Hidden Markov Model Traffic Characterisation in
Wireless Networks
Evangelos Spyrou and Dimitris Mitrakos
School of Electrical and Computer Engineering, Aristotle University of Thessaloniki,
Egnatia Odos, Panepistimioupoli, 54124 Thessaloniki, Greece
{evang spyrou, mitrakos}@eng.auth.gr
Keywords: Information Based Similarity, Euclidean distance, Wireless Traffic, Shannon Entropy, Signal-to-Interference-
and-Noise-Ratio.
Abstract: Quality of service wireless traffic that often exhibits burstiness, occasionally occurring due to mobility,
provides a critical networking issue. Traffic patterns in wireless networks are not of a traditional nature. Nodes
transmit their information in batches over a short period of time, before they lose connection. Prediction of
wireless incoming load plays an important role in the design of wireless local area networks. The issues of
load balancing and Quality of Service constraints are a major problem, which is responsible for the increase
of throughput of the network; thus, predicting traffic can be of a great assistance in the aforementioned
research directions, leading to a significant optimisation of the wireless network operation. This paper
addresses the problem of traffic prediction using Hidden Markov Models. The data is clustered using the
Information Based Similarity index that classifies different types of traffic. We show the limitation of this
approach and we finally select Euclidean distance for data clustering. Together, they provide an efficient
solution towards the solution of wireless traffic characterisation and prediction. We show the efficiency of
our scheme in a series of simulations
1 INTRODUCTION
In the field of wireless networks, requirements such
as quality of service over normal or bursty links, often
originating from mobility, are of great significance
(Jiang and Dovrolis, 2005; Alizai et al., 2009).
Wireless devices do not always follow specific traffic
patterns; on the contrary, they attempt to transmit
their packets in a bursty fashion, meaning all of them
in a short period of time, before they lose or make the
connection not reliable (Papadopoulos et al., 2015).
Such dynamic and bursty traffic cause certain
deficiencies in the network and provide an interesting
problem to investigate.
Wireless traffic prediction is a key factor in the
analysis and design of wireless local area networks
(WLAN)s (Papadopouli et al., 2005). For example,
the well-known problem of load balancing can be
addressed using Access Point (AP) traffic prediction.
In this way, a new connection with this AP may be
decided based on the prediction of the AP load. This
is an improvement of the throughput of the network;
furthermore, Quality of Service (QoS) constraints can
be satisfied.
Recently, wireless network traffic has proven to
exhibit self-similarity or long-range dependence
(Park and Willinger, 2000; Jiang et al., 2001). Self-
similarity in traffic is crucial and cannot be analysed
by traditional models. Traffic prediction from past
measurements constitutes an efficient way to acquire
traffic control when self-similar loads occur.
Optimality in forecasting still remains a major issue
(Beran, 1994). This constitutes the location of
efficient self-similar models for prediction of future
traffic fluctuations a fundamental problem.
In this paper we address the problem of
classifying wireless traffic by attempting to cluster
the data utilising the information based similarity
(IBS) index (Yang et al., 2003). We show the
efficiency of this approach as well as the problems
that may arise when integrating it to a Hidden Markov
Model (HMM). Based on the limitations of this
78
Spyrou E. and Mitrakos D.
Hidden Markov Model Traffic Characterisation in Wireless Networks.
DOI: 10.5220/0006227400780085
In Proceedings of the Fifth International Conference on Telecommunications and Remote Sensing (ICTRS 2016), pages 78-85
ISBN: 978-989-758-200-4
Copyright
c
2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
approach we select the Euclidean distance to cluster
the data in our machine learning approach.
We attempt to characterise the pattern of the
traffic by feeding the packets generated by a wireless
network to a Hidden Markov Model. The distances
we find using the Euclidean distance assist us to
cluster the data to normal, bad and bursty traffic.
Combining the two, we are able to provide substantial
information and a good characterisation and
prediction on the traffic we will be experiencing.
More specifically, we show the following
contributions:
Wes show the difference in similarity of
different types of wireless traffic using the IBS
index;
We show that the IBS index can be a good
methodology to cluster the incoming data and
characterise traffic;
We show the limitations of this approach when
integrating it to an HMM
We employ Euclidean distance to cluster the
traffic data.
