Stochastic processes and modelling have various applications in telecommunications. Token rings, continuous-time Markov chains, and fluid-flow models are used to model traffic flow and network performance. Aggregate dynamic stochastic models can model air traffic control by representing aircraft arrivals as Poisson processes. Disturbances like weather can be incorporated by altering flow rates. Wireless network models use search algorithms and location stochastic processes to track mobile users.
This presentation contains the topic as follows, probability distribution, random variable, continuous variable, discrete variable, probability mass function, expected value and variance and examples
It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
The ppt gives an idea about basic concept of Estimation. point and interval. Properties of good estimate is also covered. Confidence interval for single means, difference between two means, proportion and difference of two proportion for different sample sizes are included along with case studies.
General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
Introduction:
Life table:
Life table is a comprehensive method of describing mortality, survival and other vital events in a population.
It is composed of several sets of values showing how a group of infants who are under unchanging conditions would gradually die.
It provides concise measures of longevity of that population.
Separate tables are prepared for males and females after each decennium census.
It is also called as the “Biometer” of the population by William Farr.
This presentation contains the topic as follows, probability distribution, random variable, continuous variable, discrete variable, probability mass function, expected value and variance and examples
It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
The ppt gives an idea about basic concept of Estimation. point and interval. Properties of good estimate is also covered. Confidence interval for single means, difference between two means, proportion and difference of two proportion for different sample sizes are included along with case studies.
General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
Introduction:
Life table:
Life table is a comprehensive method of describing mortality, survival and other vital events in a population.
It is composed of several sets of values showing how a group of infants who are under unchanging conditions would gradually die.
It provides concise measures of longevity of that population.
Separate tables are prepared for males and females after each decennium census.
It is also called as the “Biometer” of the population by William Farr.
Short term traffic volume prediction in umts networks using the kalman filter...ijmnct
Accurate traffic volume prediction in Universal Mobile Telecommunication System (UMTS) networks has
become increasingly important because of its vital role in determining the Quality of Service (QoS)
received by subscribers on these networks. This paper developed a short-term traffic volume prediction
model using the Kalman filter algorithm. The model was implemented in MATLAB and validated using
traffic volume dataset collected from a real telecommunication network using graphical and r2 (coefficient
of determination) approaches. The results indicate that the model performs very well as the predicted
traffic volumes compare very closely with the observed traffic volumes on the graphs. The r2 approach
resulted in r2 values in the range of 0.87 to 0.99 indicating 87% to 99% accuracy which compare very well
with the observed traffic volumes.
A QUANTITATIVE ANALYSIS OF HANDOVER TIME AT MAC LAYER FOR WIRELESS MOBILE NET...ijwmn
Extensive studies have been carried out for reducing the handover time of wireless mobile network at
medium access control (MAC) layer. However, none of them show the impact of reduced handover time
on the overall performance of wireless mobile networks. This paper presents a quantitative analysis to
show the impact of reduced handover time on the performance of wireless mobile networks. The proposed
quantitative model incorporates many critical performance parameters involve in reducing the handover
time for wireless mobile networks. In addition, we analyze the use of active scanning technique with
comparatively shorter beacon interval time in a handoff process. Our experiments verify that the active
scanning can reduce the overall handover time at MAC layer if comparatively shorter beacon intervals are
utilized for packet transmission. The performance measures adopted in this paper for experimental
verifications are network throughput under different network loads.
Cellular wireless systems like GSM suffer from congestion resulting in overall system degradation and poor service delivery. When the traffic demand in a geographical area is high, the input traffic rate will exceed thecapacity of the output lines. This work focused on homogenous wireless network (the network traffic and resource dimensioning that are statistically identical) such that the network performance
evaluation can be reduced to a system with single cell and a single traffic type. Such system can employa queuing model to evaluate the performance metric of a cell in terms of blocking probability.
Five congestion control models were compared in the work to ascertain their peculiarities, they are Erlang B, Erlang C, Engset (cleared), Engset (buffered), and Bernoulli. To analyze the system, an aggregate onedimensional Markov chain wasderived, such that it describes a call arrival process under the assumption
that it is Poisson distributed. The models were simulated and their results show varying performances, however the Bernoulli model (Pb5) tends to show a situation that allows more users access to the system and the congestion level remain unaffected despite increase in the number of users and the offered traffic into the system.
