Modeling and generating realistic streaming media server workloads

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1 Computer Networks 51 (27) wwwelsevierom/loate/omnet Modeling and generating realisti streaming media server workloads Wenting Tang a,1, Yun Fu b,2, Ludmila Cherkasova a, *, Amin Vahdat b a Hewlett-Pakard Laboratories, 151 Page Mill Road, Palo Alto, CA 9433, United States b Department of Computer Siene and Engineering, University of California, San Diego, 95 Gilman Drive, La Jolla, CA 9293, United States Reeived 28 May 24; reeived in revised form 27 February 26; aepted 2 May 26 Available online 14 June 26 Responsible Editor: U Krieger Abstrat Currently, Internet hosting enters and ontent distribution networks leverage statistial multiplexing to meet the performane requirements of a number of ompeting hosted network servies Developing effiient resoure alloation mehanisms for suh servies requires an understanding of both the short-term and long-term behavior of lient aess patterns to these ompeting servies At the same time, streaming media servies are beoming inreasingly popular, presenting new hallenges for designers of shared hosting servies These new hallenges result from fundamentally new harateristis of streaming media relative to traditional web objets, prinipally different lient aess patterns and signifiantly larger omputational and bandwidth overhead assoiated with a streaming request To understand the harateristis of these new workloads we use two long-term traes of streaming media servies to develop MediSyn, a publily available streaming media workload generator In summary, this paper makes the following ontributions: (i) we propose a framework for modeling long-term behavior of network servies by apturing the proess of file introdution, non-stationary popularity of media aesses, file duration, enoding bit rate, and session duration (ii) We propose a variety of pratial models based on the study of the two workloads (iii) We develop an open-soure syntheti streaming servie workload generator to demonstrate the apability of our framework to apture the models Ó 26 Elsevier BV All rights reserved Keywords: Streaming media server workload; Syntheti workload generator; Media aess patterns; Temporal and stati properties; Non-stationary popularity; Zipf Mandelbrot law; File life span; Modeling * Corresponding author Tel: ; fax: addresses: wentingtang@hpom, wtang@arsightom (W Tang), fu@susdedu, yfu@yahoo-inom (Y Fu), luyherkasova@hpom (L Cherkasova), vahdat@susdedu (A Vahdat) 1 This work was originated and largely ompleted while W Tang worked at HPLabs Currently, W Tang is with Arsight In 5 Result Way, Cupertino, CA, United States 2 This work was mostly done while Y Fu worked at HPLabs during his summer internship Currently, Y Fu is with Yahoo! In 2821 Mission College Blvd, Santa Clara, CA 9554, United States /$ - see front matter Ó 26 Elsevier BV All rights reserved doi:1116/jomnet2653

2 W Tang et al / Computer Networks 51 (27) Introdution Two reent trends in network servies motivate this work, a move toward shared servie hosting enters and the growing popularity of streaming media Traditionally, servie providers over-provision their sites to address highly bursty lient aess patterns These aess patterns an vary by an order of magnitude on an average day [1] and by three orders of magnitude in the ase of flash rowds In fat, servies are often most valuable exatly when the unexpeted takes plae Consider the example of a news servie when an important event takes plae; load on CNN reportedly doubled every seven minutes shortly after 9 AM on September 11, 21 [7] Thus, we are pursuing a vision where large-sale hosting infrastrutures simultaneously provide resoure-on-demand apabilities to ompeting Internet servies [19,8] The idea is that the system an use statistial multiplexing and effiient resoure alloation to dynamially satisfy the requirements of servies subjet to highly bursty aess patterns For instane, surplus resoures resulting from troughs in aesses to one servie may be realloated to satisfy the requirements of a seond servie experiening a peak Further, Servie Level Agreements (SLAs) may speify that, under resoure onstraints, one servie should preferentially reeive resoures over other servies A seond emerging trend is the growing popularity of streaming media servies Streaming media takes the form of video and audio lips from news, sports, entertainment, and eduational sites Streaming media is also gaining momentum in enterprise intranets for training purposes and ompany broadasts These workloads differ from traditional web workloads in many respets, presenting a number of hallenges to system designers and media servie providers [13,18] For instane, transmitting media files requires more omputing power, bandwidth and storage and is more sensitive to network jitter than web objets Further, media aess lasts for a muh longer period of time and allows for user interation (pause, fast forward, rewind, et) The long-term goal of our work is to study resoure provisioning and resoure alloation at the onfluene of the above two trends: network servie hosting infrastrutures for next-generation streaming workloads A key obstale to arrying out suh a study is the lak of understanding of hanging lient aess patterns over a long period of time For both hosting enters and ontent distribution networks (CDNs), we require suh an understanding to determine, for example, how to plae objets at individual sites (potentially spread aross the network) and how to alloate resoures to individual streams and to individual lients Thus, we use long-term traes from two streaming media servies to onstrut an open-soure media workload generator alled MediSyn For MediSyn, we develop a number of novel models to apture a broad range of harateristis for network servies We also demonstrate how these models generalize to apture the harateristis of traditional web servies Overall, this paper makes the following ontributions: A primary ontribution of our work is its fous on the long-term behavior of network servies Among the features of our syntheti generator is the ability to reflet the dynamis and evolution of ontent at media sites and the hange of aess rate to this ontent over time Existing workload generators assume that there is a set of ative objets fixed at the beginning of the trae Similarly, existing tehniques assume that objet popularity remains the same over the entire duration of the experiment While these are reasonable assumptions for experiments designed to last for minutes, we are interested in long-term provisioning and resoure alloation, as well as the resoure alloation for simultaneous ompeting servies (onsider a CDN simultaneously hosting hundreds of individual servies) It was observed [2,12] that the popularity distribution in media workloads olleted over signifiant period of time (more than 6 months) does not follow a Zipf-like distribution We showed that a speial version of Zipf Mandelbrot law an be used to apture the popularity distribution in suh workloads The traditional Zipf-like distribution is a speial ase of the Zipf Mandelbrot distribution We designed a set of new models to apture a number of harateristis ritial to streaming media servies, inluding file duration, file aess prefix duration, non-stationary file popularity, new file introdution proess and diurnal aess patterns The rest of this paper is organized as follows Setion 2 outlines the workload properties that MediSyn attempts to apture and presents the workload generation proess adopted by MediSyn

