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Basic teletraffic concepts An intuitive approach (theory will come next) Focus on “calls”

Basic teletraffic concepts An intuitive approach (theory will come next) Focus on “calls”. 1 user making phone calls. TRAFFIC is a “stochastic process”. How to characterize this process? statistical distribution of the “BUSY” period statistical distribution of the “IDLE” period

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Basic teletraffic concepts An intuitive approach (theory will come next) Focus on “calls”

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  1. Basic teletraffic conceptsAn intuitive approach (theory will come next) Focus on “calls”

  2. 1 usermakingphonecalls TRAFFIC is a “stochastic process” • How to characterize this process? • statistical distribution of the “BUSY” period • statistical distribution of the “IDLE” period • statistical characterization of the process “memory” • E.g. at a given time, does the probability that a user starts a call result different depending on what happened in the past? BUSY 1 IDLE 0 time

  3. Trafficcharacterizationsuitablefortrafficengineering All equivalent (if stationary process)

  4. TrafficIntensity: example • Usermakes in average 1 calleveryhour • Eachcalllasts in average 120 s • Trafficintensity = • 120 sec / 3600 sec = 2 min / 60 min = 1/30 • Probabilitythat a userisbusy • Userbusy 2 min out of 60 = 1/30 adimensional

  5. Trafficgeneratedby more thanoneusers U1 Traffic intensity (adimensional, measured in Erlangs): U2 U3 U4 TOT

  6. example • 5 users • Each user makes an average of 3 calls per hour • Each call, in average, lasts for 4 minutes Meaning: in average, there is 1 active call; but the actual number of active calls varies from 0 (no active user) to 5 (all users active),with given probability

  7. Second example • 30 users • Each user makes an average of 1 calls per hour • Each call, in average, lasts for 4 minutes • SOME NOTES: • In average, 2 active calls (intensity A); • Frequently, we find up to 4 or 5 calls; • Prob(n.calls>8) = 0.01% • More than 11 calls only once over 1M • TRAFFIC ENGINEERING: how many channels to reserve for these users!

  8. A note on binomial coefficient computation

  9. Infinite Users Assume M users, generating an overall traffic intensity A (i.e. each user generates traffic at intensity Ai =A/M). We have just found that Let Minfinity, while maintaining the same overall traffic intensity A

  10. Poisson Distribution Very good matching with Binomial(when M large with respect to A) Much simpler to use than Binomial (no annoying queueing theory complications)

  11. Limitednumberofchannels THE most important problem in circuit switching U1 U2 • The number of channels C is less than the number of users M (eventually infinite) • Some offered calls will be “blocked” • What is the blocking probability? • We have an expression for P[k offered calls] • We must find an expression for P[k accepted calls] • As: X U3 X U4 TOT No. carried calls versus t No. offered calls versus t

  12. Channelutilizationprobability • C channels available • Assumptions: • Poisson distribution (infin. users) • Blocked calls cleared • It can be proven (from Queueing theory) that: (very simple result!) • Hence:

  13. Fundamental formula for telephone networks planning Ao=offered traffic in Erlangs Blockingprobability: Erlang-B • Efficient recursive computation available

  14. NOTE: finite users • Erlang-B can be re-obtained as limit case • Minfinity • Ai0 • M·AiAo • Erlang-B is a very good approximation as long as: • A/M small (e.g. <0.2) • In any case, Erlang-B is a conservative formula • yields higher blocking probability • Good feature for planning • Erlang-B obtained for the infinite users case • It is easy (from queueing theory) to obtain an explicit blocking formula for the finite users case: • ENGSET FORMULA:

  15. Capacity planning • Target: support users with a given Grade Of Service (GOS) • GOS expressed in terms of upper-bound for the blocking probability • GOS example: subscribers should find a line available in the 99% of the cases, i.e. they should be blocked in no more than 1% of the attempts • Given: • C channels • Offered load Ao • Target GOS Btarget • C obtained from numerical inversion of

  16. Channelusageefficiency Carried load (erl) Offered load (erl) C channels Blocked traffic Fundamental property: for same GOS, efficiency increases as C grows!! (trunking gain)

  17. example GOS = 1% maximum blocking. Resulting system dimensioningand efficiency: 40 erl C >= 53 h = 74.9% 60 erl C >= 75 h = 79.3% 80 erl C >= 96 h = 82.6% 100 erl C >= 117 h = 84.6%

  18. Erlang B calculation - tables

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