IMPACT OF CONTENTION WINDOW ON CONGESTION CONTROL ALGORITHMS FOR WIRELESS ADH...cscpconf
TCP congestion control mechanism is highly dependent on MAC layer Backoff algorithms that
predict the optimal Contention Window size to increase the TCP performance in wireless adhoc
network. This paper critically examines the impact of Contention Window in TCP congestion
control approaches. The modified TCP congestion control method gives the stability of
congestion window which provides higher throughput and shorter delay than the traditional TCP. Various Backoff algorithms that are used to adjust Contention Window are simulatedusing NS2 along with modified TCP and their performance are analyzed to depict the influence of Contention Window in TCP performance considering the metrics such as throughput, delay, packet loss and end-to-end delay
MODELLING TRAFFIC IN IMS NETWORK NODESijdpsjournal
IMS is well integrated with existing voice and data networks, while adopting many of their key characteristics.
The Call Session Control Functions (CSCFs) servers are the key part of the IMS structure. They are the main components responsible for processing and routing signalling messages.
When CSCFs servers (P-CSCF, I-CSCF, S-CSCF) are running on the same host, the SIP message can be internally passed between SIP servers using a single operating system mechanism like a queue. It increases
the reliability of the network [5], [6]. We have proposed in a last work for each type of service (between ICSCF and S-CSCF (call, data, multimedia.))[23], to use less than two servers well dimensioned and running on the same operating system.
Instead dimensioning servers, in order to increase performance, we try to model traffic on IMS nodes, particularly on entries nodes; it will provide results on separation of incoming flows, and then offer more satisfactory service.
A novel delay dictionary design for compressive sensing-based time varying ch...TELKOMNIKA JOURNAL
Compressive sensing (CS) is a new attractive technique adopted for Linear Time Varying channel estimation. orthogonal frequency division multiplexing (OFDM) was proposed to be used in 4G and 5G which supports high data rate requirements. Different pilot aided channel estimation techniques were proposed to better track the channel conditions, which consumes bandwidth, thus, considerable data rate reduced. In order to estimate the channel with minimum number of pilots, compressive sensing CS was proposed to efficiently estimate the channel variations. In this paper, a novel delay dictionary-based CS was designed and simulated to estimate the linear time varying (LTV) channel. The proposed dictionary shows the suitability of estimating the channel impulse response (CIR) with low to moderate Doppler frequency shifts with acceptable bit error rate (BER) performance.
Performance Evaluation of Finite Queue Switching Under Two-Dimensional M/G/1...Syeful Islam
Abstract—In this paper we consider a local area network (LAN) of dual mode service
where one is a token bus and the other is a carrier sense multiple access with a collision
detection (CSMA/CD) bus. The objective of the paper is to find the overall cell/packet
dropping probability of a dual mode LAN for finitelength queue M/G/1(m) traffic. Here, the
offered traffic of the LAN is taken to be the equivalent carried traffic of a one-millisecond
delay. The concept of a tabular solution for two-dimensional Poisson’s traffic of circuit
switching is adapted here to find the cell dropping probability of the dual mode packet
service. Although the work is done for the traffic of similar bandwidth, it can be extended
for the case of a dissimilar bandwidth of a circuit switched network.
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2. Stochastic process
A stochastic process or sometimes random
process (widely used) is a collection of random variables,
representing the evolution of some system of random
values over time. This is the probabilistic counterpart to a
deterministic process . Instead of describing a process
which can only evolve in one way, in a stochastic or
random process there is some indeterminacy: even if the
initial condition is known, there are several directions in
which the process may evolve.
3. Mathematical Representation
Given a probability space and a measurable
space , an S-valued stochastic process is a
collection of S-valued random variables on ,
indexed by a totally ordered set T ("time"). That is,
a stochastic process X is a collection
where each is an S-valued random variable
on . The space S is then called the state
space of the process.
5. A method of financial modeling in which one or more variables within the model
are random. Stochastic modeling is for the purpose of estimating the probability of
outcomes within a forecast to predict what conditions might be like under different
situations. The random variables are usually constrained by historical data, such as
past market returns.
Stochastic Modelling
6. Real life application
The Monte Carlo Simulation is an example of a stochastic
model used in finance.
When used in portfolio evaluation, multiple simulations
of the performance of the portfolio are done based on the
probability distributions of the individual stock returns.
A statistical analysis of the results can then help
determine the probability that the portfolio will provide
the desired performance.
stochastic modelling as applied to the insurance
industry, telecommunication , traffic control etc
7. telecommunication
When messages flow from a source to a
destination (end-to-end) through a network, parts
of a message or the whole message may be
dropped due to unavailable resources (buffer
capacity) to store the messages. The probability
of delivering a message with some data loss is
termed as loss probability. The time between the
source sending a message and the destination
receiving it is called latency or delay.
The message flow (will be called traffic
henceforth) and the network conditions are ex-
tremely stochastic in nature.
Other applications of stochastic processes in
communications include coding theory, signal
8. Token rings
Consider N independent and identical users that are
arranged logically in the form of a ring
In this model at most one user is allowed to generating a
message over the cable or ring.
