Time-series Modelling of Server to Client IP Packet Length in First Person Shooter Games

Transcription

1 Time-series Modelling of Server o Clien IP Packe Lengh in Firs Person Shooer Games A. L. Criceni, P. A. Branch, G. J. Armiage Cenre for Advanced Inerne Archiecures (CAIA) Swinburne Universiy of Technology Hawhorn, Melbourne 3122, Ausralia Absrac - Modelling raffic generaed by Inerne based muliplayer compuer games has araced a grea deal of aenion in he pas few years. In par his has been driven by a need o simulae correcly he nework impac of highly ineracive online game genres such as he firs person shooer (FPS). Time-series models are imporan elemens in he creaion of realisic raffic generaors for nework simulaors such as ns-2 and OMNeT++ as hey accoun for he correlaion beween packes. In his paper we show ha he ime-series behaviour of FPS server-o-clien packe lenghs is well modelled by processes. We repor on daa from six popular FPS games of he pas 10 years including Half-Life, Half-Life Couner- Srike, Half-Life 2, Half-Life 2 Couner-Srike, Quake III Arena and Wolfensein Enemy Terriory. For each of hese games we analyse sessions each comprising 2 o 9 players. In all cases is an effecive model. We also show ha AR models of order 1 and higher fail o capure he packe size variance as effecively as. Finally we show ha higher order ARMA models are no more effecive in describing he ime-series behaviour han he simpler models. I. INTRODUCTION The modelling of he packe raffic generaed by neworked muliplayer Firs Person Shooer (FPS) games has araced considerable ineres over he pas few years [1-8]. FPS games are ypically based on a clien-server model for nework raffic. Wih housands of FPS servers acive on he Inerne a any given ime [8], and because hey are delay and jier sensiive applicaions, undersanding and simulaing he raffic hey generae has become imporan. Since he iniial work by Borella [4], game raffic has been modelled by examining empirical packe races and fiing an appropriae sandard disribuion o he observaions [4-7]. This mehod, however, does no accoun for he correlaion beween successive packe sizes. Some models described in he lieraure acually assume ha here is no correlaion beween packes [5][6][7]. A major shorcoming of his approach is ha he correlaion beween successive packe lenghs is no reained as he packe payload lenghs are simply drawn from he appropriae disribuion. Of mos ineres in modelling FPS game raffic is he server o clien packe lengh. Cliens generae evens describing a single player s aciviy. A ypical human can rigger only a limied number of evens in any given 10ms o 40ms window. Consequenly packes from clien o server are ypically much smaller han he packes from server o clien, and exhibi very limied variaion in size. The disribuion of packe size is independen of he number of players on a given server. In conras, packes in he server o clien direcion exhibi subsanial variaions in lengh as in-game aciviy surrounding a given clien varies wih ime. This variaion is also dependen on he number of players on he server. FPS games generally have differen phases of play; some involve siuaions where players are engaged in high aciviy, whils in ohers he players are only exploring he surroundings. Since server o clien packes carry regular game-sae updaes, i would seem quesionable o simply assume here is no correlaion beween he sizes of consecuive packes received by any given clien. Raher, as phases of game play ofen span muliple server o clien ransmissions, we migh well expec o see some level of packe size correlaion. There has been some limied work ha aemps o model he correlaion beween server o clien packe lenghs in FPS games. Branch, Armiage and Criceni [9] used a Discree Markov Chain o model he clien o server packe size disribuion of a wo player game. The resuling Markov model can hen be used o predic he saisics of an N player game. The mehod does provide models ha can predic he disribuion of packe payload size for differing numbers of players. However, he model only produces packes whose sizes are ineger muliples of he median packe lengh of a wo player game. In pracice we find ha he packe lengh disribuion is no limied in his way. In his work we propose using a ime-series approach o develop models for he clien o server UDP packe payload disribuion. We show ha an model successfully capures he ime-series behaviour of six of he mos popular FPS games of he pas en years. This work was based on raffic races ha were obained from conrolled rials of popular FPS games played under known, documened condiions [10]. This paper is organized as follows. In Secion II we presen a brief review ime-series modelling, wih paricular reference o ARMA models. In Secion III we presen resuls obained by modelling he six games using he ime-series approach. We show he effeciveness of in modelling he imeseries behaviour of all six games. Finally we summarize he major findings and ouline our fuure work in Secion IV /07/$ IEEE 507 ICON 2007

