decentralised N/W
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Multi-stage N/W
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Possible paths for 1 set
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The Flow
Blocking Probability
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Lee’s Blocking Probability
-> Every network has a maximum probability of blocking
Assumptions –
1)Traffic Distribution is uniform, constant or Poisson traffic i.e. inter-arrival rate follows a pattern.2)The network is considered to be a multiple-server queuing system.3) In steady state, call arrival rate is equal to departure rate.4) During the network operation, a certain WORKLOAD is maintained which is defined by Network Utilization.
Network Utilization is the ratio of “Total no of busy links to no of input ports”
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Terminologies and Equations
p = probability that the link is busy(Occupancy, loading or utilization percentage)q = probability that the link is idle = (1-p)n = no of parallel links used to complete a connection.
Probability that all links are busy = (p)^n.
= 1 - (q)^n
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Consider a 3 stage n/w
k = no of different pathsp’ = probability that any particular inter-mediate link is busyq’ = probability that any particular inter-mediate link is idle
Probability of blocking –
B = (probability that all paths are busy) = (probability that an arbitrary link is busy)^k = (probability that atleast one link is busy)^k = (1 - (q’)^2)^k
p’ = p/βΒ = k/n
3 stage n/w
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3 stage n/w
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k
p p
p’
p’
p’
p’
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(1 – q2q3)
B = p1(1 – q2q3)
p2 p3
p1
End to End Blocking Probability
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References
1) R Syski, Introduction to Congestion Theory.2) S. S. Katz, Improved Networks and End-to-End Probability
Theory3) John C. Bellamy, Digital Telephony
Designed & Presented by : Dhawal G. Sharma
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