INTERNET-DRAFT Statisti s of In ternet P a k et Dela ys Mar h 2002 Net w ork W orking Group A. Corlett In ternet Draft CQOS In ., Irvine, CA Expiration Date: August 2002 D.I. Pullin California Institute of T e hnology S. Sargo o d Nortel Net w orks, UK Statisti s of One-W a y In ternet P a k et Dela ys < draft-Corlett-Statisti s-of-pa k et-dela ys-00.txt > 1 Status of this Memo This do umen t is an In ternet-Draft and is in full onforman e with all pro visions of Se tion 10 of R CF202 6. In ternet-Drafts are w orking do umen ts of the In ternet Engineering T ask F or e (IETF), its areas, and its w orking groups. Note that other groups ma y also distribute w orking do umen ts as In ternet Drafts. In ternet-Drafts are draft do umen ts v alid for a maxim um of six mon ths and ma y b e up dated, repla ed, or made obsolete b y other do umen ts at an y time. It is inappropriate to use In ternet-Drafts as referen e material or to ite them them other than as \w ork in progress". The list of urren t In ternet-Drafts an b e a essed at h tpp://www/ietf.org/1id-abstar ts.txt The list of In ternet-Draft shado w dire tories an b e a essed at h ttp://www.ietf.org/shado w.h tml This memo pro vides information for the in ternet omm unit y . This memo do es not sp e ify an in ternet standard of an y kind. Distribution of this memo is unlimited. 2 Abstra t The statisti al prop erties of pa k et dela ys for transmission a ross the In ternet are in v esti- gated, based on analysis of three datasets obtained using CQOS No des, ea h measured o v er sev eral da ys of on tin uous transmission. Tw o of these sets omprise high and lo w bandwidth measuremen t data for v e tors (de�ned here as a No de to No de link) from CQOS head- quarters to the Irvine Data Cen ter, while the third is a lo w-bandwidth dataset obtained from a CQOS-Irvine to London v e tor. The prin ipal results of this study ma y b e summarized as follo ws. First, the t w o lo al datasets are hara terized b y quiet p erio ds, where the 300 se ond mean dela y sho ws little v ariation, separated b y p erio ds of sev ere v olatilit y in the mean, standard deviation, minim um and maxim um dela ys. In on trast, the in ternational Corlett, Pullin & Sargo o d 1
INTERNET-DRAFT Statisti s of In ternet P a k et Dela ys Mar h 2002 dataset sho w ed only small v ariations in these quan tities o v er a four-da y measuremen t p erio d. Se ond, during the quies en t p erio ds, the probabilit y densit y fun tion of pa k et dela ys is w ell appro ximated b y a shifted exp onen tial distribution, for all three datasets. This suggests that pa k et dela ys tend to b e on en trated near the minim um dela y . Third, the pa k et orrela- tion time, de�ned b y the �rst zero- rossing of the dela y auto orrelation fun tion, exhibited a long-tailed distribution, with a v erage orrelation of order a few to ten se onds. F ourth, the p o w er sp e tra of the time series for dela y for t w o of the datasets sho w ed no salien t features orresp onding to p erio di dela y v ariation at an y time p erio d smaller than the kno wn daily hara teristi time s ales for pa k et dela y . 3 In tro du tion Kno wledge of the detailed statisti al prop erties of one-w a y pa k et dela y , pa k et loss, de- la y v ariation and other metri s is of paramoun t imp ortan e for understanding the general prop erties of In ternet transmission. This in�uen es the design and onstru tion of b oth measuremen t algorithms, the aggregate qualit y-of-servi e parameters, and the estimation of statisti al errors in urred in measuremen t strategy . Whilst there ha v e b een sev eral stud- ies [e.g. Refs 1-2℄ that ha v e onsidered measuremen t strategies for data olle tion in the assessmen t of In ternet metri s, w e kno w of only a few quan titativ e in v estigations [3-4℄ of the statisti al prop erties of pa k et dela ys a ross In ternet links. Of parti ular in terest for the presen t w ork is Mukherjee's [4℄ analysis of round-trip dela y , pa k et loss and pa k et or- derliness for pa k et