We utilise the HMM to characterise and predict
the upcoming traffic and show indexes of the
efficiency of our approach;
We show in a series of simulations the
efficiency of our approach;
This paper is structured as follows: Section 2
provides the related work, Section 3 gives the
background of the IBS index and some results,
Section 4 provides a brief background on the
Euclidean distance, Section 5 gives a background on
our HMM proposal, Section 6 provides the simulation
results of our approach, and Section 7 provides the
conclusions.
2 RELATED WORK
In (Ni et al., 2015), the authors address the resource
management for dynamic control of channel
resources and energy efficiency in modern cellular
systems. They identify that early monitoring and
forecasting if basestation traffic volumes play a key
roles in the management. Spatiotemporal network
traffic analysis is the means to a successful prediction
of traffic. To this end, they examine the
spatiotemporal features of cellular traffic generated in
a practical scenario in China. The authors analyse
basestations that exhibit similar features and they
cluster them. They elaborate on the sliding windows
sizes and encapsulate the Elman Neural Network with
wavelet transform to accomplish traffic precision.
In (Maheshwari et al., 2013), the authors aim to
tackle the issue of Quality of Service of end-user calls
for realistic traffic models. They mainly address
modelling wireless internet traffic using realistic
traffic traces. This traffic are collected from networks
and they perform forecasting on the end-to-end
Quality of Service parameters for the networks. The
traffic model is designed based on Hidden Markov
Model by taking into account the joint distribution of
end-to-end delay, packet variation and packet size.
The states that are identified are mapped to four
traffic classes. These are conversational, streaming,
interactive, and background.
In (Yadav and Balakrishnan, 2014), the issue of
traffic modeling is investigated. Typical networking
issues, such as resource allocation, quality of service,
bandwidth and congestion control are addressed. A
comparison of modeling techniques is carried out of
adaptive neuro fuzzy inference system (ANFIS) and
autoregressive integrated moving average (ARIMA)
for modeling of wireless network traffic in terms of
typical statistical indicator and computational
complexity. Furthermore, a comparative performance
evaluation is undertaken in traffic modeling showing
that ANFIS constitutes a good methodology for
prediction with respect to statistical indicators.
Moreover, it provides a reasonable description of the
conditions of a wireless network in the time domain.
The main drawback is the complexity ANFIS
introduces, even though it performs better than the
ARIMA model in the scenarios they investigate.
In (Li et al., 2014), the authors aim to examine
traffic prediction on cellular radio networks. The need
for a traffic-aware energy efficient architecture is
highlighted. To this end, traffic prediction is modeled
a traffic-aware networking is addresses. For the
former, entropy theory is utilised towards the analysis
of traffic predictability. In terms of the latter practical
prediction performance is demonstrated using the
best methodologies in the literature. Finally, the
authors suggest a blueprint regarding a traffic-
oriented software-defined cellular radio network
architecture and they show the potential applications
of traffic prediction in this architecture.
In (Rutka and Lauks, 2015), the utilisation of
neural networks for internet traffic prediction is
investigated. Specifically, the investigate traffic
prediction in the presence of self-similarity, which is
an important feature of traffic in high-speed networks
that may not be obtained by traditional traffic models.
The major aim of this work is the performance and
Hidden Markov Model Traffic Characterisation in
Wireless Networks
79
prediction error investigation using feed forward
neural networks.
In (Loumiotis et al., 2014), the efficient
management of the backhaul resources in 4G
networks is examined. The authors raise this issue in
the case that the backhaul network has been leased by
the mobile operator. Hence, the backhaul resource
allocation issue at the basestation is investigated and
aggregate traffic demand scheme is proposed using
artificial neural networks. Finally, the authors provide
evidence of the efficiency of their scheme in terms of
absolute percentage error of downlink and uplink
traffic.
In (Pan et al., 2013), the stochastic cell
transmission model is extended, in order to include
spatiotemporal characteristics of traffic and predict
short-term traffic. Initially, the authors utilise a
multivariate normal distribution-based best linear
predictor as an auxiliary dynamical system predict
boundary variables and/or supply functions.
