Network Planning Network Planning VITMM215 VITMM215 Markosz Maliosz Markosz Maliosz 1 11 1/ /0 04/2013 4/2013 Outline � Telephone network dimensioning – Traffic modeling – Erlang formulas – Exercises – Exercises 2 2
Telephone Network Telephone Network � Circuit switching Circuit switching � � Each voice channel Each voice channel is identical is identical � � For For each each call call one one channel channel is is allocated allocated � � A call is accepted if at least one channel is idle A call is accepted if at least one channel is idle � � Goal Goal: Goal: Goal : network dimensioning : network dimensioning network dimensioning network dimensioning � � Question to answer Question to answer: : How many circuits are required How many circuits are required � to satisfy subscribers’ needs to satisfy subscribers’ needs? ? � Input Input: : traffic statistics traffic statistics � – – subscribers’ behavior: when, how often are calls arriving? subscribers’ behavior: when, how often are calls arriving? how long are the call durations? how long are the call durations? 3 3 3 3 Arrival Process Arrival Process � In our case: telephone calls arriving to a In our case: telephone calls arriving to a � switching system switching system � described as stochastic point process described as stochastic point process � � we consider simple point processes, i.e. we we consider simple point processes, i.e. we � exclude multiple arrivals exclude multiple arrivals exclude multiple arrivals exclude multiple arrivals th call arrives at time T � the i the i th call arrives at time T i � i � N(t) N(t) : the cumulative number of calls in the half : the cumulative number of calls in the half- - � open interval [0; t[ open interval [0; t[ � N(t) N(t) is a random variable with continuous time is a random variable with continuous time � parameter and discrete space parameter and discrete space N N(t) (t) t t 4 4 4 4
Arrivals and Departures N(t) D(t) � N ( t ) to be the cumulative number of arrivals up to time t � D ( t ) to be the cumulative number of departures up to time t � L ( t ) = N ( t ) - D ( t ) is the number of calls at time t 5 5 N(t) N(t) Equations D(t) D(t) � Average arrival rate: λ λ(t) (t) = = N(t)/t � F(t) = area of shaded region from 0 to t in the figure the figure = total service time for all customers = carried traffic volume � Average holding time: W(t) = F(t)/N(t) � Average number of calls: L(t) = F(t)/t = W(t)N(t)/t = W(t)λ λ(t) (t) 6 6
Traffic Volume � Volume of the traffic: the amount of traffic carried during a given period of time � Traffic volume in a period divided by the length of the period is the average traffic intensity in that period = average number of calls 7 7 Traffic Variations � Traffic fluctuates over several time scales – Trend (>year) � Overall traffic growth: number of users, changes in usage � Predictions as a basis for planning – Seasonal variations (months) – Weekly variations (day) – Weekly variations (day) – Daily profile (hours) – Random fluctuations (seconds – minutes) � In the number of independent active users: stochastic process � Except the last one, the variations follow a given profile, around which the traffic randomly fluctuates 8 8
Traffic Variations Source: A. Myskja, An introduction to teletraffic, 1995 . 9 9 Busy Hour � It is not practical to dimension a network for the largest traffic peak It is not practical to dimension a network for the largest traffic peak � � describe the peak load, where singular peaks are averaged out describe the peak load, where singular peaks are averaged out � � Busy Hour = The period of duration of one hour where the volume Busy Hour = The period of duration of one hour where the volume � of traffic is the greatest. of traffic is the greatest. � Operator’s intention: spreading the traffic Operator’s intention: spreading the traffic � – – By service tariffs By service tariffs � busy hour period is the most expensive busy hour period is the most expensive � � less important calls are started outside of the busy hour, and typically last less important calls are started outside of the busy hour, and typically last � longer longer � Recommendations define how to measure the busy hour traffic Recommendations define how to measure the busy hour traffic � – There are several definitions (ITU E.600, E.500) – There are several definitions (ITU E.600, E.500) – – An operator may choose the most appropriate one An operator may choose the most appropriate one 10 10