transmission in the range 1 � 60 Hertz. Mukherjee found that, for the lo w-frequen y omp onen t of in ternet transmission, the round-trip dela y probabilit y densit y fun tion (p df ) w as w ell mo deled b y a shifted Gamma distribution, with shap e and s ale parameters whi h v aried with load and net w ork segmen t. He also noted the presen e of signi� an t slo w os illation omp onen ts in the smo othed net w ork dela ys. Some, but not all of the presen t �ndings are in broad agreemen t with these results. The la y out of this do umen t is as follo ws. In x 4 w e brie�y des rib e the presen t exp erimen ts and summarize the parameters of the resulting datasets that omprise the presen t database. The data analysis, onsisting of dela y time series, probabilit y densit y fun tions and the analysis of the dela y auto orrelation fun tion within measuremen t re ords is presen ted in x 5. In x 6 w e onsider a metri that measures the degree to whi h pa k et dela ys within individual measuremen t re ords tend to b e lustered to w ard the minim um dela y for the re ord. Finally , x 7 dis usss features of the dela y p o w er sp e tra for t w o of the dela y time series omprising the presen t database. 4 The data Datasets w ere initially obtained on four v e tors. Of these, three, whi h w e refer to as datasets # 1, # 2 and # 3 w ere measured with v e tors from CQOS headquarters to the CQOS data Corlett, Pullin & Sargo o d 2
INTERNET-DRAFT Statisti s of In ternet P a k et Dela ys Mar h 2002 6 T able 1: P arameters de�ning datasets # 1, # 3 and # 4. Bandwidith = 1 : 5 � 10 bps, pa k et length = 576 b ytes, utilization � = 1 : 0. Dataset Num b er of Measuremen t Pkts p er 300 O upan y V e tor re ords p erio d (da ys) se s ( M ). fra tion � # 1 621 2 : 2 611 0 : 0063 Lo al # 3 2033 7 : 1 9556 0 : 092 Lo al # 4 1017 3 : 5 730 0 : 0073 London en ter in Irvine, a ross a T1 In ternet onne tion. T ransmission w as o v er the In ternet, and not on a dedi ated link, so that although the t w o No des w ere ph ysi ally lose, they w ere not lose logi ally . Three di�eren t test-pa k et bandwidths w ere used for these measuremen ts. Of these, that of dataset# 2 w as later deemed to b e to o large to meet the sp e i� ations of lo w ( 1%) total measuremen t bandwidth utilization, and so only datasets # 1, and # 3 will b e dis ussed presen tly . W e refer to these as lo w and high-bandwidth lo al datsets, resp e tiv ely . T o omplemen t the ph ysi ally lo al data, dataset # 4 w as obtained from a v e tor de�ned b y t w o No des lo ated at CQOS headquarters, and in London, England, resp e tiv ely . W e all this the L ondon (lo w bandwidth) dataset. F or ea h v e tor, o v er sequen tial 300 se ond measuremen t p erio ds, M pa k ets with a �xed length of 576 b ytes w ere dispat hed using p erio di streaming in whi h the time b et w een ea h pa k et dispat h w as �xed at appro ximately 300 = M se onds. A separate �le, or measuremen t re ord, w as reated for ea h 300 se ond measuremen t p erio d. On ea h measuremen t re ord, the time at whi h transmission b egan for that re ord w as re orded, and during the measure- men t p erio d, the GPS syn hronized send and re eiv e times of ea h pa k et w ere measured and re orded. The total n um b er of sen t ( M ) and re eiv ed ( � M ) pa k ets during the p erio d w as also re orded to enable later al ulation of loss. This pro edure pro du ed a large v olume of re ords for ea h data set, from whi h detailed statisti s of pa k et dela y and loss ould b e p ost-pro essed. T able 1 sho ws the main parameters of ea h data set. The nominal o upan y fra tion � of the T1 line is al ulated from 8 P L � = � C where L = 576 b ytes is the pa k et length, P = M = 300 is the dispat h rate, C = 1 : 5 � 10 6 bps is the T1 link bandwidth and � is the utilization. In T able 1 w e ha v e used � = 1. Note that � is mo dest for datasets # 1 and # 4 but is sizable for # 3, ev en with � = 1 : 0. Corlett, Pullin & Sargo o d 3
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