Thereafter these variables and functions are input to
the stochastic cell transmission model for short-term
traffic state prediction. Stochastic cell transmission
model is relaxed by utilising the covariance structure
calibrated from the spatial correlation analysis for
probabilistic traffic state evaluation. Prediction is
carried-out in a rolling horizon manner, which is
handy for setting the predicted traffic state using real-
time measurements.
3 IBS FOR WIRELESS TRAFFIC
We consider a wireless network where nodes
communicate with respective APs to transmit their
load. We assume that the network is mobile; hence,
there is a possibility of loss of connection and
transmission in a bursty fashion. This is reflected in
the Signal-to-Interference-plus-Noise Ratio (SINR)
between the transmitter and the receiver. We employ
the SINR model appearing in (Spyrou and Mitrakos,
2015) to construct our case.
We denote as
as the SINR of the transmission
for node k to node j and it is given by
(1)
where
is the channel gain between nodes k and j,
is the transmission power of node k transmitting,
is the interfering node t’s transmission power,
is the channel gain between the interferer and the
receiver and
is the noise. For a packet to be
successfully received the following condition must be
satisfied
(2)
Where
is the SINR threshold for successful
reception of the packet. In practical scenarios, a
packet is successfully received when an
acknowledgement is received by the sender. We
consider a packet reception series
where
is the packet i. We classify each packet into
two states that represents the successful reception or
not of the packet, as it can be identified by its
acknowledgement value, as below
(3)
We map successive intervals to a binary
sequence of length m, called an m-bit “word.” Each
m-bit word,
, therefore, represents a unique pattern
of fluctuations in a given time series. By shifting one
data point at a time, the algorithm produces a
collection of m-bit words over the whole time series.
Therefore, it is plausible that the occurrence of these
m-bit words reflects the underlying dynamics of the
original time series. Different types of dynamics thus
produce different distributions of these m-bit words.
The resulting rank-frequency distribution,
therefore, represents the statistical hierarchy of
symbolic words of the original time series. For
example, the first rank word corresponds to one type
of fluctuation, which is the most frequent pattern in
the time series. In contrast, the last rank word defines
the most unlikely pattern in the time series. To define
a measurement of similarity between two signals, we
plot the rank number of each m-bit word in the first
time series against that of the second time series.
If two time series are similar in their rank order of
the words, the scattered points will be located near the
diagonal line. Therefore, the average deviation of
these scattered points away from the diagonal line is
a measure of the “distance” between these two time
series. Greater distance indicates less similarity and
vice versa. In addition, we incorporate the likelihood
of each word in the following definition of a weighted
distance,
, between two symbolic sequences,
and
.
(4)
Fifth International Conference on Telecommunications and Remote Sensing
80
where
(5)
Here
and
represent probability and
rank of a specific word,
, in time series
.
Similarly,
and
stand for probability
and rank of the same m-bit word in time series S2. The
absolute difference of ranks is multiplied by the
normalized probabilities as a weighted sum by using
Shannon entropy as the weighting factor. Finally, the
sum is divided by the value
to keep the value
in the same range of [0, 1]. The normalization factor
Z in Equation 5 is given by
(6)
Next, we will provide an example using realistic
traffic models that will show some initial results of
this approach.
We have taken measurements from a wireless
network, where we obtained the SINR values of 1000
packet transmissions. We made sure that the
configuration of the nodes were as such that there was
significant fluctuation on the signal; simulating thus,
mobility and bursty traffic. Furthermore, we have
obtained packet information from nodes'
communication, where the network is fully connected
and not connected.
Initially, we have undertaken experiments to
show the information similarity index between the
three configurations, namely no network, full
network and bursty traffic network. The values that
we collect from the comparison of the three types of
traffic leads to thresholds for the characterisation of
traffic; in short, we cluster the data based on these
values, as we can see in table 1 below:
Table 1: IBS index for different traffic classes
No – Full
No - Bursty
Full - Bursty
0.140923
0.075158
0.158906
Note that No corresponds to No Network with low
SINR, Full Network is a fully connected network with
high SINR, and Bursty is a bursty traffic network.
