Design of Traditional/Hybrid Software Project Tracking Technique: State Space Approach

Transcription

1 Design of Tradiional/Hybrid Sofware Projec Tracking Technique: Sae Space Approach MANOJ KUMAR TYAGI 1, SRINIVASAN M. 2, L.S.S. REDDY 3 1 Elecronics and Compuer Engineering 1,3 K. L. Universiy Vaddeswaram, Gunur, A.P. INDIA 1 manojkumar@kluniversiy.in, 3 drlssreddy@kluniversiy.in 2 Elecronics and Communicaion Engineering Meeru Insiue of Engineering and Technology Meeru, 255 U.P. INDIA 2 msrinivasan77@yahoo.com Absrac: - Sofware projecs are required o be racked during heir execuion for conrolling hem. According o sae space approach, he racking problem leads us o have a projec sae ransiion model and projec saus model. A key facor in modeling sofware projecs is o model he projec wih uncerainy involved in he parameers relaed o projec sae ransiion model and projec saus model. Tradiional/Hybrid sofware projec racking echnique is formulaed, modeled wih sae space approach in plan-space and execuion-space, and simulaed using discree even simulaion. The uncerainy considered here is onological ha modeled as a normal disribuion using an approximaion mehod. The sae space model consiss of projec-sae ransiion equaion and projec-measuremen equaion, in plan-space, and i is formulaed wih Mone Carlo mehod in execuion-space. The developed sae space model is used o rack saus of he radiional/hybrid projec. The projec is execued wih an ieraive and incremenal developmen process. Wih Mone Carlo simulaion runs, simulaion resul shows he variaion in onological uncerainy ieraion-wise, boh individually and cumulaively, and he effec of uncerainy on projec saus, by showing projec saus in execuion-space and plan-space. Besides, he projec compleion somewhere during he las ieraion is shown wih simulaion. Key-Words: - Onological Uncerainy, Normal Disribuion funcion, Sae-Space Model, Tradiional Projec, Hybrid Projec, Mone Carlo Simulaion, Discree Even Simulaion, Execuion-Space, Plan-Space. 1 Inroducion How sofware projecs are modeled for racking by considering sae-space view? This quesion is no aken ino consideraion during sofware projec racking. According o sae-space view, sofware projecs sar wih iniial sae, raverse hrough inermediary saes, and move o final sae. These have wo views: plan-space view and execuion-space view. Generally, he execuion-space view differs wih plan-space view; as sofware projecs, consising of boh he echnical and managerial aciviies, involve unknown facors including services, cos, schedule, size, produciviy, lack of informaion, ambiguiy, characerisics of projec paries, radeoffs beween rus and conrol mechanisms, and varying agendas in differen sages of he projec life cycle ([1], [2]). As a general rule, uncerainy arises in any aciviy involving unknown facors, which affecs he aciviy [3, p. 2-4]. Mehods for sofware developmen, a se of pracices for sofware developmen, are based on plan-based, agile, or hybrid sofware developmen philosophy ([4], [5]). Boh agile and plan-driven philosophies have a home ground area of projec characerisics in which each clearly works bes, and where he oher will have difficulies [6]. Hybrid approaches ha combine boh philosophies are feasible and necessary for projecs ha combine a mix of agile and plan-driven home ground characerisics ([6], [7]). In his paper, hybrid approach is derived wih following requiremens volailiy phenomena parially, i.e., allowing he changes o he already specified requiremens which were documened before saring he projec execuion; bu no allowing he new requiremens requesed by cusomers during execuion; while E-ISSN: Issue 11, Volume 1, November 213

