Performability Analysis Considering Debugging Behaviors for Open Source Solution

Transcription

1 Inernaional Journal of Performabiliy Engineering Vol 9, No, January 03, pp 3- RAMS Consulans Prined in India Performabiliy Analysis Considering Debugging Behaviors for Open Source Soluion Inroducion YOSHINOBU TAMURA and SHIGERU YAMADA Graduae School of Science and Engineering, Yamaguchi Universiy, Japan Graduae School of Engineering, Toori Universiy, Japan (Received on February 6, 0, revised on Sepember 4, 0) Absrac: A large scale open source soluion composed of several open source sofwares is now aracing aenion as he nex-generaion sofware developmen paradigm because of he cos reducion, quick delivery, and work saving The esing phase of open source soluion means he binding esing and sysem esing Generally, i makes no sense o perform he uni esing of open source soluion, because he uni esing means he es for open source sofware Then, i is very imporan for sofware managers o assess he binding saus of open source soluion In his paper, we propose a new approach o sofware performabiliy analysis based on sochasic differenial equaions in order o consider an ineresing aspec of he collision saus during he binding-phase of open source sofwares in open source soluion Especially, we derive several performabiliy assessmen measures from our sochasic differenial equaion model Also, we analyze acual sofware faul-coun daa o show numerical examples of sofware performabiliy assessmen considering he componen collision for several open source sofwares Moreover, we show ha he proposed performabiliy analysis can assis improvemen of qualiy for he large scale open source soluion eywords: Performabiliy, reliabiliy, open source sofware/soluion, sochasic differenial equaions Open source sofware (OSS) sysems which serve as key componens of criical infrasrucures in he sociey are sill ever-expanding now The successful experience of adoping OSS includes GNU/Linux operaing sysem, Apache HTTP server, and so on[] However, he poor handling of he qualiy and cusomer suppor prohibis he progress of OSS This paper focuses on he problems of sofware qualiy, which prohibi he progress of OSS Many OSS's are used because of he cos reducion, quick delivery, and work saving Also, he developmen cycle of OSS has been repeaed wihou a break I is imporan for sofware projec managers o assess he reliabiliy of open source soluion developed under several OSS's A presen, a large scale open source soluion by using several OSS's is now aracing aenion as he nex-generaion sofware developmen paradigm because of he cos reducion, quick delivery, and work saving Also, he large scale open source soluion has such a unique feaure ha i is composed of several OSS's For many OSS's, here are no esing phases for heir developmen cycles However, he open source soluion has he esing phase such as he binding phase of OSS's wih debugging process Then, i is very imporan o be able o connec several open source componens Also, i is need o consider he irregular flucuaion associaed wih he early binding phase of open source soluion Thereby, he sofware projec managers can consider he characerisics of open source soluion In case of considering he effec of he debugging process on enire sysem in he developmen of a mehod of reliabiliy *Corresponding auhor s amura@yamaguchi-uacjp 3

2 4 Yoshinobu Tamura and Shigeru Yamada assessmen for OSS, i is necessary o grasp he siuaion of regisraion for bug racking sysem, he combinaion saus of OSS's, he degree of mauraion of OSS, ec Moreover, if he size of he sofware sysem is large, he number of fauls deeced during he operaing phase becomes large, and he change of he number of fauls which are deeced and removed hrough each debugging becomes sufficienly small compared wih he iniial faul conen a he beginning of operaion Therefore, in such a case, i is appropriae o use a sochasic model wih coninuous sae space in order o describe he sochasic behavior of he faul-deecion process such as he open source soluion Many sofware reliabiliy growh models (SRGM's)[] have been applied o assess he reliabiliy for qualiy managemen and esing-progress conrol of sofware developmen On he oher hand, he effecive mehod of dynamic debugging managemen for new disribued developmen paradigm as ypified by he open source projec has only a few presened[3-6] In his paper, we focus on an open source soluion developed under several OSS's We propose a sochasic differenial equaion model in order o consider he OSS componen collision of open source soluion Moreover, we assume ha he sofware faul-deecion rae depends on he ime, and he sofware faul-repor phenomena on he binding phase of open source soluion keep an irregular sae Especially, we derive several performabiliy assessmen measures from our sochasic differenial equaion model Also, we show ha he performabiliy analysis proposed here can assis improvemen of qualiy for open source soluion developed under several OSS's Model Descripion Le N ( be he number of deeced fauls in he open source soluion by binding ime ( 0) Suppose ha N ( akes on coninuous real values Since laen fauls in he open source soluion are deeced and eliminaed during he binding phase, N ( gradually increases as he esing procedures go on Thus, under common assumpions for sofware reliabiliy growh modeling, i is considered he convenional linear differenial equaion Generally, i is difficul for users o use all funcions in open source soluion, because he connecion sae among open source componens is unsable in he binding-phase of open source soluion Considering he characerisic of open source soluion, he sofware faul-repor phenomena keep an irregular sae in he early sage of binding-phase Moreover, he addiion and deleion of sofware componens are repeaed under he developmen of each OSS sysem, ie, we consider ha he sofware failure inensiy depends on he ime Therefore, we consider he following sochasic differenial equaion[7], [8]: dn( = { b( + σγ ( µ ( }{ a N( }, () d where b ( is he sofware faul-deecion rae a binding ime and a non-negaive funcion, a he expeced number of he iniial inheren fauls, σ is a posiive consan represening a magniude of he irregular flucuaion, γ ( a sandardized Gaussian whie noise, and µ ( he collision level funcion of OSS componen By using Io s formula, he soluion of Eq() is obained under he iniial condiion