2 II. TIME-SERIES MODELLING A. Background Mos of he lieraure regarding he characerizaion of muliplayer FPS game raffic is concerned wih undersanding he long-erm disribuion of packe iner-arrival imes and packe lenghs. However, for a complee raffic model we mus accoun for he way in which packe lenghs and iner-arrival imes change from one packe o he nex. Some simulaion models of FPS raffic derived from empirical daa have implicily assumed ha here is no correlaion beween successive packes [5, 6, 7]. I is imporan ha his assumpion be invesigaed if realisic simulaions are o be implemened. In his paper we carry ou he invesigaion using echniques from ime-series analysis. Time-series modelling aemps o describe he underlying naure of a phenomenon, which is represened by a sequence of observaions, in order o forecas fuure values. The heory of ime-series modelling is well esablished and is widely used [11]. We begin by reviewing ime-series models wih he aim of applying hese o model he behaviour of he server o clien packe lengh for FPS games. B. ARMA Process Mixed auoregressive / moving average (ARMA) models have been successfully used o model user behaviour in neworked games [3], LAN raffic [12] and ATM raffic[13]. In his paper we show ha hey can be very successfully used o model he behaviour of FPS game nework raffic as well. For a Saionary ime-series X, we define an ARMA(p,q) process as: φ ( B) X = θ ( B ) Z (1) where φ(b) is he auoregressive polynomial of degree p and θ(b) is he moving average polynomial of order q φ(b) = p 1 φ B φ B 1 p (2) q θ ( B) = 1+ θ1b θqb (3) and B is he backshif operaor defined as: i B X = X i i = 0, ± 1, ± 2... (4) The innovaions Ζ in (1) are assumed o be independen idenically-disribued (iid) random variables wih zero mean and variance σ 2. If θ(z) = 1 we have a pure auoregressive (AR) process, whils if φ(z) = 1 we have a pure moving average process (MA). Tradiional Box-Jenkins ARMA models describe saionary ime-series [11]. Inuiively a ime-series is saionary if he saisical properies such as he mean and he variance are no ime dependen. Generally if he values of he ime-series flucuae abou a consan mean value wihou a rend hen he ime-series is saionary. The auocorrelaion funcion (ACF), or auocovariance funcion, of a random process describes he similariy of he process wih iself a differen poins in ime (lag). Thus he ACF can be considered as a measure of he memory of he process. Generally speaking if he ACF dies off quickly hen he process is saionary. The auocorrelaion funcion (ACF) of an ARMA(p,q) or a pure AR(p) process is eiher a damped exponenial or a damped sinusoid, whils for a pure MA(q) process he ACF cus off abruply afer lag q. The ACF is a powerful ool ha helps idenify if he process is saionary and if i is a pure MA(q) process. The parial auocorrelaion funcion (PACF) removes he effecs of shorer lag auocorrelaion from he correlaion esimae a longer lags. The parial auocorrelaion of an AR(p) process cus off abruply afer lag p. The order p of he AR process can be esimaed by looking for he poin where he PACF becomes zero. If he process is purely Markov han i can be modelled using an AR(1) model. An AR(1) process is a special case of he ARMA(p,q) process wih θ(z) = 1 and p = 1. The model is given by he equaion: X φ X + Z = 1 1 (5) Applying his o he packe lengh daa (5) saes ha he curren server o clien packe payload size X is relaed o he size of he las packe sen X -1 and an error erm Ζ (he innovaions). C. Akaike s Informaion crierion (AIC) The Akaike informaion crierion (AIC) [14] is a commonly used model selecion crierion ha is used o choose he bes fi ARMA model. The AIC penalizes models wih a large number of parameers, hus using he AIC can help preven over-fiing of he model o he daa se. We will use his measure laer in he paper, o compare he effeciveness of differen game raffic models. III. RESULTS We begin by using saisics obained from real raffic races o invesigae which ime-series models are suiable for modelling he ime-series behaviour of FPS game raffic. Iniially we invesigae he use of an AR(1) model. We show ha he AR(1) model is only moderaely successful in describing he correlaion beween packe lenghs. We hen invesigae he model and show ha i is much more successful. We also compare empirically derived server o clien packe size disribuions wih synheically derived AR(1) and models and show ha is superior. We sudied he server o clien packe payload size imeseries for six popular FPS games: Wolfensein Enemy Terriory (ETPRO), Quake III Arena (Quake3), Half-Life (HLDM), Half-Life 2 (HL2DM), Half-Life Couner-Srike (HLCS), Half- Life 2 Couner-Srike (HL2CS). 508