2 radiional approach does no follow requiremens volailiy phenomena. In he pas, considerable research has been conduced on improving he effeciveness of projec managemen. However, much of he work has concenraed on developing and evaluaing esimaion and conrol ools used for sofware projecs ([8], [9]), as opposed o model he sofware projecs wih uncerainy ([1], [1]-[12]) for racking. Sofware projec combines applicaion domain knowledge, compuer science, saisics, behavioral science, and human facor issues. One of he saisical research and educaion challenges is providing models wih appropriae error disribuions (uncerainy) for sofware projecs [13]. This paper develops a sae space model of sofware projec racking by considering sae-space view. The developed sae space model is used o rack he saus of radiional/hybrid projec which is execued wih an ieraive and incremenal developmen process [14]. 2 Relaed Work Sofware projec modeling has been an imporan field of sudy since 195, s onwards. Tradiionalmodels such as Work Breakdown Srucure (WBS), Gan Model, Criical Pah Mehod (CPM) Model, PERT Model, AND-OR Graph Model, Peri Ne Model, Sochasic Peri ne-based Model, Design Ne Model ([9],[]) are used o suppor he operaional issues. The Merix model is a sochasic model for sofware projec duraion esimaion using Mone Carlo simulaion over an aciviy graph [16].The Projec Monioring wih Sakeholders Model is based on he measuremen informaion model defined by ISO/IEC 939, and added sakeholder, s ( a purchaser and a developer) goal, key goal indicaor(kgi),key performance indicaor(kpi), correcive acion, and check iming[17]. The Anipaern Bayesian Nework Model provides he mahemaical model of a projec managemen anipaern and can be used o measure and handle uncerainy in mahemaical erms [18]. The Sofware Projec Tracking lieraure ([19], [2]) consiss of GANTT Char, SLIP Char, TIMELINE Char, CPM, PERT, COST Chars, S-Curve based mehods such as Inegraed Cos/Schedule/Work mehod and Earned Value Analysis are used for cos or schedule racking. Having gone hrough he lieraure, we found some issues which are no considered for racking he sofware projecs as The sae-space view of sofware projecs has no been considered for sofware projec modeling. Lile consideraion has been given o projec modeling for racking wih due consideraion for uncerainy relaed o sofware developmen produciviy, requiremen s- specificaion documen. There is a need of sofware projec racking echnique designed wih sae-space approach and considering he above issues. Here we have developed a sae space model represening radiional/hybrid sofware projec racking echnique considering uncerainy. The model is capable o rack radiional/hybrid sofware projec saus in plan-space or execuion-space. 3 Model Building The radiional/hybrid sofware projec racking model is developed using he sae space approach ([21], [22]). The model has developed based on a case sudy described in Mike Cohn, s Book[23]. The case sudy here involves a myhical gamedevelopmen company Bomb Sheler Sudios. In his sudy, a game ermed Havannah was developed wih agile philosophy. Here, radiional sofware projec racking model considers uncerainy relaed o sofware developmen produciviy; while hybrid sofware projec racking model considers uncerainy relaed o requiremens volailiy phenomenon, and sofware developmen produciviy. Besides he definiion of he model boundaries and model granulariy, he mos imporan design decisions were relaed o he ypically observed behavior paerns ( reference mode ) of developmen projecs. The reference mode was defined by he dynamics of produc evoluion, i.e. a produc is developed wih ieraive and incremenal process model, i.e. each produc incremen implemens cerain ypes of requiremens. 3.1 Dynamics of Produc Evoluion The developmen of sofware produc is done incremenally wih equal periods (ieraion). During each period one incremen is developed. 3.2 Dynamics of Requiremens Generaion A he beginning of each ieraion, a fixed se of frozen-requiremens seleced from requiremens specificaion documen o sar wih is known. Here we assume ha requiremens volailiy phenomena cause modificaion o lefover requiremens for hybrid projec, bu no for radiional projec. This leads new requiremens o be generaed during he E-ISSN: Issue 11, Volume 1, November 213

