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## On Network Traffic Modeling Framework: A Case Study with Public Safety Network

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Title: On Network Traffic Modeling Framework: A Case Study with Public Safety Network

1
On Network Traffic Modeling FrameworkA Case
Study with Public Safety Network
University of Science and Technology
2
Contents Framework on network traffic
probability models
• Recent open issues for future research
Framework on network traffic probability models
• 1. Part I. Probability model
• Simple standard or mixed advanced? How to
overcome a spike and tail problem? Robust method?
How we develop the good methods?
• Results of Public Safety Network
• 2. Part II. Probability model of
blocking/delay
• PSTN-Erlang formula or IP Erlang formula
for loss and delay? An appropriate algorithm for
IP Erlang formula? Good methods!
• Results of Public Safety Network
• 3. Part III. Traffic and Probability model
connected to capacity and network planning
• GoS and capacity of a system? An appropriate
algorithm for GoS, system capacity planning?
Results of Public Safety Network
• 4. Results and the model validations in the case
of Public Safety Network

3
PART I. Research Trends on Network Traffic
Fitting Models
• Mixed models as traffic advanced models
• (mixed lognormals, mixed pareto, mixed erlangs,
pareto plus lognormals.)
• Standard models as traffic candidate models
• (Lognormal model, Shifted Lognormal, Pareto
model, Erlang model, Weibull model)
• On the world, there are 60 more standard models
• But for network traffic fitting model, these
above named are exact candidates.

Studies are going on
Big issues on a spike, a tail
4
PART I. My Research work on this Network Traffic
Fitting Models
• (Mixed lognormals, mixed pareto, mixed erlangs,
pareto plus lognormals.)
• Standard models as candidates
• (Lognormal model, Shifted Lognormal, Pareto
model, Erlang model, Weibull model)

Studies are going on .
• 1. B. Tuyatsetseg, Parametric-Expectation
Maximization Approach for Call Holding Times of
IP enabled Public Safety Networks. WASET,
Zurich, Switzerland, online. issue 73, pp.
568-575, Jan 2013.
• B. Tuyatsetseg, B. Otgonbayar, Modeling Call
Holding Times of Public Safety Network,
International Journal on Computational Science
Applications (IJCSA), Australia, vol. 3, no. 3,
pp. 1-19, June 2013.
• B.Tuyatsetseg, B.Otgonbayar, Traffic Modeling of
Public Safety Network, in Proc IEEE-APNOMS2013,
Hiroshima , Japan. 25-27, Sep 2013

Big issues on a spike, a tail
5
The algorithm of my proposed mixed lognormal
model, its performance on the Emergency Traffic
Traffic random variables for
ALGORITHM INPUT the traffic values based on
experiment or
simulation
Hidden traffic variables plus observed variables
• Initialize parameters
• 2. First stepevaluate
• 3. Second step maximize
• where
• 4. Evaluate log likelihood, once likelihoods or
parameters converge, the algorithm is done
• Else

Evaluate ex.values (3) using (1), (2)
Iteratively maximize (3)
Likelihood of lognormals (ex.values) (3)
ALGORITHM OUTPUT weights,
scale, location
parameters of all components
6
Challenging steps to develop a mixture lognormal
model
• 1. MLE (3 parameters weight, location and scale)
through maximum log likelihood function.
• 2. The marginal distribution is described
through Bayesian theorem to compute the
expression of unobserved traffic data that is
iterative process untill likelihood or parameters
converge
• 3. The expected value of complete traffic data
set log likelihood through both the function of
log likelihood and the marginal distribution.

7
Log likelihood computation of a mixture of
lognormal parametric model
Logn fn
Likelihood function
Loglikelihood function (to estimate the set of
parameters for the mixed lognormal distributions
that maximize the likelihood function.
These formulas were proved mathematically in my
previous journal publications.
8
comparison on log likelihoods
• MLE for simple lognormal distribution
• MLE for a mixture of lognormal distributions
• where indicator function for individual i that
comes from the lognormal component with

(1a)
The formula was proved mathematically in my
previous journal publications.
9
MLE parameters computation of a mixture of
lognormals
• The weights of a lognormal components (number of
density in j divided by total number of density)
• The means of a lognormal components (for each
density i, its assignment mean to each j
lognormal components)
• The variance of lognormal components
• (for each density I, its
• assignment variance to each j lognormal
components)

(1)
These formulas were proved mathematically in my
previous journal publications.
10
Marginal distribution computation
Bayesian analytical expression (2) is used to
compute the marginal distribution, (posterior
probability) of on and
(2)
evaluated at

These formulas were proved mathematically in my
previous journal publications.
11
Expected value computation
The expected value (3) of the log likelihood
is iterative, as a function of Bayesian and log
likelihood function for
(3)
Marginal distribution (2)
Log likelihoods of lognormals (1a)
is the current value at iteration , for
These formulas were proved mathematically in my
previous journal publications.
12
The implementation algorithm performance ,
explanation by formulas
• Compute (3) ex.value using (1) weights or mixing.
coeff (2) posterior prob.