Busy Hour Measurements � ADPH (Average Daily Peak Hour) – one determines the busiest hour separately for each day (different time for different days), and then averages over e.g. 10 days � TCBH (Time Consistent Busy Hour) – a period of one hour, the same for each day, which gives the greatest average traffic over e.g. 10 days � FDMH (Fixed Daily Measurement Hour) – a predetermined, fixed measurement hour (e.g. 9.30-10.30); the – a predetermined, fixed measurement hour (e.g. 9.30-10.30); the measured traffic is averaged over e.g. 10 days 11 11 Traffic Model � Average arrival rate: Average arrival rate: λ λ(t) (t) – – depends on time, however it depends on time, however it � has a very strong deterministic component according to has a very strong deterministic component according to the profiles the profiles � In the busy hour period the average arrival time is In the busy hour period the average arrival time is � considered stationary: considered stationary: λ λ, , and the arrival process is and the arrival process is considered as a Poisson process with intensity considered as a Poisson process with intensity λ considered as a Poisson process with intensity considered as a Poisson process with intensity λ λ λ – – Time homogenity Time homogenity – – Independence Independence � The future evolution of the process only depends upon the actual The future evolution of the process only depends upon the actual � state. state. � Independent of the user Independent of the user(!) (!) – – modeling all users in the same way modeling all users in the same way � � The average holding time ( The average holding time ( W(t) W(t) ) is also considered to be ) is also considered to be � stationary, and exponentially distributed with intensity stationary, and exponentially distributed with intensity µ µ 12 12
Traffic Model Traffic Model � N(t) N(t) – – Poisson Poisson process process: : � Poisson Poisson – in time interval ( – in time interval ( t t , , t t + τ] the + τ] the number of calls follows a Poisson number of calls follows a Poisson distribution with parameter distribution with parameter λτ λτ – – Expected number of calls Expected number of calls = = λ λ τ τ – – λ λ = = arrival intensity arrival intensity [1/ [1/hour hour] ] Exp. Exp. � W( W(t) = t) = W W – – exp exp. . distribution distribution � – – Expected value Expected value = = 1/ 1/µ µ = = h h – – h h – – average holding time average holding time [ [min min] (!) ] (!) f(x; f(x; µ µ) = ) = µ µe e - -µ µx x 13 13 13 13 Traffic Intensity Traffic Intensity � A A – – traffic intensity traffic intensity � – – A A = = λ λ * * h h – – A [1], A [1], often written as often written as Erl (Erlang) Erl (Erlang) � Example Example: : individual subscriber individual subscriber � – – – λ – λ λ = 3 λ = 3 = 3 [1/ = 3 [1/ [1/hour [1/hour hour] hour] ] ] – – h h = 3 [ = 3 [min min] ] = = 0.05 [ 0.05 [hour hour] ] – – A = A = 3 3 [1/ [1/hour hour]* 0.05 [ ]* 0.05 [hour hour] ] = = 0.15 0.15 [Erl] [Erl] � Example Example: 10 000 : 10 000 line switch line switch � – – λ λ = 20 000 = 20 000 [1/ [1/hour hour] ] – – h h = 3 [ = 3 [min min] ] = = 0.05 [ 0.05 [hour hour] ] – – A = 20 000 [1/ A = 20 000 [1/hour hour]* 0.05 [ ]* 0.05 [hour hour] ] = = 1000 1000 [Erl] [Erl] 14 14 14 14
Typical Traffic Intensities Typical Traffic Intensities � Typical traffic intensities per a single Typical traffic intensities per a single � source are (fraction of time they are being source are (fraction of time they are being used) used) – – – private subscriber 0.01 – private subscriber 0.01 private subscriber 0.01 - private subscriber 0.01 - - 0.04 Erlang - 0.04 Erlang 0.04 Erlang 0.04 Erlang – – business subscriber 0.03 business subscriber 0.03 - - 0.06 Erlang 0.06 Erlang – mobile phone 0.03 Erlang – mobile phone 0.03 Erlang – – PBX (Private Branch Exchange) 0.1 PBX (Private Branch Exchange) 0.1 - - 0.6 Erlang 0.6 Erlang – – coin operated phone 0.07 Erlang coin operated phone 0.07 Erlang 15 15 Traffic Modeling � Agner Krarup Erlang (1878 – 1929) – Danish mathematician, statistician and engineer � Conditions: – n identical channels – Blocked Calls are Cleared (BCC) – Blocked Calls are Cleared (BCC) – The arrival process is a Poisson process with intensity λ – The holding times are exponentially distributed with intensity µ (corresponding to a mean value 1/µ) � The traffic process then becomes a pure birth and death process, a simple Markov process – A= λ/µ 16 16
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