310 Int'l Conf. Par. and Dist. Proc. Tech. and Appl. PDPTA'16

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1 310 Int'l Conf. Par. and Dst. Proc. Tech. and Appl. PDPTA'16 Akra Sasatan and Hrosh Ish Graduate School of Informaton and Telecommuncaton Engneerng, Toka Unversty, Mnato, Tokyo, Japan Abstract The end-to-end delay s one of the mportant servce ndcators of the Internet applcatons. Knowng the characterstcs of the end-to-end delay seems very sgnfcant to provde users better net-related servces. Ths paper measures end-to-end delay between a fxed ste n Japan and several stes outsde Japan perodcally and clarfes actual delay dstrbutons n shape of hstograms. Then, t compares each measured hstogram and normal dstrbuton wth the same mean and standard devaton as those of hstogram and shows most hstograms are normally dstrbuted. Keywords: End-to-end delay, png, normal dstrbuton, correlaton factor 1 Introducton People are nowadays able to access nformaton exstng all over the world quckly and smply through the nternet whch spread as nfrastructure. The packet transfer tme between the servce requrng sde and offerng one s a man servce performance rulng factor n the nternet. Therefore to get some knowledge about the dstrbuton of the end-to-end delay of ths network s necessary to desgn and acheve a servce. End-to-end delay should be measured as one way delay to a destnaton from an orgnal sender. However, t s dffcult to know one way delay convenently because there have to nstall measurng equpment n both of sendng sde and recevng sde and have to be operated synchronously. Therefore t s general that only one sde measures the round trp delay nstead of one-way end-to-end delay. Ths round trp delay s called RTT (Round Trp Tme). An exstng study [1] shows RTT obeys Gamma dstrbuton and another [2] explans that RTT follows Pareto dstrbuton when a network s congested and does lognormal dstrbuton when a network s not n congeston. We however thnk t necessary to re-examne RTT dstrbuton because those exstng study results are obtaned n the perod when hgh speed access crcuts dd not exst and the network traffc was much smaller. In [3], we have already measured RTT usng png command to some countres and studed resemblances between the measured results and lognormal dstrbuton accordng to the result of [2] but faled to show the resemblance adequately. The reason of falng gettng the resemblance seemed lack of consderaton of outlers of measured values. Based on the estmaton n [3], ths paper revsts the ssue and studes resemblances between ths actually measured results and a normal dstrbuton by consderng the outlers of measured values usng IQR (Interquartle range). Secton 2 descrbes measurng method and condtons. In secton 3, we show expermental results. Secton 4 studes resemblances between the measured results after excludng outlers and a normal dstrbuton. Secton 5 concludes ths paper. 2 Measurng method and condtons 2.1 Measurng method of RTT We measure RTT usng png command. Png commands are perodcally sent from a PC n our laboratory by use of "ExPng" [5] and the results are logged. 2.2 Measurng specfcaton of RTT Measurement cycle 10 mn. (6161 tmes n total) Measurement perod Aprl 29, 2015 at 06:03 p.m. June 18, 2015 at 01:42 p.m. (51 days) Measurement target USA free web server (000webhost.com), Germany free web server (Host-ed.net), Unversty of Venna, Hgher Unversty of San Andrés, The Unversty of Sydney, Unversty of Narob, Harvard Unversty, The Unversty of Brtsh Columba and Tungha Unversty Measurement place Ish laboratory, Toka Unversty, Mnato, Tokyo, Japan. 3 Expermental results The results of measurng experment are shown as hstograms n Fgures 1 through 9. The horzontal axs shows the measured RTT and the vertcal axs shows the frequency of RTT per 2ms tme slot. The average and the standard devaton of all the RTT measured for each destnaton s also shown n each fgure.