3 338 W Tang et al / Computer Networks 51 (27) Setion 3 outlines the real-world workloads used tin our study and introdues the models used in Medi- Syn and disusses their speifis We review previous related work in Setion 5 Finally, we onlude with a summary and future work in Setion 6 2 Media workload properties and their generation in MediSyn Aurate workload haraterization is ritial for suessful generation of realisti workloads A syntheti media workload generator an produe traes with targeted, ontrollable parameters and desired distributions for performane experiments studying effetive streaming media delivery arhitetures and strategies For suh experiments, the generated workload must not only mimi the highly dynami resoure-utilization patterns found on today s media systems but also provide flexible means to generate more intensive, bursty and diverse workloads for future media systems Challenges to designing a useful analytial workload generator inlude: identifying essential properties of workloads targeted by syntheti workload generators, and those that most affet the behavior of hosting enters, designing appropriate mathematial models that losely reprodue the identified workload properties from real traes In this setion, we highlight the main properties of streaming media workloads modeled in MediSyn and how these properties are omposed together during workload generation proess in MediSyn We partition media workload properties in two groups: stati and temporal properties Stati properties provide the harateristis of the underlying media fileset, reflet the aggregate, quantitative properties of lient aesses (independent of the aess time), and present the properties of individual file aesses Stati properties inlude: file duration that represents the advertised duration of the file (in seonds), file enoding bit rate that reflets the rate (in bits/s) used for file enoding and that defines bandwidth requirements for the file transfer, file aess popularity that defines the number of aesses to a file within a ertain period of time, file aess prefix that represents the elapsed time of the requested media file when the play ended (a play is ended prematurely when the lient hits the stop button) Temporal properties reflet the dynamis and evolution of aesses to media ontent over time, and determine the ordering and the timing of session arrivals The temporal properties of media workloads inlude: new file introdution proess that reflets at what rate the new ontent is introdued at the media site (and hene, when it appears in media workload), file life span that defines the file popularity hanges over a daily time sale within a ertain period of time, diurnal aess pattern that speify how the number of aesses to a site varies during a given period of time, eg, a day MediSyn s goal is to generate a syntheti trae representing a sequene of file aesses to media servie This proess onsists of generating values/distributions for all the properties introdued above for eah media file One all the file s properties are generated, MediSyn generates a sequene of aesses to eah file aordingly to the assigned popularity distributions and file temporal properties At the end, all the media sessions for all the files are ombined and sorted aording to a global time and merged together to generate the syntheti trae 3 Main models of workload generation in MediSyn This setion desribes the models used in Medi- Syn to apture stati and temporal properties of streaming media workloads Throughout this paper, we use two representative streaming media server logs, olleted over a period of years, to demonstrate the hosen properties and to validate our mathematial models introdued to reflet these properties The streaming media server logs represent two different media servies: HP Cor- Table 1 Summary for two media logs used to develop property models in MediSyn HPC HPL Log duration 29 months 21 months Number of files Number of sessions 666,74 14,489