3 A. AR(1) Models For Various FPS Games In his secion we show ha whils AR(1) models capure some of he ime-series behaviour of FPS games, hey fail o capure he naure of he variance. Our aim is o obain as simple a ime-series model as possible ha will capure he variance and disribuion of empirical packe size for he differen games, whils reaining he correlaion srucure. Simple models are easy o implemen in a simulaor and generally hey will run faser han a more complex model. The simples model ha we can aemp o fi is he AR(1) or MA(1) model. Some examples of he ACF of he server o clien packe size are shown Fig. 1 for various games up o lag 60. We see ha he ACF dies off exponenially and does no cu off abruply herefore we are confiden ha he process is AR(p) or ARMA(p,q), bu no MA(q) [11]. According o Branch e al. [9] he correlaion beween successive packes of FPS games can be modelled by a Markov chain. In his case he server o clien packe payload size of he curren packe depends only on he payload size of he las packe generaed. An AR(1) process (also known as a Markov process) can also be used as a model in his siuaion. We fied AR(1) models o each game. Tables 1 and 2 show ha he AR(1) model fails o capure he variance of he empirical daa. Fig. 2 shows some examples of he server o clien packe size disribuion. We can see ha he AR(1) model is a reasonable fi for some games and combinaions of players, bu again i fails o accuraely esimae he variance. The exreme values of he synheic disribuion less han he mode are especially a problem as here is a small non-zero probabiliy of generaing negaive packe lenghs (refer o Fig. 2). We also see ha he synheic disribuion is generally wider and he mode is generally less han ha of he empirical disribuion. As he widh of he disribuion is relaed o he variance we need o compare he variance of he wo disribuions. Table 2 and Table 3 presen he resuls for he variance of he empirically obained server o clien packe size and ha of he synheic AR(1) model. The resuls are shown for ETPRO and HL2DM for 2 o 9 players. The resuls for he oher games are similar, bu for reasons of breviy are no presened here. We see ha he variances of he AR(1) synheic process are consisenly approximaely double ha of he empirical process. As he variance of he synheic process is much higher han he empirical variance, we can conclude ha he AR(1) process is no suiable o model he series. Higher order AR models were ried, bu wih a similar lack of success. A. Parial Auocovariance Funcion PACF Examinaion of he parial auocovariance funcions (PACF) reveals ha a pure auoregressive model may no be suiable, since he PACF decays exponenially and does no cu off abruply as is he case for a pure AR(p) process. This behaviour suggess ha he underlying process is more likely o be ARMA [11] (See Fig. 3). B. ARMA Models For Various FPS Games In his secion we show ha an process is successful in modelling he clien o server packe size disribuion of he six FPS games. Various ARMA models were fied o he empirical daa o deermine wheher he synheic ime-series model could beer mach he empirical daa han does he AR(1) model. The simples ARMA model ha can be fied is he. Resuls for his model are presened in Table 4 and Table 5 and he plos are shown in Fig 4. From hese resuls we see ha he fi from he is far superior o he AR(1) model. The resuls from Table 6 and Table 7 show ha he variance of he synheic disribuion is similar o ha of he empirical daa. Of paricular significance is ha higher order ARMA models, ARMA(1,2), ARMA(2,1) and ARMA(2,2), did no show significan improvemen over he. In Table 8 and Table 9 we show he effec of using higher order ARMA models. There is lile or no advanage in doing so when compared o. The oher FPS games have similar resuls o hose in Table 8. The AIC was used as a measure of how good he fi of a paricular model was. All of he models had a similar AIC value, hus here is no reason o choose a model oher han. Table 1 of AR(1) model for ETPRO Game: ETPRO Players Synheic Table 2 of AR(1) model for HL2DM Game: HL2DM Players Synheic

