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Traffic Analysis
Steady state analysis using Discrete Markov Chains.
Ecuadorian case.
Julio César Hidalgo
@julio_hidalgo
Telephony service providers in Ecuador.
Mobile and Fixed (JUNE 2013)
 3 mobile operators and many fixed operators.
 17.34 M of mobile suscribers.
 2.36 M of fixed suscribers.
 19.7 M of telephony suscribers.
 Dividing these suscribers in four categories:
 CL 60.3%
 MS 25.9%
 CNT Mobile 1.8%
 Fixed 12%
60%
26%
2%
12%
Markov Model
 A Markov chain model is specified by identifying:
 The set of states S={1, …., m}
 The set of posible transitions, namely, those pairs (i,j) for which pij ≥ 0, it means,
they are positive values.
 Memoryless property.
 The Markov chain specified by this model is a sequence of random variables X0, X1,
X2, ….. Xm. that take values in S and which satisfy
P( Xn+1 = j | Xn = i, Xn-1 = in-1, …… , X0 = i0 ) = pij
Transition Matrix
 In this case, we use the traffic from and to operators.
0.9100 0.0624 0.0050 0.0226
0.1701 0.7953 0.0059 0.0287
0.5086 0.2590 0.1298 0.1027
Fixed 0.0594 0.0425 0.0025 0.8956
FixedTO
FROM
Transition Matrix at steady state
 In this case, we can use Chapman Kolgomorov equation to solve this system to
n-step, but, it could be solved using Matlab when
Πj ≈ P(Xn=j)
 It means, we power the matrix to a big number.
 Assumptions:
 Prices and Interconnections costs are the same in the large period of analysis.
 We consider all telephony customers.
 Mobile subscribers are considered by operator and fixed clients in one large
category.
Transition Matrix to infinity
 The result is the matrix at steady state.
0.5842 0.2241 0.0056 0.1972
0.5842 0.2241 0.0056 0.1972
0.5842 0.2241 0.0056 0.1972
Fixed 0.5842 0.2241 0.0056 0.1972
FixedTO
FROM
Preliminary Results
 If we multiply this result matrix by a market share vector like the first one
proposed in slide 2, we can obtain the possible market share if regulators does
nothing in the market.
 60.3% 58.4%
 25.9% 22.4%
 1.8% 0.5%
 12% 19.7%
 Club effect is large in Ecuador as you can check in slide 4. It means that mobile
subscribers prefer to call users where they also belong to.
 Fixed operators would have an opportunity to grow in suscribers or in traffic.
 Market share would change a bit in a large period. It means, Claro would mantain
its dominance and Movistar would decrease in clients. CNT mobile would reduce its
market.
Fixed

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做(mqu毕业证书)麦考瑞大学毕业证硕士文凭证书学费发票原版一模一样做(mqu毕业证书)麦考瑞大学毕业证硕士文凭证书学费发票原版一模一样
做(mqu毕业证书)麦考瑞大学毕业证硕士文凭证书学费发票原版一模一样
 

Cadenas de markov para tráfico onnet efecto club

  • 1. Traffic Analysis Steady state analysis using Discrete Markov Chains. Ecuadorian case. Julio César Hidalgo @julio_hidalgo
  • 2. Telephony service providers in Ecuador. Mobile and Fixed (JUNE 2013)  3 mobile operators and many fixed operators.  17.34 M of mobile suscribers.  2.36 M of fixed suscribers.  19.7 M of telephony suscribers.  Dividing these suscribers in four categories:  CL 60.3%  MS 25.9%  CNT Mobile 1.8%  Fixed 12% 60% 26% 2% 12%
  • 3. Markov Model  A Markov chain model is specified by identifying:  The set of states S={1, …., m}  The set of posible transitions, namely, those pairs (i,j) for which pij ≥ 0, it means, they are positive values.  Memoryless property.  The Markov chain specified by this model is a sequence of random variables X0, X1, X2, ….. Xm. that take values in S and which satisfy P( Xn+1 = j | Xn = i, Xn-1 = in-1, …… , X0 = i0 ) = pij
  • 4. Transition Matrix  In this case, we use the traffic from and to operators. 0.9100 0.0624 0.0050 0.0226 0.1701 0.7953 0.0059 0.0287 0.5086 0.2590 0.1298 0.1027 Fixed 0.0594 0.0425 0.0025 0.8956 FixedTO FROM
  • 5. Transition Matrix at steady state  In this case, we can use Chapman Kolgomorov equation to solve this system to n-step, but, it could be solved using Matlab when Πj ≈ P(Xn=j)  It means, we power the matrix to a big number.  Assumptions:  Prices and Interconnections costs are the same in the large period of analysis.  We consider all telephony customers.  Mobile subscribers are considered by operator and fixed clients in one large category.
  • 6. Transition Matrix to infinity  The result is the matrix at steady state. 0.5842 0.2241 0.0056 0.1972 0.5842 0.2241 0.0056 0.1972 0.5842 0.2241 0.0056 0.1972 Fixed 0.5842 0.2241 0.0056 0.1972 FixedTO FROM
  • 7. Preliminary Results  If we multiply this result matrix by a market share vector like the first one proposed in slide 2, we can obtain the possible market share if regulators does nothing in the market.  60.3% 58.4%  25.9% 22.4%  1.8% 0.5%  12% 19.7%  Club effect is large in Ecuador as you can check in slide 4. It means that mobile subscribers prefer to call users where they also belong to.  Fixed operators would have an opportunity to grow in suscribers or in traffic.  Market share would change a bit in a large period. It means, Claro would mantain its dominance and Movistar would decrease in clients. CNT mobile would reduce its market. Fixed