4 W Tang et al / Computer Networks 51 (27) porate Media Solutions Server (HPC) and HPLabs Media Server (HPL) We define a session as a lient aess to a partiular file Table 1 briefly summarizes the workloads In Table 1, the HPC media server shows more ativities than the HPLabs server While the HPLabs server serves a small number of researh-oriented ommunities within HP, the HPC workload represents a reasonably busy media server with 3 8 lient sessions everyday with peak rate at 12, sessions per day Given this differene, it beomes even more interesting whether we an design ommon models that are apable of generating these diverse enterprise media workloads In the paper, we hosed to use a visualization help for presentating our models and results Most of the figures are used to visually haraterize the nature of studied workloads and help in understanding the main workload properties and their speifis We used MatLab for fitting our data with distribution andidates In partiular, we used v 2 (hi-squared) and k 2 for goodness-of-fit measurement based on [22,21] 31 Stati properties Number of files Number of files Duration (se) Duration Prior studies [12,3] observed that media files might be lassified into a set of groups aording to their durations Different workloads an be grouped based on the ontent of media files hosted by a streaming servie For example, musi sites may have file durations from 3 to 5 min, while movie sites may have file durations from one and half to two hours While a partiular workload might be aptured by a ertain statistial distribution, the same distribution may fail to apture another workload In our ase, although the file duration distribution of the HPC trae an be modeled by a heavy-tail distribution suh as a Weibull distribution [15], the same distribution fails to apture the file duration distribution of the HPL trae As shown in Figs 1(a) and 2(a), the file durations in our traes are onentrated around a set of hot points These hot points are usually some ommon durations, semantially meaningful to a partiular type of media ontent Based on this observation, we lassify these hot points into a set of groups and use a set of normal distributions to model the grouped file duration distribution as shown in Figs 1(a) and 2(a) Here, eah group is modeled by a normal distribution with the mean (l) of eah distribution defined by the hot point of that group The standard deviation (r) of eah normal distribution determines the onentration of the durations within that group Note that we do not use segmented probability density funtions (PDFs) to model the duration distribution We assume a hot point an affet the entire duration sope rather than just a segment Thus, we use an aggregated distribution, whose PDF sums the PDFs of all normal distributions proportionally To proportionally sum all duration groups, we assoiate eah group with a ratio determined by the number of files in the group ompared with the total number of files in the trae So the normal distribution PDF of eah group is normalized against the ratio of that group If only a fration of a normal distribution for a group is used, normalization is performed on the adopted fration of the distribution For example, sine the mean of (a) (b) Duration (se) Fig 1 PDF of the HPC duration distribution: (a) four normal distributions to apture the four peaks and (b) the aggregate distribution of the four normal distributions

5 34 W Tang et al / Computer Networks 51 (27) Number of files Number of files Duration (se) Duration (se) Fig 2 PDF of the HPL duration distribution: (a) five normal distributions to apture the five peaks and (b) the aggregate distribution of the five normal distributions Table 2 Parameters of the normal distributions for the HPC trae Group l r Ratio 63% 1% 18% 9% Table 3 Parameters of the normal distributions for the HPL trae Group l r Ratio 19% 26% 3% 1% 15% the first group in Table 2 is, only half of the normal distribution is used Tables 2 and 3 present the (a) (b) Number of files Number of files Duration (se) mean (l), the standard deviation (r) and the ratio of eah normal distribution for the HPC and HPL trae respetively They show that the HPC and HPL traes have different hot points In MediSyn, users an speify a set of duration groups with different l, r and ratios based on the nature of the media workload they want to generate For eah duration group, MediSyn generates a sequene of durations aording to the ratio and the normal distribution of the group We use the rejetion method [15] to generate the duration sequene aording to the parameterized normal distribution Fig 3(a) and (b) shows the durations generated by MediSyn to simulate the HPC workload based on the parameters presented in Tables 2 and 3 We use k 2 disrepany measure introdued by Vern Paxson [26] to ompare the duration set generated by MediSyn with the original data set The k 2 value is 114 (a) (b) Duration (se) Fig 3 PDF of the MediSyn duration distribution: (a) Four normal distributions to apture the four peaks and (b) the aggregate distribution of the four normal distributions

6 W Tang et al / Computer Networks 51 (27) Enoding bit rate Sine most of ommerial media servers are designed to stream media files enoded at some onstant bit rates, the urrent version of MediSyn is designed to only generate a set of onstant bit rates for the underlying fileset MediSyn models enoding bit rates by a disrete distribution, where the value of eah bit rate and the ratio of the bit rate oupied in the fileset an be speified Based on the disrete distribution provided by users, MediSyn generates a sequene of bit rates for the fileset and mathes the bit rate with the file duration randomly, sine we observe that there is no orrelation between them in our traes (the orrelation oeffiient is 144) Frequeny HPC log HPL log Popularity rank Fig 4 The original popularity distributions of the HPC trae and the HPL trae on a log log sale 313 Popularity Earlier studies [13,18] found that media file popularity an often be aptured by a Zipf-like distribution A Zipf-like distribution states that the aess frequeny of the ith most popular file is proportional to 1/i a If the frequenies of files and the orresponding popularity ranks are plotted on a log log sale, a Zipf-like distribution an be fitted by a straight line A larger a implies more sessions are onentrated on the most popular files Some syntheti workload generators [6,17] also adopt a Zipf-like distribution in generating file popularity However, several studies [2,12,3,5,9] analyzing the properties of workloads olleted over signifiant periods of time observed that for some web and streaming media workloads, a Zipf-like distribution does not aurately apture the file popularity distribution The popularity distribution of these workloads shows a irular urve on a log log sale For referene, Fig 4 shows the file popularity distributions of the HPC and the HPL traes over the entire trae periods on a log log sale They are more like irular urves similar to those distributions notied in previous web studies [5,9] and media workload studies [2,12] If we use a straight line (a Zipf-like distribution) to fit the irular urve and generate session frequenies based on the value of a obtained by urve fitting, the generated frequenies must be skewed from the original session frequenies Breslau et al [9] alulated a by exluding the top 1 files For our traes, not only the beginning but also the end of the urves annot be fitted by straight lines Moreover, sine the most popular files are espeially important for syntheti streaming media workloads, we annot ignore the first 1 files Zipf Mandelbrot law Zipf Mandelbrot law [25] is a disrete probability distribution, whih is a generalized Zipf distribution The law an be desribed as C f ðxþ ¼ ðx þ kþ a ; ð1þ where x is the file popularity rank, k is a onstant, C is a normalization onstant, a is the same P as the parameter of Zipf distribution C ¼ N i¼1 1=ði þ kþa We observe that irular urves of file popularity an be aptured by Zipf Mandelbrot law k-transformation To failitate users to selet popularity distributions in our workload generator, we provide a simple transformation (k-transformation) that an assist the parameter fitting of Zipf Mandelbrot law and intuitively illustrate the meaning of the parameters The k-transformation is defined as follows: given x as a file rank, y as the orresponding aess frequeny for the file, the following k-transformation an transform x and y to a Zipf-like distribution between x k and y k with the same a, x k ¼ x þ k x 1 ð2þ k x y k ¼ y þ k y 1 ð3þ k y where k x and k y are sale parameters Sine y k ¼ C k =x a k (C k is the normalization onstant),

