COMT 429

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Computing Resource Requirements for Circuit

Switched Networks

Introduction

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Resource Usage Prediction

• How many simultaneous requests?

2

3

1

4

Resource

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Probability of Resource Usage

• Measure the subscriber resource usage over a specific period of time.

• The probability of resource usage is defined as the fraction of the observation time during which the subscriber was occupying the resource

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In Voice Networks(Circuit Switching)

• Total Amount of Usage per unit time (usually one hour).

• Erlangs–Hours of usage per hour of observation–30 3-minute calls in one hour = 1.5 Erlangs

• CCS–Number of 100 sec usage increments per

hour of observation–30 3-minute calls in one hours = 54 CCS

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Resource Demand

• Compute the traffic per subscriber (in Erlangs)

• For example, a subscriber makes 6 minutes of calls in one hour– Traffic is 6/60 = 0.1 Erlangs

• Probability of trunk usage by one subscriber equals the traffic (in Erlangs) from that subscriber (10% in the example)

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In General

• We can measure the total traffic generated by a group of subscribers

• We may not know the exact number of subscribers, or

• We may not want to recompute our design if the number of subscribers changes slightly

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For now, however

• Assume that the number of subscribers is known, and “small”

• Assume for simplicity that each subscriber in the group generates the same amount of traffic

• Assume that the subscribers are “independent” in their choice to use network resources

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Possible Answers

• How many resource requests are possible?

2

3

1

4

Resource range is

0 to N units of resources

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A simple question

• What is the probability of N simultaneous resource requests?

• For notation, we use “h” as the traffic per subscriber (in Erlangs)

• In our example– N = 4– h = 0.1

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The Answer

P(N;h)h N

P(4;0.1)(0.1)4

10 4

0.01%

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Another Simple Case

• The probability that there will be no resource request– One subscriber will not use a resource

with probability (1-h)

P(0;h)(1 h)N

P(0;0.1)(0.9)4

0.656166%

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Another question

• The probability of exactly three simultaneous resource requests

• Three user have h*h*h probability of requesting a resource

• The remaining users must not be requesting resources

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A tempting answer

• For x requests, combine x probabilities of requesting a resource with N-x probabilities of not requesting a resource

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Are these different answers?

2

3

1

4

2

3

1

4

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Each combination of users has to be counted

• How many different selections of x subscribers can I pull from a total pool of N subscribers

N

x

Cr (N,x)

N!

x!(N x)!

4

3

Cr (4,3)

4!

3!1!24

64

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The General Answer

• Also called the binomial distribution

B (x,N,h)N

x

h x (1 h)(N x )

B (3,4,0.1)4(0.1)3 (0.9)0.00360.36%

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Assignment

• Now: Compute the probabilities for all 6 cases possible with N=5, h=0.1

• For next class: Build a spreadsheet which computes the binomial distribution (probability and cumulative) given N and h, and graph the distribution for N=15, h=0.02