We selected an 8 value word, in order to mimic
the bursty traffic that wireless network usually
exhibit. We see that the IBS index for the Bursty
Traffic - Full Network is similar to the Full Network
-No Network configuration. This is the case, due to
the existence of the bursts that lead the IBS index
method to move the index towards the existence of a
fully connected network.
Subsequently, we may include these values as
thresholds in our machine learning implementation,
in order to identify different states of traffic.
However, using IBS to distinguish between these two
traffic classes may result in an ambiguity in the state
identification. This shows that the IBS may not locate
the states that correspond to these different traffic
patterns. Moreover, another limitation is that the IBS
index method requires to collect at least 9 samples to
be able to calculate a distance between the current
state and the distance of the new value, in order to
compare it to the thresholds. This does not allow us
to investigate our problem at the single value
granularity that will allow us to see the events that
will occur.
4 EUCLIDEAN DISTANCE FOR
WIRELESS TRAFFIC
The potential limitations of the IBS index lead us to
employ the Euclidean distance for the data clustering.
This method allow us to investigate the data at the
single value, since it calculates the distance between
the current state and the incoming value to compare
their distance with our defined threshold. This will
give us the opportunity to examine events at the value
level, without requiring a set of values to be compared
against another set.
The Euclidean distance in terms of machine
learning is the distance measure between a pair of
samples p and q in an n-dimensional feature space and
it is given by
(7)
The Euclidean is often the default distance used
in approaches such as the K-means clustering
(MacQueen,1967) to locate the k closest point of a
sample point.
Hidden Markov Model Traffic Characterisation in
Wireless Networks
81
5 HMM FOR WIRELESS
TRAFFIC
We selected the Hidden Markov Models (Eddy,
1996) to classify and predict traffic in our network
due to the fact the predictions may be made using the
last recorded value, as opposed to other machine
learning techniques, such as neural networks (Kosko,
1992), which requires a plethora of historic data, in
order to be trained..
Hidden Markov models (HMMs) are the most
popular means of temporal classification. Informally
speaking, a hidden Markov model is a variant of a
finite state machine. However, unlike finite state
machines, they are not deterministic. A normal finite
state machine emits a deterministic symbol in a given
state. Further, it then deterministically transitions to
another state. Hidden Markov models do neither
deterministically, rather they both transition and emit
under a probabilistic model (Rabiner and Juang,
1986).
Formally, an HMM is essentially a Markov model
where a series of observed outputs
is available drawn from an alphabet
.
Furthermore, he have the existence of states
provided by a state alphabet
.
The transition between states i and j is represented
by the respected value in the state transition
matrix
. Moreover, the probability of generating
the output observation is modelled as a hidden state.
To this end, we define
where
is the matrix which encodes the probability
of the hidden state producing the output
provided
that the state at the corresponding time was s
j
.
We used a similar approach as the one in
(Dunham et al., 2004). Essentially, the HMM we
developed is a time-varying Markov Chain, which
consists of entities that perform tasks, in order to
reach a predicted value.
Initially, HMM performs the clustering action.
The data that arrives from the wireless devices join a
specific cluster labeled by the centroid is calculated
using the following equation:
(8)
Where xi is a set of n points of a dimension
In order to store an incoming value into a cluster,
it is essential to calculate the distance between
already existent states and the incoming value. The
distance is found using equation (7) described in the
previous section.
The present value is declared as a new state if the
value of its distance with the already existent states is
bigger than the value of a defined threshold. On the
other hand, the incoming value is similar to an
existent state, whose values are closer to the incoming
value. The completion of the clustering initiates the
building of the HMM. Given the Markov Chain at
time t and the clustering result at t +1 the Markov
Chain is updated at time t +1. First, the state transition
probability between two successive points is
calculated. Thereafter, the time sequence is updated
with the state transition probability. Furthermore, the
HMM includes a procedure of self-evaluation by
calculating certain metrics of its performance such as
the Normalised Absolute Ratio Error (NARE) and the
Root Means Square (RMS) error.