7 342 W Tang et al / Computer Networks 51 (27) C k ðy þ k y 1Þ=k y ¼ ððx þ k x 1Þ=k x Þ a ; ð4þ C k k a x y ¼ k y ðx þ k x 1Þ a þ 1 k y : ð5þ Eq (5) is a entered Zipf Mandelbrot distribution The parameters C and a of the Zipf Mandelbrot distribution on x and y an be desribed as C = C k k a x k y, k = k x 1 We also introdue a onstant a =1 k y Fig 5 shows the relationship between x k and y k of the HPC and HPL traes on a log log sale respetively We observe that they are perfetly straight lines The a value of the Zipf k-transformation is derived through linear regression [14] Table 4 shows some ritial parameters related to the urve fitting of the two workloads As shown in the table, R 2 is 995 for both the HPC and HPL traes, indiating that straight lines fit both the distributions very wellthe reason that the original traes do not show perfetly straight lines at the heads of the urves is that there is little differentiation in the frequenies of the most popular files (with smaller x) It an be attributed to the fat that a long-term trae Frequeny HPC log HPL log Popularity rank Fig 5 The popularity distributions after Zipf k-transformation on a log log sale Table 4 Parameters of Zipf k-transformation of the HPC and the HPL traes Trae a R 2 k x k y Maximum frequeny Number of files HPC HPL an ollet enough files with similar popularities over time, and thus these files an be onsidered as a group (equivalene lass), where a group rank will be a better refletion of the file popularities Intuitively, the effet of the k-transformation is that the popularity follows a Zipf-like distribution if we hek every group of k x files We divide x by k x to sale the file ranks so that the ((i 1)k x + 1)th rank beomes the ith rank and reflet now the orresponding file group rank So we atually move all points on the log log sale along the x-axis to the left and squeeze the points to a more straight line Similarly, the reason that the traes do not show perfetly straight lines at the tails of the urves is that there is not enough differentiation in the number of files with the lowest frequenies So we divide y by k y to squeeze those points along the y-axis on the log log sale The value of k y is not neessarily the same as k x However, MediSyn uses the same value for k x and k y based on our observations for both the HPC and HPL traes, whih we simply refer to as k The sale parameter k of our k-transformation is similar to the sale parameter k of a general Pareto distribution [1] An explanation for the k-transformation is that the original frequeny sequene annot be fitted by a Zipf-like distribution starting from rank 1, but it an be fitted into part of a Zipf-like distribution starting from rank k x To desribe this file rank starting from k x by a Zipf-like distribution, we have to divide its original rank by k x Similar explanation an be applied for k y For popularity generation, instead of speifying the total number of requests, we hoose to follow traditional load generator style to ask users to speify the maximum aess frequene of the most popular file and then generate other file s popularity based on Zipf Mandelbrot law To generate a sequene of frequenies, users of MediSyn only need to speify the maximum frequeny M for the most popular file, the number of files N, the sale parameter k, and the Zipf-like distribution parameter a MediSyn omputes the frequeny of the most popular xth file (x 2 [1,N]) using the following formula:! M k ð xþk 1 Þ a 1 k þ 1; k ð6þ

8 W Tang et al / Computer Networks 51 (27) Frequeny HPC log MediSyn HPC HPL log MediSyn HPL Duration rank Popularity Fig 6 Comparison between the popularity distribution generated by MediSyn and the original traes on a log log sale Table 5 Correlation oeffiient between file popularity and file duration Workload Correlation oeffiient HPC frequeny HPL frequeny HPC rank HPL rank where M k ¼ M 1 þ 1 Fig 6 ompares the frequenies generated by MediSyn with the original fre- k quenies in our traes To determine whether there is a orrelation between file duration and file popularity, we ompute the orrelation oeffiient between file popularity and file duration for both of our workloads Table 5 shows these results We use both the file frequeny and the file rank as the popularity metri to ompute the orrelation oeffiient Duration Popularity rank Fig 7 Popularity rank vs duration for the HPC trae Popularity rank Fig 8 Popularity rank vs duration for the HPL trae Figs 7 and 8 show the relationship between popularity and file duration for the HPC and HPL traes Overall, we observe no strong orrelation between file popularity and file duration So file duration and file popularity are randomly mathed in MediSyn We also hek for possible orrelation between popularity and enoding bit rate One again, there is no orrelation between them, so MediSyn mathes popularity and enoding bit rate randomly 314 Prefix One major harateristis of streaming workloads is that a signifiant amount of lients do not finish playing an entire media file [12,3] Typially, this reflets the browsing nature of lient aesses, lient time onstraints, or QoS-related issues Most inomplete sessions (ie terminated by lients before the video is finished entirely) aess only the initial segments of media files In the HPC (HPL) trae, only 29% (126%) of the aesses finish the playbak of the files 5% (6%) of the aesses in the HPC (HPL) trae last less than 2 min This high perentage of inomplete aesses as well as a high number of sessions aessing only the initial part of the file reate a very speial resoure usage model, whih is widely onsidered for streaming media ahe design [24] We refer to the duration between the start of a media session and the time when the session is terminated by the lient as the prefix duration of the session, or simply the prefix Figs 9 and 1 show the histogram for the prefixes of two typial example files in the HPC trae The spikes in the

