With of the wireless network system. So various

With
the rapid growth in wireless technology different applications are vividly
applied in smartphone. Now a day’s smartphones are widely used as the simple
and most common devices for communication. The multi-featured attributes of smartphone
devices are widely acceptable across the world for various ways of
communications like data services and voice. With the repeated use of these
services the demand for wireless networks increases rigorously. It becomes a
challenging task for the service providers to maintain the Quality of Service
(QoS) and cost effectiveness by upgrading the technical and infrastructural
features of the wireless network system. So various issues consisting of system
design, congestion control, and admission control should be addressed more
efficiently to provide multi-class services through desired wireless
networks.  To upgrade the service quality
and also to achieve the finest performance there is a dire need to understand
the nature of the fluctuation and underneath pattern (particularly the scaling,
self-similarity property and stationarity) of the wireless network traffic
data. But with the growth of different factors like call drop rate and call
arrival rate, the performance of network traffic in mobile is highly affected.
So it has become a necessity to understand the nature of fluctuations of these
two parameters. In this paper an initiative has been taken to uncover the
nature of the scaling behaviour and time dependency of the frequency
(stationarity or non-stationarity) of occurrence of the two parameters, daily
busy hour call arrivals and dropped calls, of a local mobile switching centre
during 3rd March, 2005 to 31st October, 2015 as shown in
Figure 1 which can be treated as the signatory representative of any wireless
network traffic.The maximum number of call attempts in the peak hour of a day
is defined as busy hour call initiation. The resource of a network can be
limited to or can be upgraded as per requirements depending on the maximum call
arrival and the call drop caused due to congestion. A concurrent study of busy
hour call initiation and daily dropped call time series may give a feasible
nature of the incoming traffic pattern, the call congestion, grade of service
and blocking probability.

In this work
Hurst exponent has been calculated for revealing the scaling behaviour of the  time series, daily busy hour arrival call and
call drop. Two different methods like Rescaled Range analysis (R/S) method and
General Hurst Estimation (GHE) method (Hurst, Black, & Sinaika, 1965)
have been used to calculate the Hurst Exponents to understand the nature of the
signals with respect to different scales to identify the signals as fractional
Brownian motion i.e. whether they are stationary or non-stationary. There are
many limitations of calculating Hurst exponent using other methods. So to get a
non-controversial conclusion about the scaling property of the time series, it
will be useful to apply more than one method to estimate the Hurst Exponent.
Hence two methods (mentioned above) have been chosen to calculate the Hurst
Exponent. Thus confirming the authenticity of the conclusions taken out of the
results.

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Stationary or
non-stationary behaviour of the data series could be completed by analysing the
fluctuating nature of the busy hour call initiation rate and call drop rate. A
non-stationary signal has changing frequency whereas stationary signal has
constant frequency. The signals are checked with respect to time. The analysis
for non-stationary behaviour is necessary due to: 1) asymptotic analysis which
will not be applicable for the regression model with non-stationary variables.
Usually “t-ratios” does not follow a t-distribution, and hence valid tests
about the regression parameters cannot be undertaken. 2) The properties of the
signal are highly affected by the stationary or non-stationary behaviour.
Different methods can be used to check the stationary/ non-stationary behaviour
of the signals. Continuous Wavelet Transform (CWT) based method has been
implanted in this paper to determine the nature of frequency dependency of the
wireless network traffic.  The advantages
of using CWT are: a) simultaneous localization in time and frequency domain and
is computationally fast. ii) Wavelets have the great advantage of being able to
separate the fine details in a signal. Very small wavelets can be used to
isolate very fine details in a signal, while very large wavelets can identify
coarse details. It decomposes a signal into component wavelets.

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