(9)
(10)
where O(t) is the observed profile, P(t) is the predicted
profile, N is the length of the dataset and t is the time
variable of the t
th
tuple in the input dataset.
Then the HMM reaches the prediction phase.
Initially, the transition probability of the current state
is calculated. The product of the transition probability
with the states vector for each sensor recording
provides the predicted value of the wireless network
traffic. If a node has no connections with another
Fifth International Conference on Telecommunications and Remote Sensing
82
node, then the HMM assumes that the current node is
connected to itself.
6 RESULTS
We obtained data from a wireless network that
consisted of nodes that exhibited bursty traffic and no
connectivity due to mobility. Thereafter, we input
the data to our HMM to check the identification of
different states. We set the threshold that the HMM
recognises a new state to be the SINR threshold for
successful transmission of a packet.
As we can see in Figure 1, the HMM finds two states,
which correspond to the no connection between the
nodes and the burst of successful packet
transmissions. There is an identification of events that
shows the frequency of the identification of the states.
Finally, we see a similar result in the increment of the
states in the third figure, moving from the state of no
connection to the state of connected network.
Similarly, in Figure 2 we see the identification of a
single state, since the data we put in our HMM does
not extend from the value of the SINR threshold. In
the events identification subfigure of figure 1 we see
that different events are not emerging when a network
is not connected; on the contrary, a single state exists
dictating that the HMM can identify the presence of a
disconnected network. In the same way, we see the
next two subfigures of figure 1 that dictate the
existence of a single state of a not connected network
Figure 1: Results for HMM with Bursty Traffic
Events Histogram Bursty
Events Increment Bursty
Events Identification Bursty
Events Identification No Net
Events Histogram No Net
Events Increment No Net
Figure 2: Results for HMM with No Net Traffic
Hidden Markov Model Traffic Characterisation in
Wireless Networks
83
In terms of performance, we calculated the RMS
and NARE for each of the two scenarios. As we can
see in table 1, the performance of the HMM is
reasonably good with NARE values in the range of
0.20 – 0.26 and RMS from 0.58 – 0.88.
Table 2: RMS and NARE of the two scenarios.
NARE
RMS
No Net
0.2576
0.5838
Bursty
0.2091
0.8730
Subsequently, we see that the events identification
does not show any peaks to indicate that there is a
state that has not been found. The above show us that
we may have a reasonable mechanism that will be
able to classify and predict traffic in a wireless
network.
7 CONCLUSIONS
In this paper, we addressed the classification and
prediction of wireless traffic using HMMs. We
employed two clustering techniques, in order to
clarify the states of the data to be input in the HMM.
The first one was the IBS index, which is usually
used in physiological signals. We performed three
experiments, obtaining the distances between three
types of network traffic, namely No Network, Full
Network and Bursty Traffic. We have seen that we
get a difference in two of the three experiments; thus,
resulting in a clear threshold identification for the
identification of different traffic states. However, two
of the three traffic classes exhibit a very similar
distance; hence, the recognition of a new state by the
HMM will be ambiguous. Furthermore, the nature of
the IBS require bunches of signal values to be
examined in order to locate the distance of the data to
be evaluated.
Hence, we decided to use the Euclidean distance,
which allows us to get a distance between the current
state and the incoming value at a single value level;
thus, identifying at a greater granularity the traffic
patterns.
We put our approach to the test using two traffic
files, one of the showing bursty traffic and a second
with no connection. The HMM was able to locate the
traffic patterns and identify the right number of states
and events. We believe that this is an efficient
approach for traffic pattern classification and
prediction.
For future work, we aim to put our approach to a
real network implementation, in order to obtain useful
information regarding the operation of the HMM to
low-power energy constraint devices.
REFERENCES
Alizai, M. H., Landsiedel, O., Link, J. A´ . B., Go¨tz, S.,and
Wehrle, K. (2009). Bursty traffic over bursty links. In
Proceedings of the 7th ACM Conference on Embedded
Networked Sensor Systems, pages 71–84. ACM.
Beran, J. (1994). Statistics for long-memory processes,
Volume 61. CRC press.