3 Performabiliy Analysis Considering Debugging Behaviors for Open Source Soluion 5 N as follows[9],[0]: ( 0) = 0 { b( s) ds ( W ( )}, N( = a exp 0 σµ () where W ( is a one-dimensional Wiener process which is formally defined as an inegraion of he whie noise γ ( wih respec o ime Using soluion process N ( in Eq(), several sofware reliabiliy measures can be derived Moreover, he inensiy of inheren sofware failures in case of b( b ( and b( b ( are respecively defined as: 0 0 ( dne( dhe( ds = d d, a N ( a H ( b (3) e dns( dh s( ( ds = d d, a N ( a H ( b (4) s e s ω µ ( = e, (5) where H e ( and H s ( mean he exponenial SRGM and he delayed S-shaped SRGM, respecively, based on nonhomogeneous Poisson process (NHPP), b is he sofware failure rae per inheren faul, and ω he parameer of sabiliy for he open source soluion Our modeling echnique is based on he sochasic differenial equaions[9],[0] We propose new approaches o he characerisics of open source soluion, ie, he binding-phase, he complex and large scale sysem, and he confusion period in open source soluion Our model can easily comprehend he characerisics of such as large scale open source soluion by using Eq (5) Therefore, he ransiion probabiliy disribuion of hese wo models are obained as follows: N e ( = a exp b σµ ( W ( (6) 3 Parameer Esimaion [ { }], ( + bexp{ b ( W ( )} N s ( a[ σµ ] = (7) In his secion, he esimaion mehod of unknown parameers a, b, and σ in Eq () is presened The join probabiliy disribuion funcion of he process N ( is denoed as P(, y;, y; L;, y ) (8) Pr[ N( ) y, L, N( ) y N( ) = 0] Is densiy of Eq (8) is denoe as 0

4 6 Yoshinobu Tamura and Shigeru Yamada p(, y ;, y ; L;, y P(, y;, y; L; y y L y Since N ( akes on coninuous values, he likelihood funcion, l, for he observed daa ( k, yk ) ( k =,, L, ) is consruced as follows: l = p, y ;, y ; L;, y ) (0) ), y ( For convenience in mahemaical manipulaions, he following logarihmic likelihood funcion is used: L = logl () The maximum-likelihood esimaes â, bˆ, and σˆ are he values making L in Eq () maximize These can be obained as he soluions of he following simulaneous likelihood equaions: L L L = = = 0 a b σ 4 Sofware Reliabiliy Assessmen Measures Considering he expeced number of fauls deeced up o operaion ime, he densiy funcion of W ( is given by: W ( f ( W ( ) = exp π Informaion on he cumulaive number of deeced fauls in he sysem is imporan o esimae he siuaion of he progress on he debugging procedures Since N ( is a random variable in he proposed model, is expeced value can be a useful measure I can be calculaed from Eq() as follows[9],[0]: σ µ ( E[ N( ] = a exp b( s) ds +, 0 E[ N ( is he expeced number of fauls deeced up o ime where )] Also, he expeced number of remaining fauls can be obained as follows: E[ ( ] = a E[ N( ] (5) N r Moreover, he mean ime beween sofware failures is useful o measure he propery of he frequency of sofware failure-occurrence (or faul-deecion) Then, he insananeous MTBF(denoed by MTBF ) is approximaely given by: I ( = dn( E d ) (9) () (3) (4) MTBF I (6)