Wiring center
A
B
C
D
E
9. When a user with a message to transmit
receives the free token, the user holds on to
the token and transmits the message onto
the ring or cable.
Frame circles the ring and is removed by
the transmitting station.
Each station interrogates passing frame, if
destined for station, it copies the frame into
local buffer.
Once the user completes transmission, the
busy token is converted into a free token
and passed along the ring.
10. Re-inserting token on the ring
Choices:
1. After station has completed transmission
of the frame.
2. After leading edge of transmitted frame
has returned to the sending station
11. Networks: Token Ring and FDDI 11
A A A
A A A A
t=0, A begins frame t=90, return
of first bit
t=400, transmit
last bit
A
t=490, reinsert
token
t=0, A begins frame t=400, last bit of
frame enters ring
t=840, return of first
bit
t=1240, reinsert
token
12. In probability theory, a continuous-time
Markov chain (CTMC) is a mathematical
model which takes values in some finite or
countable set and for which the time spent
in each state takes non-negative real
values and has an exponential distribution.
It is a continuous-time stochastic
process with the Markov property which
means that future behaviour of the model
depends only on the current state of the
model and not on historical behaviour.
13. To model the system as a CTMC, one
could assume that the packets are
generated according to a Poisson process,
the length of the packets are exponentially
distributed.
The propagation time is also exponentially
distributed. Since all the users are
identical, a CTMC of the form {(X(t), Y (t), t
≥ 0} model where X(t) is the number of
messages in the network and Y (t) is the
status of the token (free or busy) at time t.
Using the steady state distribution of the
CTMC, performance measures such as
14. Traffic Models
Traffic flowing through the networks can be classified
into several types. Depending on the network segment,
all messages are broken down into either packets or
cells.
Packets:
The length or size of a packet ranges anywhere from
60 bytes to 1500 bytes and generally follows a
bimodal distribution.
ATM Cells:
The length of ATM cells is fixed at 53 bytes.
15. Hierarchical Networks
Telecommunication networks are typically hierarchical in nature. Some
frequently used stochastic models for traffic flow are explained in this
section.
Traffic can be classified into four level
1. Application Level
• The traffic generated by an application, say, http or telnet
or ftp which can vary significantly based on the protocols
they follow
16. 2. Source Level :
Each workstation or computer can be thought of
as a source that generates traffic. This traffic
comprises of the traffic generated by different
applications that are running on the source.
Therefore the traffic that flows on a link that
exits the computer is a mixture of the different
applications. The process of mixing is known as
multiplexing.
17. 3. Aggregate Level
Several computer, printers, etc are connected together to
form a local area network (LAN). The traffic on a LAN pipe
is the aggregated traffic that is multiplexed from all the
sources.
4. Backbone Level
The LANs are connected together by means of a backbone
(say, the Internet backbone), and this forms the Metropolitan
Arean Networks (MANs) or the Wide Area Networks
(WANs). The traffic on a MAN/WAN pipe is the combination
of the traffic from several LANs.
18. In the fluid-flow models it is assumed that traffic is in the
form of fluid which flows through a pipe at different rates at
different times. For example, fluid flows at rate r(1) bytes
per second for a random amount of time t1, then flows at rate
r(2) bytes per second for a random amount of time t2, and so
on. This behaviour can be captured as a discrete stochastic
process that jumps from one state to another whenever the
traffic flow rate changes. This can be formalized as a
stochastic process {Z(t), t ≥ 0} that is in state Z(t) at time t.
Fluid flows in the pipe at rate r(Z(t)) at time t.
Fluid-flow Traffic Models
19. Aggregate Dynamic Stochastic Model For ATS
Air traffic control can be simplified using stochastic
modelling.
Here we assume the aircrafts arriving at an airport as a
Poisson distribution and compute the average delay
incurred due to constraints of landing aircraft
we assume that each aircraft in Centre i independently
travels to Centre j (or leaves the airspace for j = 0) between
time-steps k and k + 1 with probability pij[k]. We denote
the total number of aircraft that flow from Centre i to
Centre j between times k and k + 1 by Uij[k]. For small
enough ∆T, it can be shown that the conditional distribution
for the flow Uij[k] given the Centre count si[k] is well-
approximated by a Poisson random variable, with mean
pij[k] si[k] .
20. Now that we have characterized the flows of aircraft in
our model, the state variable update can be specified by
accounting for the number of aircraft entering and leaving
each Centre i between times k and k + 1:
1)
This update rule defines the temporal evolution of our
aggregate stochastic model.
In our application of the aggregate model, it is not
Equation 1 that we propagate forwards in time.
