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Computing Resource Requirements for Circuit Switched Networks

Computing Resource Requirements for Circuit Switched Networks. Introduction. Resource Usage Prediction. How many simultaneous requests?. 1. Resource. 2. 3. 4. Probability of Resource Usage. Measure the subscriber resource usage over a specific period of time.

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Computing Resource Requirements for Circuit Switched Networks

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  1. Computing Resource Requirements for Circuit Switched Networks Introduction

  2. Resource Usage Prediction • How many simultaneous requests? 1 Resource 2 3 4

  3. 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

  4. 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

  5. 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)

  6. 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

  7. 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

  8. Possible Answers • How many resource requests are possible? 1 Resource range is 0 to N units of resources 2 3 4

  9. 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

  10. The Answer

  11. Another Simple Case • The probability that there will be no resource request • One subscriber will not use a resource with probability (1-h)

  12. 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

  13. A tempting answer • For x requests, combine x probabilities of requesting a resource with N-x probabilities of not requesting a resource

  14. Are these different answers? 1 1 2 2 3 3 4 4

  15. 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

  16. The General Answer • Also called the binomial distribution

  17. 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

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