9 344 W Tang et al / Computer Networks 51 (27) Ratio Prefix (se) Fig 9 A typial aess prefix distribution of short duration media file Ratio Prefix (se) Fig 1 A typial aess prefix distribution of long duration media file figures orrespond to suessfully ompleted media sessions for the files, while the other prefixes in the figures are inomplete sessions We observe that there is a strong orrelation between the file duration and the prefix distribution: Complete sessions The fration of omplete sessions of a file highly depends on the file duration A short file tends to have more omplete sessions For example, the file durations in Figs 9 and 1 are 723 s and 4133 s respetively The file in Fig 9 has more omplete sessions than that in Fig 1 We use r to denote the ratio of omplete sessions for a file ompared with the total number of sessions for the file Fig 11 shows the relationship between file duration and r We an observe that the r of eah file highly depends on the file duration Inomplete sessions The prefix distribution of inomplete sessions of a file depends on the file duration Fig 9 reflets that the prefixes of inomplete sessions for a short-duration media file an be aptured by an exponential distribution While for a long-duration file as shown in Fig 1, the prefixes of inomplete sessions annot be aptured by an exponential distribution Thus, the overall prefix distribution of a media workload highly depends on eah file s prefix distribution, whih in turn depends on the duration of the file There is not a straightforward solution to diretly apture the overall prefix distribution for the entire workload To generate eah file s prefix distribution, we first generate r for the file, then model the distribution of inomplete sessions for the file based on the assigned r To generate r for a file, we need to determine the relationship between r and the file duration as shown in Fig 11 We observe that the ontour of the dotted area in Fig 11 follows a Zipf-like distribution To obtain this urve, we segment the durations of all files into 1-min bins The maximum r value of eah bin (denoted as r max ) onstitutes the ontour of the dotted area in Fig 11 Fig 12 shows the relationship between r max of eah bin and the duration (in minutes) for the orresponding bin on a log log sale Beause the maximum value of r max is 74, the urve is flat in the beginning The other points an be fitted with a straight line Thus, we an use a Zipf-like distribution to apture the r Duration (se) Fig 11 Fration of omplete sessions (r s) versus the orresponding media file durations

10 W Tang et al / Computer Networks 51 (27) r Duration (min) Fig 12 r max of all bins versus the orresponding bin duration on a log log sale distribution of r max for all bins We also observe that the r values for other files within a bin, are uniformly distributed between and the r max value of the bin So, to generate r for eah file, MediSyn first lassifies files into 1-min bins based on their durations Then, MediSyn generates r max for eah bin For files in eah bin, their r values are hosen aording to a uniform distribution between and r max of the bin Through this proess, the r of eah file an be determined After the r value of eah file is determined, the distribution of inomplete sessions needs to be determined As mentioned above, depending on the file duration, it ould be aptured by an exponential distribution or a mix of an exponential and a uniform distribution Additionally, both Figs 9 and 1 show a similar shape in the beginning of the distributions within a ertain range of duration We observe that for more than 9% of the media files in the HPC trae, the distributions of prefixes within the first 5 min an be fitted by exponential distributions These results onfirm similar findings for an eduational workload studied by Almeida et al [3] Given the fat that prefixes within a ertain duration range (eg, the first 5 min) oupy a high perentage of total inomplete sessions, we introdue a ut-off point and use the following method to model the prefix distribution of a given media file: If a media file duration is less than the ut-off point, its inomplete prefixes are modeled by an exponential distribution If a media file duration is longer than the ut-off point, the distribution of inomplete prefixes is modeled by the onatenation of two distributions The distribution of inomplete prefixes less than the ut-off point is modeled by an exponential distribution The distribution of the remaining inomplete prefixes longer than the ut-off point is approximated by a uniform distribution In the HPC trae, the ut-off point is 5 min Users of MediSyn an speify their own ut-off point We use the following denotations: r e defines the ratio of inomplete sessions whose prefixes are within the ut-off point ompared with the total number of sessions of the file, r u defines the ratio of inomplete sessions whose prefixes are longer than the ut-off point ompared with the total number of sessions of the file If a file duration is less than the ut-off point, r u is Given r for a file, MediSyn needs to generate the values of r e and r u for the file The strategy is to generate r e for the file and to set r u =1 r r e Fig 13 shows the relationship between r and r e for all files in the HPC trae We an see that for a given r, the value of r e is bounded on both the lower and upper sides If we denote the maximum of all r values as R max (74 for the HPC trae), the upper bound r upper e and the lower bound r lower e of a given r an be omputed by Eqs (7) and (8) respetively r upper e ¼ 1 r ð7þ r lower e ¼ r upper e ð:6þ:4r =R max Þ ð8þ r e Ratio Upper bound Lower bound r Fig 13 r e versus r