Instead, we propagate expectations and variances of the
si[k], using equations that are derived from Equation 1,
and that have a very simple structure
(Uji[k](Uij[k)-si[k]1]si[k
21. the conditional expectation for the number of aircraft in Center i
is
which is a linear function of the time-k Centre counts. Finally, by
taking the expectation with respect to the time-k Centre counts
s[k], given the initial Centre counts s[0], we find that
E( si[k + 1] | s[0] ) = E( si[k]|s[0]) -
Thus, we see that the expected number of aircraft in Centre i at
time k+1givens[0] can be written as a linear function of the
expected Centre counts at time k given s[0].
),)ëi[k][k]pji[k]sj((]si[k]pij[k)s[k]|1]s[kE(
)ëi[k]]s[0])pji[k|(E(sj[k]])s[0])pij[k|(E(si[k]
22.
23. The U.S. ATS is subject to disturbances that change rates of aircraft
flow in parts of the network.
Many of these flow-altering disturbances, which are often inclement
weather events in parts of the airspace, cannot accurately be
predicted in advance.
Furthermore, although the disturbance event may directly affect only a
small part of the airspace, the resulting changes in flows and Sector/
Centre counts may propagate throughout the network.
Since our model for the U.S. ATS is stochastic, we can naturally in-
corporate stochastic disturbances that alter flows in the model.
By computing the expected behaviour and variability of Centre counts
and flows in the model, regions of the airspace that may be prone to
capacity excesses due to the weather events can be identified.
In turn, the model may suggest improved methods for managing
traffic flow in response to weather disturbances.
Disturbances:
24.
25. Given that a particular set of disturbances has occurred, we can
calculate statistics of Centre counts with our basic model, using the
appropriate set of model parameters (which are modified from their
nominal values based on the particular disturbances that have
occurred).
In turn, we can calculate statistics of Centre counts without prior
knowledge of the disturbances, by scaling the predicted statistics for
each set of disturbances with the probability that these disturbances
occur, and then summing these scaled statistics.
In this way, the dynamics of an ATS that is subject to stochastic
disturbances can be modelled and analyzed. One possible shortcoming
of this approach for modelling stochastic disturbances is the
computational complexity resulting from the large number of
disturbances that may need to be considered. (For example, if there are
10 different weather events that may or may not be present on a given
day, we must consider 2^10 = 1024 possible combinations of
disturbances.)
Given certain special conditions on the location of disturbances, the
computational complexity can sometimes be reduced by considering
the change in the system’s dynamics due to each disturbance
separately, and then combining these individual responses.
26. Wireless Network Models
One of hottest research topics in telecommunications is wireless
communications technology and a survey paper would certainly be
incomplete without describing some of the on-going research work in
mobile communications. However, the field is relatively new and most
of the techniques are not well-established. Therefore only a brief
summary of some of the current papers in the area of stochastic models
in wireless networks are presented here.
Almost all the forementioned traffic models, performance analysis,
flow control, congestion control, etc do not make any assumptions
about whether the networks are at least partially wireless or not. It is to
be noted that mobile communications where the users (sources and
destinations) are mobile are called wireless communication here. Since
the sources and destinations are not static an important problem is to
locate the users to send and receive messages.
27. Awduche et al describe location management issues
that involve tracking compo-nents that maintain
dynamic data on the locations of mobile stations
through a distributed database. The main focus is on a
search component that prescribes the manner in which
the wireless network is to be paged so as to determine
the location of mobile stations whose whereabouts are
unknown. The methods used are based on search
theory where a stochastic sequential framework that
systematically determines the location of mobile
stations situated within a group of cells. Search
algorithms are hence developed.
28. A Poisson-arrival location model (PALM) was
introduced in which customers arrive according to a
non-homogeneous Poisson process and move
independently through a general location state space
according to a location stochastic process. That was
extended to a version of PALM to study communicating
mobiles on a highway. Leung et al stress the need for
combining tele-traffic theory and vehicular traffic
theory. Their numerical results indicate that both the
time-dependent behaviour and the mobility of vehicles
play important roles in determining the system
performance.
29. •Other Topics
One of the most critical factor that will enable QoS provisioning in high-
speed networks is pricing. F.P. Kelly and colleagues have developed
some optimal pricing models .
•ATM switch design and router design involve significant amount of
stochastic modeling, particularly queueing. All the multiclass scheduling
policies (polling, static priority, waited fair queueing, etc) can be
implemented on the currently available switches and routers.
•All the models considered here were unicast where traffic flows from a
single source to a single destination. There are interesting stochastic
models for multicasting (single source and a few destinations like an
Internet classroom with students globally located) and for broadcasting
(single source and all nodes as destinations) applications.
•Several scenarios in telecommunication networks (such as client-server
systems) can be modeled as Queueing Networks. Walrand [76] provides
several applications of Queueing Networks in Telecommunications.