Iteratively maximize (3) independently
This implementation algorithm is used in
emergency incoming traffic simulation , with
results in next pages.
13
The mixed model of traffic, its lognormal
components of the proposed algorithm
CHALLENGE First of all, we should prove the
exact formulas for MLE (weight, location,
scale/shape)
of the mixed log function
MLE conditions
Location (mean) shape (var)
14
. PART I. My research results
• (Mixed lognormals, mixed pareto, mixed erlangs,
pareto plus lognormals.)
• Standard models as candidates
• (Lognormal model, Shifted Lognormal, Pareto
model, Erlang model, Weibull model)

Studies are going on .
• 1. B. Tuyatsetseg, Parametric-Expectation
Maximization Approach for Call Holding Times of
IP enabled Public Safety Networks. WASET,
Zurich, Switzerland, online. issue 73, pp.
568-575, Jan 2013.
• B. Tuyatsetseg, B. Otgonbayar, Modeling Call
Holding Times of Public Safety Network,
International Journal on Computational Science
Applications (IJCSA), Australia, vol. 3, no. 3,
pp. 1-19, June 2013.
• B.Tuyatsetseg, B.Otgonbayar, Traffic Modeling of
Public Safety Network, in Proc IEEE-APNOMS2013,
Hiroshima , Japan. 25-27, Sep 2013

Big issues on a spike, a tail
15
The scenario of the existing Public Safety
Network in Mongolia (EIN), its traffic mixed
model results
• Mass traffic influences to emergency incoming
traffic
• Ambulance(103)
• Police (102)
• Fire (101)
• Hazard (105)

16
The comparison on TRAFFIC pattern of Mongolian
EIN, some simple statistics
• for Mongolian biggest holiday and the
continuous peak period traffic.
• Emergency mass traffic
• Ambulance call traffic (103) 57
• 10275.45 seconds seamless
• Traffic value 1.3 Erlangs
• Police call traffic (102)
• 38
• 7150.692 seconds seamless
• Traffic value 0.7 Erlangs
• Fire call traffic (101)
• 3.4
• 4664.076 seconds seamless
• Traffic value 0.45 Erlangs
• Hazard call traffic (105)
• 2.6
• 2532.098 seconds seamless
• Traffic value 0.2 Erlangs
• Total 60 channels equally distributed but
traffic has a huge difference.

17
Part I. Numerical results of traffic mixed
model Results on Emergency Total traffic,
Ambulance, Police, Fire, and Hazard incoming
traffic
• Time series model
• Probability model

18
The model validation via Quantile-Quantile
(Q-Q)Results on Emergency incoming traffic
• On Tail validation,

19
PART II. Research Trends on Network probability
• Erlang Traffic analysis for Video over IP
• (Robust probability model of loss/delay , its
development??)
• Standard Erlang Traffic analysis
• (Probability of Loss
• Probability of Delay)
• for wired and wireless conventional
voice communications

Studies are going on .
for b0(z-1) factorial prod(1b) t
((T)b)/factorial ss t end
.
20
PART II. Research on Network probability of
• Erlang Traffic analysis for Video over IP
• (Robust probability model of loss/delay , its
development??)
• This is one result of my research on the Video
over IP transfer
• Standard Erlang Traffic analysis (Probability
of Loss
• Probability of Delay) for wired and wireless
conventional voice communications

Studies are going on
for b0(z-1) factorial prod(1b) t
((T)b)/factorial ss t end
.
21
Why the Video over IP model? its application of
Public Safety Network
• Video surveillance based on real time monitoring
using video camera for crime prevention.
• The real time video delivering to the emergency
center through IP network.
• This Video over IP transfer is the exact one MASS
Traffic producer in the case of PSN. For this
reason, we have to model the exact computation
method, algorithm to evaluate the performance of
this Video over IP traffic.
• Hence the modeling of video over IP is the one
main component of the framework.

