SCENARIOS FOR TRANSITION FROM CIRCUIT SWITCHED TO PACKET SWITCHED
Computing Resource Requirements for Circuit Switched Networks
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Transcript of Computing Resource Requirements for Circuit Switched Networks
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?
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1
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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?
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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?
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1
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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)!
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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