5 Performabiliy Analysis Considering Debugging Behaviors for Open Source Soluion 7 5 Performabiliy Assessmen Measures for Open Source Soluions I is imporan for he projec managers o undersand he performabiliy in binding-phase for open source soluion In his paper, he performabiliy raio is given by he following equaion as he performabiliy measure for open source soluion: PR( where ( means he mean ime o correcion as follows: MTTR( E[ N( ], = (7) MTTR he down ime of open source soluion a ime Generally, MTTR MTTR( = γ ( d (8) 0 In his paper, we define he densiy funcion ypes of correcion ime as follows: λ γ ( = λe, (9) where λ is he rae parameer of he exponenial disribuion Similarly, he sample pah of performabiliy raio for open source soluion is given as follows: 6 Numerical Examples PR noise ( λ N( λ = (0) We focus on a large scale open source soluion based on he Apache HTTP Server [], ApacheTomca [], MySQL [3] and JSP (JavaServer Pages) The faul-coun daa used in his paper are colleced in he bug racking sysem on he websie of each open source projec 6 Reliabiliy Assessmen Resuls The sample pahs of he esimaed numbers of deeced fauls in Eq (), N ˆ ( ) 's, in case of b( b ( and b( b ( are shown in Figs and, approximaely From Figs and, we can confirm ha he sample pah has variable in he early binding-phase as he ineresing aspec of large-scale open source soluion, ie, our model can cover he collision saus in he binding-phase of OSS's

6 8 Yoshinobu Tamura and Shigeru Yamada Figure : The Sample Pah of he Esimaed Number of Deeced Fauls, N (, in case of b( b ( Figure : The Sample Pah of he Esimaed Number of Deeced Fauls, N (, in case of b( b ( 6 Performabiliy Assessmen Resuls The performabiliy raio, PR ( 's, in case of b( b ( and b( b ( are shown in Figs 3 and 4, approximaely Moreover, Figs 5 and 6 show he sample pah of he performabiliy raio, PR noise ( 's, in case of b( b ( and b( b ( From Figs 3~6, we found ha he performabiliy of open source soluion growh as he binding procedures go on Especially, Figs 5 and 6 show ha he performabiliy raio s decrease as he influence of he inflecion poin of S-shaped curve in he early binding phase

7 Performabiliy Analysis Considering Debugging Behaviors for Open Source Soluion 9 Figure 3: The Esimaed Performabiliy Raio, PR (, in case of b( b ( Figure 4: The Sample Pah of Performabiliy Raio, PR noise (, in case of b( b ( Figure 5: The Esimaed Performabiliy Raio, PR (, in case of b( b (

8 0 Yoshinobu Tamura and Shigeru Yamada Figure 6: The Sample Pah of Performabiliy Raio, PR noise (, in case of b( b ( 7 Conclusions We have focused on he open source soluion which is known as he large scale sofware sysem, and discussed he mehod of performabiliy assessmen for he open source soluion developed under several OSS's A presen, a new paradigm of disribued developmen ypified by such open source projecs will evolve a a rapid pace in he fuure Especially, i is difficul for he sofware managers o assess he performabiliy for he large scale open source soluion as a ypical case of nex-generaion disribued developmen paradigm Our mehod may be useful as he mehod of performabiliy assessmen for he large scale open source soluion Acknowledgemens: This work was suppored in par by he Gran-in-Aid for Scienific Research (C), Gran No and No 5050 from he Minisry of Educaion, Culure, Spors, Science, and Technology of Japan References [] E-Sof Inc, Inerne Research Repors hp://wwwsecuriyspacecom/s_survey/daa/ [] Yamada, S Elemens of Sofware Reliabiliy-Modeling Approach yorisu--shuppan, Tokyo, 0 [3] MacCormack, A, J Rusnak, and C Y Baldwin Exploring he Srucure of Complex Sofware Designs: An Empirical Sudy of Open Source and Proprieary Code Informs Journal of Managemen Science, 006; 5 (7): [4] uk, G Sraegic Ineracion and nowledge Sharing in he DE Developer Mailing Lis Informs Journal of Managemen Science, 006; 5(7):03-04 [5] Zhoum, Y and J Davis Open Source Sofware Reliabiliy Model: An Empirical Approach Proceedings of he Workshop on Open Source Sofware Engineering (WOSSE), 005; 30(4): 67-7 [6] Li, P, M Shaw, J Herbsleb, B Ray, and P Sanhanam Empirical Evaluaion of Defec Projecion Models for Widely-deployed Producion Sofware Sysems Proceeding of he h Inernaional Symposium on he Foundaions of Sofware Engineering (FSE-), 004: 63-7 [7] Arnold, L Sochasic Differenial Equaions-Theory and Applicaions, John Wiley & Sons, New York, 974 [8] Wong, E Sochasic Processes in Informaion and Sysems, McGraw-Hill, New York, 97 [9] Yamada, S, M imura, H Tanaka, and S Osaki Sofware Reliabiliy Measuremen and Assessmen wih