4 Table 3 of model for ETPRO. Game: ETPRO Players Synheic Payload size ETPRO 2 pls Payload size HL2CS 2 pls Payload size ETPRO 9 pls Payload size HL2CS 9 pls Table 4 of model for HL2DM. Game: HL2DM Players Synheic Payload size HL2DM 2 pls 3 1 Payload size HL2DM 9 pls Auocovariance epro 2 players Auocovariance hl2cs 2 players Payload size QUAKE3 2 pls 8 6 Payload size QUAKE3 9 pls Auocovariance hldm 2 players Auocovariance hl2dm 2 players Payload size HLDM 8 pls Payload size HLCS 2 pls Figure 1 ACF Plos for various 2 player games Figure 2 Packe Size Disribuion AR(1) model. 510

5 PACF of ETPRO 2 pls 0.8 PACF of ETPRO 9 pls 5 Payload size ETPRO 2 pls Payload size ETPRO 9 pls PACF of QUAKE3 9 pls 0.6 PACF of HL2CS 9 pls 5 Payload size HL2CS 2 pls 5 Payload size HL2CS 9 pls Figure 3 PACF Plos for various games Payload size HL2DM 2 pls Payload size HL2DM 9 pls Table 5 of ARMA(p,q) model for ETPRO. Game: ETPRO ARMA Players (1,2) (2,1) (2,2) Table 6 of ARMA(p,q) model for HL2DM. Game: HL2DM ARMA Players (1,2) (2,1) (2,2) Payload size HLDM 2 pls Payload size QUAKE3 9 pls Payload size HLDM 9 pls Payload size QUAKE3 2 pls Figure 4 Packe Size Disribuion model. 511

6 IV. CONCLUSION AND FURTHER RESEARCH In his paper we have shown ha he is a saisfacory model for he ime-series behaviour of he server o clien packe size lengh of six popular FPS games. We have shown ha i is superior o he AR(1) (Markov) models used previously by ohers. We have also shown ha higher order ARMA models provide lile or no advanage in describing he ime-series behaviour compared wih he simpler models. Furher research in his area will involve beer undersanding he innovaions of he model and in invesigaing echniques for exrapolaing he model o games wih much larger numbers of players. Finally i is worh noing ha he ulimae purpose of his work is o develop simulaions o explore real world problems. Tha is perhaps he mos imporan fuure work ha we plan o carry ou. V. REFERENCES [1] J. Färber, " Traffic Modelling for Fas Acion Nework Games," Mulimedia Tools and Applicaions, vol. 23, pp , [2] F. Wu-chang, C. Francis, F. Wu-chi, and J. Walpole, "A raffic characerizaion of popular on-line games," IEEE/ACM Trans. New., vol. 13, pp , [3] T. Henderson and S. Bhai, "Modelling user behaviour in neworked games," in 9h ACM Inernaional Conference on Mulimedia (ACM Mulimedia). Oawa, Canada, [4] M. S. Borella, "Source Models of Nework Game Traffic," Proceedings of neworld+inerop '99, Las Vegas, NV, May [5] T. Lang, G. Armiage, P. Branch, and H. Choo, "A Synheic Traffic Model for Half-Life," in Ausralian Nework and Telecommunicaions Conference (ATNAC) Melbourne, Ausralia, [6] T. Lang, P. Branch, and G. Armiage, "A synheic raffic model for Quake3," in ACM SIGCHI Inernaional Conference on Advances in compuer enerainmen echnology Singapore: ACM Press, 2004, pp [7] J. Farber, "Nework Game Traffic Modelling." NeGames 2002 conference, Braunschweig, April [8] G. Armiage, M. Claypool, and P. Branch, Neworking and Online Games - Undersanding and Engineering Muliplayer Inerne Games. UK: John Wiley & Sons, [9] P. A. Branch, G. Armiage, and A. L. Criceni, "Modelling Server o Clien IP raffic in Firs Person Shooer Games," CAIA Technical Repor , February Cenre for Advanced Inerne Archiecures. [10] "SONG Daabase," Cenre for Advanced Inerne Archiecures, hp://caia.swin.edu.au/sicrc, [11] G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasing and Conrol (Revised Ediion). San Francisco: Holden- Day, Inc., [12] A. M. S. Basu, and S. Klivansky, "Time series models for inerne raffic," in IEEE Infocom 96. San Fransisco, California,, [13] A. T. D. Heyman, and T. V. Lakshman, "Saisical analysis and simulaion sudy of video eleconference raffic in ATM neworks," IEEE Trans. on Circuis and Sysems for Video Technology, [14] C. Chafield, The Analysis of Time Series: An Inroducion, 6h ed. London: Chapman and Hall CRC Press,