1. COMT 4291 Computing Resource Requirements for Circuit Switched Networks Introduction

2. COMT 4292 Resource Usage Prediction How many simultaneous requests? 2 3 1 4 Resource

3. COMT 4293 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. COMT 4294 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. COMT 4295 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. COMT 4296 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. COMT 4297 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. COMT 4298 Possible Answers How many resource requests are possible? 2 3 1 4 Resource range is 0 to N units of resources

9. COMT 4299 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. COMT 42910 The Answer

11. COMT 42911 Another Simple Case The probability that there will be no resource request –One subscriber will not use a resource with probability (1-h)

12. COMT 42912 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. COMT 42913 A tempting answer For x requests, combine x probabilities of requesting a resource with N-x probabilities of not requesting a resource

14. COMT 42914 Are these different answers? 2 3 1 4 2 3 1 4

15. COMT 42915 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. COMT 42916 The General Answer Also called the binomial distribution

17. COMT 42917 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