11 346 W Tang et al / Computer Networks 51 (27) Cumulative distribution funtion Session prefixes (se) Fig 13 plots these alulated upper and lower bounds The upper bound is aused by the limitation that the sum of r, r e, and r u is 1 The lower bound hanges from 6% of the upper bound to the same as the upper bound while r inreases from to R max So during workload generation, for a given r, MediSyn generates the value of r e aording to a uniform distribution between the orresponding upper bound r upper and the lower bound r lower After generating r, r e and r u for eah media file, MediSyn still needs to generate the mean (l) ofthe exponential distribution for the inomplete prefixes Sine eah file has its own exponential distribution for prefixes, we have to derive the distribution for the l s of all media files Analysis of session prefixes in the HPC trae shows that l s of all media files follow a normal distribution MediSyn generates a sequene of prefixes aording to the generated ratios of r, r u, r e and l for eah file Then, these prefixes are randomly mathed with all the sessions of the file In this way, MediSyn an generate all session prefixes for every file Fig 14 shows the umulative distribution funtion (CDF) of the prefixes in the HPC trae ompared with the CDF of the prefixes generated by MediSyn 32 Temporal properties HPC log MediSyn Fig 14 CDFs of the prefixes generated by MediSyn and the HPC trae 321 Causes of temporal loality in media workloads olleted over long period of time Temporal referene loality, whih is universally observed in web and media workloads [13,12,4], is the primary fator that affets session arrival ordering Temporal loality states that reently aessed objets are likely to be aessed in the near future in the aess stream Two fators an ause the temporal loality in the aess stream: skewed popularity distribution and temporal orrelation [11,16] Sine popular files have a higher probability to be aessed within the aess stream, a file s popularity ontributes to its temporal loality If we randomly permute the aess stream, the temporal loality aused by skewed popularity is still preserved under reordering However, temporal loality aused by temporal orrelation annot be preserved under random permutation In MediSyn, to generate a stream of session arrivals exhibiting proper temporal loality, we need to learly understand and distinguish the auses of temporal loality To hek the existene of possible temporal orrelation among sessions for the same files in our traes, we ompare referene distanes [4] between the original HPC trae and a randomly permuted HPC trae Let s 1,s 2,,s n be the stream of aesses representing the media sessions of the entire HPC trae Let s i1 ; s i2 ; ; s im be the sequene of sessions to the same file f i The referene distanes of s i2 ; s i3 ; ; s im are defined as i 2 i 1, i 3 i 2,, i m i m 1 We alulate the referene distanes for all the files and their sessions over the entire HPC trae Then we apply similar proedure to the randomly permuted HPC trae Fig 15(a) shows the histogram of the referene distanes in the original HPC trae on a log log sale The X-axis shows the referene distanes, and the Y- axis shows the number of sessions in the original HPC trae for the orresponding referene distane Fig 15(b) shows the histogram of the referene distanes in the randomly permuted HPC trae on a log log sale It an be observed that two urves are not the same In Fig 15(b), there are less referenes with small distanes For example, there are 122,765 referenes with distane 1 in Fig 15(a) But there are only 5468 referenes with distane 1 in Fig 15(b) Sine in Fig 15(b), referene distanes are only determined by the file popularity, we assume the reason that Fig 15(a) and (b) are not the same is that there is temporal orrelation among sessions for the same files over the entire trae To verify whether our media traes exhibit shortterm temporal orrelation, we alulate referene distanes within every day and sum the number of referenes with the same distane over all days for the HPC trae Then, we permute aesses within

12 W Tang et al / Computer Networks 51 (27) Fig 15 (a) Referene distanes alulated over the entire trae period in the original HPC trae and (b) referene distanes alulated over the entire trae period in the permuted HPC trae Number of referenes Number of referenes (a) Referene distane 1 (b) Referene distane Fig 16 (a) Referene distanes alulated within eah day in the original HPC trae and (b) referene distanes alulated within eah day in the permuted HPC trae every day and alulate referene distanes again for the permuted trae The results are shown in Fig 16(a) and (b) We observe that there is almost no differene between the original trae and the permuted trae on referene distanes This implies that there is no temporal orrelation for sessions within a single day and that temporal loality of sessions within a single day is purely determined by the file popularity distribution within that day The analysis above implies that temporal orrelation in media workloads olleted over long period of time is due to long-term temporal orrelation exhibited on a daily time sale, and that there is no temporal orrelation for sessions within a single day These observations motivate our hoie of temporal properties in MediSyn The temporal properties desribed below intend to reflet the dynamis and evolution of aesses to media ontent over time and to define the proper temporal loality and long-term temporal orrelation found in media workloads 322 New file introdution proess One reent study [12] observes that aesses to new files onstitute most of the aesses in any given month for enterprise media servers We envision that this aess pattern is even more pronouned for media news and sports sites While for eduational media sites the rate of new file introdution and aesses to them might be different, we aim to design a generi parameterized model apable of apturing the speifis of new ontent introdution for different media workloads Among the design goals of our syntheti generator is the ability to reflet the evolution of media ontent provided by different media sites over a long period of time

