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. 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.