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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