22
Part II. Blocking/Delay probability analysis on
Voice traffic to IP video traffic
• Voice Traffic Probability
• of Loss and Probability of Delay
• The average holding time
• The call arrival rate
• The total number of available channel
• The total number of calls
• Blocking and delay probability depends on
• IP Video Traffic Probability of Loss and
Probability of Delay
• Average transfer time per frame in unit
• Number of frames per unit, ( for ex, 25-30 frames
in one sec for MPEG-4)
• Packet frame arrival rate per unit
• Packet frame transfer (Service) rate per unit
• All resource utilization or traffic intensity for
resources
• Blocking and delay probability depends on erlang

?
Experiment
Computation
Experiment
Simulation
Computation
Simulation
23
Video over IP Traffic Results
• Loss of the video over IP depends on traffic

Appropriate formulas for the proposed analysis
• Delay of the video over IP depends on traffic

Results VBR method is most appropriate method
than CBR for CCTV-Video over IP traffic
loss/delay using
24
Video over IP Traffic simulation verification ,
Video over IP-Traffic loss analysis
Results VBR method is the most appropriate
method to transfer video over IP than CBR for
CCTV-Video over IP traffic loss/delay
25
Part III. On Traffic Capacity Region and network
planning
• Fundamental theories for capacity region and
network planning
• Queue theory , Markob theory ,
Erlang-C/Erlang-B theory
• Fundamental parameters for capacity region and
network planning
• Call Conversation Time,
• Arrival rate ,
• Service rate,
• Probability models (optimum traffic model
parameters, blocking and delay model parameters)
• Described parameters for Network capacity and
planning
• Resource utilization,
• Utilization efficiency,
• Number of links of queuing system,
• Bandwidth,

Sequence
26
The algorithm steps for a network traffic -
capacity region and network planning
• Second , third stages .. based on Erlang load
and probability of delay other parameters
• First stage
• Final stage
• The base chart for the traffic capacity region.
• (Call Holding Time per call, Number of calls
per unit time, Arrival rate , Service rate,
Resource utilization, utilization efficiency,
Traffic model parameters, number of links of
queue system )
• Probability of waiting , Grade of Service (GoS)
should less than 1.)

27
RESULT ON EMERGENCY NETWORK
CAPACITY REGION
• Peak/Congested period analysis
• As a result of robust algorithm, we can
get a chance to see Erlang capacity region for
the system capacity and the net planning
• Pc - Prob of delay
• E - Average of Traffic
• N - Number of emergency links/agent
• GoS - Grade of Service
• (GoS) , prob of waiting less than
threshold level, secs

28
Model validation by four parameters (K-S test,
pdf, cdf, ccdf)
• 1. Probability pdf results, parameters, weight
coeff,
• 2. Head/body behavior results (cdf),
• 3. Tail behavior results (ccdf),
• 2. Kolmogorov Smirnov test (K-S),
• 3. Miminum D.max values (distance between
proposed method and real data),
• 4. Minimum Error (the error of the model),
• 5. Convergence of the algorithm.

29
Results on more validation parameters
(Emergency Ambulance case)
Models/ parameters Dmax Error P value (K-S) P value (Chi-Sq)
Mixed Lognormal 0.00768755 0.46(10-4) 0.98 0.87
Gen pareto 0.048 0.37(10-3) 0.884 0.71
Shifted /Ln 0.059 0.18(10-3) 0.832 0.64
Lognormal 0.061 0.07(10-3) 0.73 0.61
Weibull 0.07 0.19(10-3) 0.39 0.27
30
On contribution of my research
• This researchs contribution is complicated
fundamental computational complicated tasks , as
well as the implementation algorithm development,
the study of Public Safety Network in Mongolia
• For me,
• 1. Mathematical formulas were proved and
verified and then published in Switzerland and
Australian computational journals in 2013 1,
2, 3, 5
• In this conference, the traffic model framework.
case study with Public Safety Network .The base
algorithms were done for this process. Results
were verified,
• 3. The contribution may be for fundamental area
as well for network performance analysis and
special application area. Also the algorithm of
the approaches may be used in networks.
• 4. It may be one base method for dynamic
bandwidth method/bandwidth provisioning because
the model described traffic in detailed manner
with main functions.

31
References
• B. Tuyatsetseg, Parametric Modeling Approach for
Call Holding Times of IP based Public Safety
Networks. WASET. Switzerland, online journal.
issue 73, pp. 568-575, Jan 2013.
• B. Tuyatsetseg, B. Otgonbayar, Modeling Call
Holding Times of Public Safety Network,
International Journal on Computational Science
Applications (IJCSA), Australia, vol. 3, no. 3,
pp. 1-19, June 2013.
• B. Tuyatsetseg, B. Otgonbayar, An Adaptive
Scheduling Scheme to Efficient Emergency Call
Holding Times in Public Safety Network, in Proc.
IFOST2013, Ulaanbaatar, Mongolia, June 28-July 3,
2013.
• J. Wang, H. Zhou, L. Li, and F. Xu, Accurate
long-tailed network traffic approximation and its
queueing analysis by hyper-Erlang distributions,
in Proc. IEEE conf. Local Computer Networks, pp.
148 - 155, 2005.
• B.Tuyatsetseg, B.Otgonbayar, Traffic Modeling of
Public Safety Network, in Proc IEEE-APNOMS2013,
Hiroshima , Japan. 25-27, Sep . 2013.

32
• Thank you for your attention
• Questions?