3 ieraions and updaed o he requiremen s specificaion documen. These new requiremens do no produce major changes in he sofware being buil, bu leads o more cusomer saisfacion. Typically, he number of new requiremens shows a ceiling effec, i.e. he new requiremens do no reflec modificaion or replacemen of already implemened requiremens. 4 Design of Tradiional/Hybrid Sofware Projec Tracking Technique According o sae-space approach, he sofware projec racking echnique consiss of projec saespace and saus-space. The projec sae-space and saus-space are collecion of projec saes and projec sauses respecively. The sofware projec sars wih esimaed iniial-sae, raverse hrough inermediae saes, o final sae in plan-space and execuion-space. The sofware projec plan-space and execuion-space represen he projec plan behavior and execuion behaviour respecively. The projec behavior is defined wih projec sae and is saus. As sofware projec ransis in is sae-space, he projec saes are used o derive projec sauses in saus-space, during plan-space and execuion-space. Generally, he projec execuion behavior differs wih plan behavior due o uncerainy wih projec environmen. The projec is racked o conrol. Sofware projec racking echniques are designed wih sae-space approach ([21], [22]) in plan-space, and as well using Mone Carlo mehod [24] in execuion-space. The sae-space model, consising of sofware projec sae-ransiion model and sofware projec measuremen model, is used o model a sofware projec racking echnique. The following equaions (1) and (2) are used o represen a sofware projec racking echnique in plan-space and execuion-space, respecively. Sofware Pr ojec Sae Transiion Model S 1 A S Sofware Pr ojec Measuremen Model M H S Sofware Pr ojec Sae Transiion S 1 A S N 1 Sofware Pr ojec Measuremen Model M H S V Model (1) (2) Where A and H represen a sae-ransiion marix and measuremen ransiion marix, respecively. N and V represen a projec sae noise (uncerainy) and measuremen noise vecor due o which sofware projecs deviae from plan. S and M represen sae vecor and measuremen vecor, respecively. Above equaions represen, he way a new sae S is 1 modeled as a linear combinaion of he previous sae S in plan-space and boh he previous sae S and some projec uncerainy and how projec saus inernal sae S. 1 N in execuion-space; M is derived wih he 5 Sae Space Modeling-A Novel Approach During he life of sofware projecs, heir execuion behavior differs wih plan behavior due o uncerainy wih projec environmen. The sofware projec, during execuion, is described as a sochasic-process ([25], [26]); which changes is sae over he life of a projec. Here, we are developing a new approach for modeling he sofware projec racking echnique which considers sae-space view for racking radiional/hybrid sofware projecs in plan-space and execuion-space. The Mone Carlo mehod, which uses random numbers from a given probabiliy disribuion o compue somehing [24], is used o develop sofware projec sae ransiion model and projec saus model in execuion-space. 5.1 Sae-Space Model: Tradiional/Hybrid Sofware Projec Tracking Technique Formulaion The sofware projec behaves differenly in planspace and execuion-space. This happens due o uncerainies wih eam-capabiliy and requiremensspecificaion documen. The projec is planned wih uniform eam-capabiliy and requiremens volailiy phenomena. The eam-capabiliy represens he workload seleced o be compleed during ieraion. Due o requiremens volailiy phenomena, here are changes o he requiremens-specificaion documen. The projec-sae is described wih wo parameers as P, and RR represening requiremens seleced o be compleed during an ieraion, and remaining E-ISSN: Issue 11, Volume 1, November 213

4 requiremens o be compleed for projec compleion respecively. Fig.1 represens he projec sae a saring and ending poin of (+1) h ieraion. Fig. 1. Represenaion of Projec-Sae a (+1) h Ieraion The projec is sared wih iniial-sae [P, RR ] T =[16,132] T, where T represens marix ranspose operaion. Team-Capabiliy represened by P, depends on he working capabiliy of he developers, used o selec workload a saring of some ieraion. There are hree echniques-hisorical Values, Make a Forecas, and Run an Ieraion, for esimaing i [23]. Here, i was esimaed iniially wih hisorical values echnique. I is uniform in plan-space and varying wih onological uncerainy in execuion-space. I is affeced wih he facors such as schedule-pressure, communicaion/moivaion, size-esimaion, workforce-experience level, ([27]-[3]) ec in execuion-space. Their ne-effec on eam-capabiliy is a random variable ϵ p represening onological uncerainy. Team-Capabiliy during las ieraion is used for selecing he workload for presen ieraion. P P 1 1 P RR P +1 P P p 1 Plan Space Execuion Space RR +1 (3) (4) Remaining-Requiremens o be compleed for projec compleion a he end of (+1) h ieraion, represened by RR +1, is calculaed