13 348 W Tang et al / Computer Networks 51 (27) (months) Sine we design MediSyn to support detailed resoure alloation studies, we must aount for the dynami introdution of new ontent and its relative popularity The proess of new file introdution mimis how files are introdued at a media site and attempts to answer the following questions: What is the new file arrival proess on a daily time sale? What is the new file arrival proess within an introdution day? To model new file arrival on a daily level, we apture the time gap measured in days between two 25 Number of introdution days Number of new files introdued per introdution day Fig 19 The number of new files introdued per introdution day Number of introdution days Frequeny New file introdution gap (day) Fig 17 New file introdution gaps measured in days for the HPC trae Number of introdution days New file introdution gap (day) Fig 18 New file introdution gaps measured in days for the HPL trae File introdution gap in days Fig 2 The histogram and the PDF of the new file introdution gap for the HPC trae introdution days and the number of new files introdued in eah introdution day Fig 17 shows the distribution of new file introdution gaps measured in days for the HPC trae The distribution depited in Fig 17 an be aptured by a Pareto distribution with a = 2164 Fig 2 shows the histogram of the original trae and the PDF of the fitted Pareto distribution Fig 18 shows the introdution gap distribution for the HPL trae, whih an be aptured by an exponential distribution with l = 4275 Fig 21 shows the histogram of the original trae and the PDF of the fitted exponential distribution We enter the exponential distribution at x = 1 MediSyn an generate new file introdution time gaps aording to one of three possible distribu-

14 W Tang et al / Computer Networks 51 (27) Frequeny File introdution gap in days Fig 21 The histogram and the PDF of the new file introdution gap for the HPL trae Number of files New file introdution gap (se) within a day x 1 4 Fig 23 New file introdution time gaps within an introdution day tions: (1) a Pareto distribution, (2) an exponential distribution, (3) a fixed interval If users speify a Pareto distribution for the new file introdution proess, files tend to be introdued into the system lustered over time If the introdution proess is speified by an exponential distribution, the new file arrival proess is a Poisson arrival proess, whih means the interarrival times are independent The fixed interval is used to model some artifiial introdution proess with regular patterns Sine there may be multiple new files introdued in a given day, we must also model the number of files introdued per introdution day Fig 19 shows the distribution for the number of files introdued in a given day for the HPC trae The distribution an be fitted by a Pareto distribution with a = Fig 22 shows the histogram and the PDF of the fitted Pareto distribution After determining the number of files introdued in a given day, MediSyn needs to model the new file arrival proess within that day We model this proess by apturing the gap between two file arrivals Fig 23 shows the time gaps for new files introdued within a day Sine the distribution is too sparse on time sale of seonds, we measure the time gaps at multiples of 9 s (15 min) The distribution an be aptured by a Pareto distribution with a = 173 Due to the properties of Pareto distribution, if we only model the time gap between two file arrivals Frequeny 6 4 Number of files Number of files introdued per introdution day Time (hour) Fig 22 The histogram and the PDF for the number of new files introdued per day Fig 24 The start times of new file introdution within introdution days

15 35 W Tang et al / Computer Networks 51 (27) Number of files Time (hour) Fig 25 The rotated start times of new file introdution within introdution days MediSyn generated file introdution time (se) 8e+7 7e+7 6e+7 5e+7 4e+7 3e+7 2e+7 1e+7 Introdution Time Correlation 1e+7 2e+7 3e+7 4e+7 5e+7 6e+7 7e+7 8e+7 HPC file introdution time (se) Fig 26 The orrelation of file introdution time between the HPC workload and the workload generated by MediSyn and start to introdue new files from the beginning of a day, then most of the files will be introdued in the beginning of every day So we also apture the start times of new file introdution proess within every introdution day Fig 24 shows this distribution Sine it looks like a rotated normal distribution with the peak at, we rotate the distribution by 12 h as shown in Fig 25 This is a normal distribution with mean 43,2 s and standard deviation 21,6 s Fig 26 shows the orrelation of file introdution time between the HPC workload and a workload generated by MediSyn to simulate the HPC workload The orrelation oeffiient is 9889 So the generated file introdution time sequene mathes the original trae quite well 323 Life span Sine temporal orrelation is observed in media workloads, an independent referene model ombined with a global popularity distribution [9] is insuffiient for a syntheti workload generator to generate a file aess stream SURGE [6] uses a stak distane model to generate web referene streams with referene loality Both the independent referene model [9] and the stak distane model [6,4] assume that eah file s popularity is stationary over the entire trae period and that eah file is introdued at the start of the trae Sine we observe non-stationary popularity in streaming media workloads, suh models are unsuitable for generating session arrivals in streaming media workloads A new property alled life span has reently been proposed in [12] to measure the hange in aess rate of newly introdued files Life spans reflet the timeliness of aesses to the introdued files We observe that aesses to a media file are not uniformly distributed over the entire trae period Instead, most aesses for a file our shortly after the file is introdued, with aess frequeny gradually dereasing over time For example, for the HPC (HPL) log, 52% (51%) of the aesses our during the first week after file introdution, while only 16% (1%) of the aesses our during the seond week, et Hene, the file aess frequeny (file popularity) hanges over time In other words, file popularity is non-stationary over the trae period This phenomenon implies that session arrivals might be very bursty when new files are introdued at a site To aurately model the non-stationarity of file popularity, we use the new file introdution proess to mimi how media files are introdued at the media sites, as we desribed above In addition, eah file has its own life span, whih haraterizes its hanging popularity after the file s introdution Thus, the global file popularity distribution, the file introdution proess and life spans of individual files, all together apture the popularity hange of media files over the entire trae We define the relative aess time of a file as a random variable whose value is the time measured in days when the file is aessed by a lient after the file is introdued The distribution of a file s relative aess times desribes the temporal orrelation of all aesses to the file We also all this distribution the life span distribution of the file In our traes, we observe two types of life span distributions as illustrated in Figs 27 and 28 respetively