Dunham, M. H., Meng, Y., and Huang, J. (2004).Extensible
markov model. In Data Mining, 2004. ICDM’04. Fourth
IEEE International Conference on, pages 371– 374.
IEEE.
Eddy, S. R. (1996). Hidden markov models. Current
opinion in structural biology, 6(3):361–365.
Jiang, H. and Dovrolis, C. (2005). Why is the internettraffic
bursty in short time scales? In ACM SIGMETRICS
Performance Evaluation Review, volume 33, pages
241–252. ACM. Jiang, M.,
Nikolic, M., Hardy, S., and Trajkovic, L. (2001).Impact of
self-similarity on wireless data network performance.
In Communications, 2001. ICC 2001. IEEE
International Conference on, volume 2, pages 477–
481. IEEE.
Kosko, B. (1992). Neural networks and fuzzy systems: a
dynamical systems approach to machine intelligence/
book and disk. Prentice Hall, Upper Saddle River.
Li, R., Zhao, Z., Zhou, X., Palicot, J., and Zhang, H. (2014).
The prediction analysis of cellular radio access
network traffic: From entropy theory to networking
practice. IEEE Communications Magazine, 52(6):234–
240.
Loumiotis, I., Adamopoulou, E., Demestichas,
K.,Kosmides, P., and Theologou, M. (2014). Artificial
neural networks for traffic prediction in 4g networks. In
International Wireless Internet Conference, pages 141–
146. Springer.
Maheshwari, S., Mahapatra, S., Kumar, C. S., and Vasu,K.
(2013). A joint parametric prediction model for
wireless internet traffic using hidden markov model.
Wireless networks, 19(6):1171–1185.
MacQueen, J. (1967, June). Some methods for
classification and analysis of multivariate observations.
In Proceedings of the fifth Berkeley symposium on
mathematical statistics and probability (Vol. 1, No. 14,
pp. 281-297).
Ni, F., Zang, Y., and Feng, Z. (2015). A study on cellular
wireless traffic modeling and prediction using elman
neural networks. In 2015 4th International Conference
on Computer Science and Network Technology
(ICCSNT), volume 1, pages 490–494. IEEE.
Pan, T., Sumalee, A., Zhong, R.-X., and Indra-Payoong,N.
(2013). Short-term traffic state prediction based on
temporal–spatial correlation. IEEE Transactions on
Intelligent Transportation Systems, 14(3):1242–1254.
Papadopouli, M., Shen, H., Raftopoulos, E., Ploumidis,M.,
and Hernandez-Campos, F. (2005). Short-term traffic
forecasting in a campus-wide wireless network. In 2005
IEEE 16th International Symposium on Personal,
Indoor and Mobile Radio Communications, volume 3,
pages 1446–1452. IEEE.
Fifth International Conference on Telecommunications and Remote Sensing
84
Papadopoulos, G. Z., Kotsiou, V., Gallais, A.,Chatzimisios,
P., and No¨el, T. (2015). Wireless medium access
control under mobility and bursty traffic assumptions in
wsns. Mobile Networks and Applications, 20(5):649–
660.
Park, K. and Willinger, W. (2000). Self-similar network
traffic and performance evaluation. Wiley Online
Library.
Rabiner, L. and Juang, B. (1986). An introduction to hidden
markov models. ieee assp magazine, 3(1):4–16.
Rutka, G. and Lauks, G. (2015). Study on internet traffic
prediction models. Elektronika ir Elektrotechnika,
78(6):47–50.
Spyrou, E. D. and Mitrakos, D. K. (2015). On the
Homogeneous transmission power under the sinr
model. In 2015 ICTRS. SCITEPRESS.
Yadav, R. K. and Balakrishnan, M. (2014). Comparative
evaluation of arima and anfis for modeling of wireless
network traffic time series. EURASIP Journal on
Wireless Communications and Networking, 2014(1):
1-8.
Yang, A. C.-C., Hseu, S.-S., Yien, H.-W., Goldberger,
A.L., and Peng, C.-K. (2003). Linguistic analysis of the
human heartbeat using frequency and rank order
statistics. Physical review letters, 90(10):108103.
Hidden Markov Model Traffic Characterisation in
Wireless Networks
85
