Abstract In This paper, the fractalityand stationarity of a typical wireless network has been investigated byexposingthe scaling pattern and nature of frequency fluctuation of the two crucialparameters,the daily peak hour call arrival number and daily call drop number, allied witha wireless network.
The time series of these two parameters (03. 03.2005 to31.
10.2015), of a sub-urban local mobile switching centre, have been consideredfor revealing the nature of scaling (fractality) and stationary behaviour usingstatistical methodologies. Having the knowledge about the fractality, HurstExponent for the time series have been considered using the methodologies like GeneralHurst Estimation (GHE) and R/S. It has been observed that both the time series show Short Range Dependent (SRD) anti-persistentbehaviour.
Continuous Wavelet Transform (CWT) method has been used to find out thestationarity/non-stationarity of the data-series where both the time series exhibitthe nonstationarity. Theseobservations direct to conclude that the both the time series are not a random henomenonbut complex.However both the series found to have non-linearity and stability. 1. INTRODUCTION Withthe rapid growth in wireless technology different applications are vividlyapplied in smartphone. Now a day’s smartphones are widely used as the simpleand most common devices for communication.
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The multi-featured attributes of smartphonedevices are widely acceptable across the world for various ways ofcommunications like data services and voice. With the repeated use of theseservices the demand for wireless networks increases rigorously. It becomes achallenging task for the service providers to maintain the Quality of Service(QoS) and cost effectiveness by upgrading the technical and infrastructuralfeatures of the wireless network system. So various issues consisting of systemdesign, congestion control, and admission control should be addressed moreefficiently to provide multi-class services through desired wirelessnetworks. To upgrade the service qualityand also to achieve the finest performance there is a dire need to understandthe nature of the fluctuation and underneath pattern (particularly the scaling,self-similarity property and stationarity) of the wireless network trafficdata.
But with the growth of different factors like call drop rate and callarrival rate, the performance of network traffic in mobile is highly affected.So it has become a necessity to understand the nature of fluctuations of thesetwo parameters. In this paper an initiative has been taken to uncover thenature of the scaling behaviour and time dependency of the frequency(stationarity or non-stationarity) of occurrence of the two parameters, dailybusy hour call arrivals and dropped calls, of a local mobile switching centreduring 3rd March, 2005 to 31st October, 2015 as shown inFigure 1 which can be treated as the signatory representative of any wirelessnetwork traffic.The maximum number of call attempts in the peak hour of a dayis defined as busy hour call initiation.
The resource of a network can belimited to or can be upgraded as per requirements depending on the maximum callarrival and the call drop caused due to congestion. A concurrent study of busyhour call initiation and daily dropped call time series may give a feasiblenature of the incoming traffic pattern, the call congestion, grade of serviceand blocking probability.In this workHurst exponent has been calculated for revealing the scaling behaviour of the time series, daily busy hour arrival call andcall drop. Two different methods like Rescaled Range analysis (R/S) method andGeneral Hurst Estimation (GHE) method (Hurst, Black, & Sinaika, 1965)have been used to calculate the Hurst Exponents to understand the nature of thesignals with respect to different scales to identify the signals as fractionalBrownian motion i.e.
whether they are stationary or non-stationary. There aremany limitations of calculating Hurst exponent using other methods. So to get anon-controversial conclusion about the scaling property of the time series, itwill be useful to apply more than one method to estimate the Hurst Exponent.Hence two methods (mentioned above) have been chosen to calculate the HurstExponent. Thus confirming the authenticity of the conclusions taken out of theresults.Stationary ornon-stationary behaviour of the data series could be completed by analysing thefluctuating nature of the busy hour call initiation rate and call drop rate.
Anon-stationary signal has changing frequency whereas stationary signal hasconstant frequency. The signals are checked with respect to time. The analysisfor non-stationary behaviour is necessary due to: 1) asymptotic analysis whichwill not be applicable for the regression model with non-stationary variables.Usually “t-ratios” does not follow a t-distribution, and hence valid testsabout the regression parameters cannot be undertaken. 2) The properties of thesignal are highly affected by the stationary or non-stationary behaviour.
Different methods can be used to check the stationary/ non-stationary behaviourof the signals. Continuous Wavelet Transform (CWT) based method has beenimplanted in this paper to determine the nature of frequency dependency of thewireless network traffic. The advantagesof using CWT are: a) simultaneous localization in time and frequency domain andis computationally fast. ii) Wavelets have the great advantage of being able toseparate the fine details in a signal. Very small wavelets can be used toisolate very fine details in a signal, while very large wavelets can identifycoarse details. It decomposes a signal into component wavelets.2.
Experimental dataset: First and foremost the real time data arerecorded in the Server positioned in the Mobile Switching Centre (MSC) of theISP. The recorded data sets collected from the ISP sited in our city for theperiod 3rd March, 2005 to 31st October, 2015used for exclusivelyresearch purpose. The data can not be exported commercially, it comprises ofcall initiation, call holding time, call drops and its causes, time and delayof hand-off etc. From these dataset the call initiation and the call dropstatistics for each hour of a day have been considered such as the peak hourcall initiation and the call drop statistics have been taken for analysis.