16 W Tang et al / Computer Networks 51 (27) Ratio Ratio Life span (day) Fig 27 A regular lifespan Life span (day) Fig 28 A news-like lifespan To generate a sequene of regular life spans and news-like life spans, we need to model the distributions of the mean (l) and the standard deviation (r) for regular life spans, and the distributions of a for news-like life spans Our analysis of the HPC and HPL traes shows that these parameters follow normal distributions Table 6 shows the parameters for these normal distributions derived from the HPC log to apture the parameters of regular life spans (l and r) and news-like life spans (a) There is a strong orrelation between file popularity and life span shape A file with a higher popularity rank tends to have a higher probability for having a news-like life span Fig 29 shows the PDF for this probability The distribution an be aptured by an exponential distribution File ranks have been transformed between and 1 so that l for the exponential distribution is independent of the number of media files generated In the HPC trae, we observed 82 news-like life spans out of the 4 most popular files Users of MediSyn an speify their own ratio aording to the workload they want to generate A workload inluding more files with news-like life spans has a more bursty aess pattern Table 6 The parameters for the distributions (normal distributions) of the parameters in lognormal and pareto life span distributions Normal distribution paramaters Lognormal l Lognormal r Pareto a l r Sine most files in our traes have life spans similar to Fig 27, we all this type of life span a regular life span News-like streaming ontents typially have life span distributions similar to Fig 28, where most aesses our shortly after the file introdution and the aess frequeny diminishes relatively quikly So we refer to this kind of life span as news-like life span We experimented with gamma, Pareto, exponential and lognormal distributions to fit the relative aess times of our traes Although gamma distributions an somehow apture both news-like and regular life spans, the ombination of Pareto and lognormal distributions an better fit them Thus, news-like life spans follow Pareto distributions, and regular life spans follow lognormal distributions Ratio Normalized file rank ( 1] Fig 29 PDF that a file at a ertain rank has a Pareto life span distribution

17 352 W Tang et al / Computer Networks 51 (27) Diurnal aess pattern Earlier studies observed the diurnal aess patterns for streaming media workloads [13,18,2, 3,17] The diurnal aess pattern defines how the number of aesses to a site varies during a given period of time, eg, a day Diurnal aess patterns might signifiantly vary for different media sites For mixed media workloads utilizing a shared infrastruture, the diurnal aess patterns have to be taken into aount when designing the optimal support for effiient resoure alloation Additionally, the diurnal aess pattern is important for apturing the burstiness of resoure onsumption within a given time period The diurnal aess patterns are defined using the seond time sale in our syntheti workload generator, eg, within a day After determining the life span and the global popularity of every file, MediSyn an generate the number of aesses for every day of a file s life span Distributing these aesses over a day is hallenging beause we wish to model both session interarrival time and diurnal aess patterns Fig 3 shows a typial session interarrival time distribution for a file measured in a day It is a heavy-tail distribution and an be fitted by a Pareto distribution better than an exponential distribution However, if we generate all interarrival times within a day based on this Pareto distribution, it is diffiult to simultaneously ensure diurnal pattern Fig 31 shows the interarrival time distribution for the same file within one hour of the same day This distribution is not a heavy-tail distribution and an be aptured by an exponential distribution Thus, if we an Ratio Gap (se) Fig 31 The PDF of session aess interarrival time gaps for a file measured in an hour determine the number of aesses in eah hour of a day aording to a ertain diurnal pattern, we an use an exponential distribution to generate the interarrival times of the aesses in this hour Thus, we an both generate the diurnal pattern and satisfy the observed exponential distribution for interarrival times Diurnal aess patterns are universally observed by other streaming workload analyses But we do not expliitly find diurnal patterns for single files We only observe an aggregate diurnal aess pattern for all file aesses Fig 32 shows the average ratios of aesses in eah hour for all files in the HPC trae In MediSyn, a user an speify a global diurnal pattern like Fig 32, whih ontains a set of bins Ratio Ratio Gap (se) Fig 3 The PDF of session aess interarrival time gaps for a file measured in a day Hour Fig 32 The session aess diurnal pattern for the HPC trae Eah bin is an hour

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