9 Performabiliy Analysis Considering Debugging Behaviors for Open Source Soluion Sochasic Differenial Equaions IEICE Transacions on Fundamenals, 994; E77-A(): 09-6 [0] Tamura, Y and S Yamada Reliabiliy Analysis based on Jump Diffusion Model for an Open Source Sofware Journal of Compuer Science and Engineering, February 0; (): -8 [] The Apache HTTP Server Projec The Apache Sofware Foundaion hp://hpdapacheorg/, (accessed on Nov 0 0) [] Apache Tomca The Apache Sofware Foundaion hp://omcaapacheorg/, (accessed Nov 0 0) [3] MySQL Oracle Corporaion and/or is affiliaes hp://wwwmysqlcom/,(accessed Nov 0 0) Yoshinobu Tamura received his BSE, MS, and PhD degrees from Toori Universiy in 998, 000, and 003, respecively From 003 o 006, he was a Research Assisan a Toori Universiy of Environmenal Sudies From 006 o 009, he was a Lecurer and Associae Professor a Faculy of Applied Informaion Science of Hiroshima Insiue of Technology, Hiroshima, Japan Since 009, he has been working as a Associae Professor a he Graduae School of Science and Engineering, Yamaguchi Universiy, Ube, Japan His research ineress include reliabiliy assessmen for open source sofware He is a regular member of he Informaion Processing Sociey of Japan, he Operaions Research Sociey of Japan, he Sociey of Projec Managemen of Japan, and he IEEE Dr Tamura received he IEEE Reliabiliy Sociey Japan Chaper Awards in 007 and he Research Leadership Award in Area of Reliabiliy from he ICRITO in 00 Shigeru Yamada received his BSE, MS, and PhD degrees from Hiroshima Universiy in 975, 977, and 985, respecively From 988 o 993, he was an associae professor a he Faculy of Engineering of Hiroshima Universiy, Japan Since 993, he is a professor a he Deparmen of Social Managemen Engineering, Graduae School of Engineering, Toori Universiy, Toori-shi, Japan He has published numerous echnical papers in he area of sofware reliabiliy models, projec managemen, reliabiliy engineering, and qualiy conrol He has auhored several books ha include: Inroducion o Sofware Managemen Model (yorisu Shuppan, 993), Sofware Reliabiliy Models: Fundamenals and Applicaions (JUSE, Tokyo, 994), Saisical Qualiy Conrol for TQM (Corona Publishing, Tokyo, 998), Sofware Reliabiliy: Model, Tool, Managemen (The Sociey of Projec Managemen, 004), Qualiy-Oriened Sofware Managemen (Morikia Shuppan, 007), and Elemens of Sofware Reliabiliy (yorisu Shuppan, 0) Dr Yamada received he Bes Auhor Award from he Informaion Processing Sociey of Japan in 99, he TELECOM Sysem Technology Award from he Telecommunicaions Advancemen Foundaion in 993, he Paper Award from he Reliabiliy Engineering Associaion of Japan in 999, he Inernaional Leadership Award in Reliabiliy Engg Research from he ICQRIT/SREQOM in 003, he Bes Paper Award a he 004 Inernaional Compuer Symposium, he Bes Paper Award from he Sociey of Projec Managemen in 006, he Leadership Award from he ISSAT in 007, he Inernaional Leadership and Pioneering Research Award in Sofware Reliabiliy Engineering from he SREQOM/ICQRIT in 009, and he Bes Paper Award from he IEEE Reliabiliy Sociey Japan Chaper in 0 He is a regular member of he IPSJ, he ORSJ, he Japan SIAM, he REAJ, JIMA, he JSQC, he SPM Japan, and he IEEE