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3 312 Int'l Conf. Par. and Dst. Proc. Tech. and Appl. PDPTA'16 resemblance by use of correlaton coeffcent between each measured RTT hstogram and the normal dstrbuton wth the same mean and varance as those of each hstogram. The results are shown n Table 1. As shown n the Table1, the correlaton coeffcent of any par of sample and normal dstrbuton s rather small (less than 0.6). Hence, t s dffcult to conclude that the normal dstrbuton gves reasonable approxmaton to the measured RTT hstograms. Ths result s also shown n [3]. 4 Consderaton 4.1 A dstrbuton of RTT and normal dstrbuton The shape of the RTT hstograms seems smlar to that of the normal dstrbuton from Fg.1 through 9. Then we research 4.2 Excludng outlers Secton 4.1 uses the average and standard devaton calculated from all samples. But there are samples whose values are extremely devated from the average. They are called An outler s a value n a statstcal samples whch does not ft a pattern that descrbes most other data ponts. More specfcally, a value that les r* IQR beyond the upper or lower quartle. Hence, we exclude outlers usng quantles because outlers may affect estmaton of the dstrbuton. Frst, each RTT data s rearranged n an ascendng order of the value. Next we fnd the values bottom 25th percentle (frst quartle) Q1 and bottom 75th (top 25th) percentle (thrd quartle) Q3. Then, accordng to the followng formula, we get the boundary of outlers, O L and O U. Outler ( Lower) O Outler ( Upper) O IQR Q3 Q1 We researched data between OL and OU. L U Q1 r IQR Q3 r IQR Although generally "r" s 1.5, we adopt r=3 to exclude extreme outlers only.

4 Int'l Conf. Par. and Dst. Proc. Tech. and Appl. PDPTA' San Andres Table2 shows an average and a standard devaton of all measured data and those of data after excludng outlers. Also t shows the rate of number of sample after excludng outlers to that of all elements measured. It shows that the average s unchanged ndependent of outler excluson but the standard devaton becomes much smaller after excludng extreme outlers. Normal dstrbuton wth an average and a standard devaton calculated from the data wthout extreme outlers and measured hstogram are shown for each country n fgures 10 through 18. In addton, correlaton coeffcents are summarzed n Table3.

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6 Int'l Conf. Par. and Dst. Proc. Tech. and Appl. PDPTA' Composte dstrbuton The RTT dstrbuton of the USA server has several peaks (Fg.1). Hence we study whether t can be expressed wth the composton of several dstrbutons or not. Accordng to studes untl secton 4.2, the average almost concdes wth the mode n hstograms approxmated wth just a sngle dstrbuton. Let the delay of the maxmum frequency and delay of the 2nd largest frequency be d 1 and d 2, respectvely and so forth. We assume that samples n the neghborhood of peak belongs to a normal dstrbuton wth the average delay, d, group all the samples nto several groups belongng to the dfferent normal dstrbuton and then each standard devaton s estmated. Here let the composte dstrbuton dst(x), then; dst ( x) a NORM ( x,, ) where a d a s roughlyestmated from the measurements 1 Here we choose 4 values from the hghest frequency ( =1, 2, 3, 4) and get a composte dstrbuton. Fg.19 shows measured hstogram and the composte dstrbuton. Moreover we get a correlaton coeffcent of them. be approxmated as a composte dstrbuton that conssts of several normal dstrbutons. 5 Conclusons Ths paper has tred to clarfy the characterstcs of RTT by contnuous measurement usng png. We have sent png commands to and logged the results of USA, Germany, Unversty of Venna, Hgher Unversty of San Andrés, The Unversty of Sydney, Unversty of Narob, Harvard Unversty, The Unversty of Brtsh Columba and Tungha Unversty. As a result, we found out that the RTT has a very stable value. The dstrbutons wthout extreme outlers have hgh correlaton wth the normal dstrbuton. Further study s needed to consder the resemblance by a dstrbuton besdes the normal dstrbuton, quanttatve study of resemblance by ch-square testng, consderaton of the relaton between number of hops and RTT, and more precse nvestgaton of the composte dstrbuton. 6 References [1] Kaor Kobayash, Masaru Ohta, Tsuyosh Katayama. Analyss and Evaluaton of Packet Delay Tme on Internet ; IEICE techncal report, NS2001-5, pp (2001) (n Japanese). [2] K. Fujmoto, S. Ata and M. Murata. Statstcal Analyss of Packet Transmsson Delay n the Internet ; IEICE techncal report, IN , pp (2000) (n Japanese). [3] Sho Tohyama, Kalkattaw Suhal, Alamr Zzo, Go Gun and Hrosh Ish. Analyss of end-to-end delay characterstcs ; IEE-CMN, CMN , pp (2015) (n Japanese). [4] Akra Sasatan, Nozomu Hrata, Natsuk Okabe and Hrosh Ish. A study on end-to-end delay dstrbuton of the ; IEE-CMN, CMN , (2016) (n Japanese). [5] ExPng, It can be sad that the shape of measured hstogram and one of the composte dstrbuton are smlar. We get a hgh correlaton coeffcent (0.807). Accordngly the hstogram can