as follows: (i)team-capabiliy represened by P is used for selecing he workload o be compleed for (+1) h ieraion, which are no affeced wih requiremensvolailiy phenomena. (ii)requiremens lef over during (+1) h ieraion, which are affeced wih requiremens-volailiy phenomena([31]-[34]), is (RR -P ). ϒ is a sochasic variable conrolling he changes occurring in he already specified requiremens of he produc. Esimaing ϒ inroduces he onological uncerainy, represened by ϵ u, for remainingrequiremens o be compleed for projec compleion a he end of (+1) h ieraion in execuion-space. New requiremens generaed due o requiremensvolailiy phenomena is ϒ(RR -P ), which are o be added. Therefore, remaining-requiremens a he end of (+1) h ieraion is find ou by adding: Requiremens lef over during (+1) h ieraion, which are affeced wih requiremens-volailiy phenomena, is (RR -P ); and New requiremens generaed due o requiremens-volailiy phenomena is ϒ(RR -P ); in plan-space and in addiion o i adding ϵ u ; in execuion-space. RR +1 = ϒ(RR -P )+ (RR -P ) RR RR 1 1 Space ( 1) P ( 1) RR Plan Space ( 1) P ( 1) RR Execuion u 1 Onological uncerainy (noise) is defined as inheren variabiliy concerning he parameers used o model he sysem [35]. Normal noise is a popular choice which inerferes wih human decision-making [36]. The onological uncerainy represened by random variables ϵ p, and ϵ u, has been modeled by using an approximaion mehod, which derives normally disribued random numbers by summing several uniformly disribued random numbers x i according o he following formula ([37],pp.8) y k i 1 x i 1 2 k 12 k 2 As k (5) (6) 1 ( 7 ) Where y is random variable following a normal-disribuion wih mean and sandard deviaion 1. The sae space model for sofware projec racking echnique has been developed by using difference equaions describing he dynamics of sofware projec in plan-space. The developed model is used o represen radiional/hybrid projec in planspace. Equaions (3) and (5) describe he projec sae ransiion in plan-space. P +1 = P RR +1 = ( ϒ+1) P + ( ϒ+1) RR P 1 1 P RR RR ( 1) P ( 1) RR 1 (8) (9) The projec saus is described wih remaining requiremens o be compleed for projec compleion, projec velociy, effor remaining o complee he projec, and eam srengh a ime, represening eiher sar or end of some ieraion. A ime, i relaes o he sae of he projec as follows: remainingrequiremens = RR projecvelociy = RR -1 RR E-ISSN: Issue 11, Volume 1, November 213

5 efforremaining = β RR, Where β represens a facor which is used for convering remaining requiremens ino effor remaining. Assume a review of hisorical daa indicaes ha he organizaional produciviy for produc of his ype is 4 sory-poins/ person-ieraion. Based on a burdened labor rae of $ 2 per personieraion, he cos/sory-poins is 2/4 = 5 $/ sory-poins. Then β is calculaed as follows β = (5 $/ sory-poins)/(2 $/ person-ieraion) =1/4 person-ieraion/ sory-poins. eamsrengh = P remainingr equiremen s P 1 RR projecvel ociy RR 1 RR efforrema ining P RR eamsreng h 1 P RR (1) (11) (12) (13) The sofware projec sae ransiion equaion in marix form for sofware projec racking echnique in plan-space has been derived wih equaions (8), and (9); and sofware projec measuremen equaion in marix form for sofware projec racking echnique in plan-space has been derived wih equaions (1), (12) and (13). Equaion (14) represens a sae space model for sofware projec racking echnique in planspace. Sofware Pr ojec Sae Transiion Equaion P 1 1 P RR 1 ( 1) ( 1) RR Sofware Pr ojec Measuremen Equaion remainingr equiremens 1 P efforrema ining RR eamsreng h 1 (14) Equaions (11) and (14) are used o rack he saus of radiional/hybrid sofware projec in planspace. The sae space model for sofware projec racking echnique has been developed by using difference equaions describing he dynamics of sofware projec in execuion-space. The developed model is used o represen radiional/hybrid projec in execuion-space. Equaions (4) and (6) describe he projec sae ransiion in execuion-space. P +1 = P + ϵ p+1 RR +1 = ( ϒ+1) P + ( ϒ+1) RR + ϵ u+1 The projec saus is described wih remaining requiremens o be compleed for projec compleion, projec velociy, effor remaining o complee he projec, and eam srengh a ime, represening eiher sar or end of some ieraion. A ime, i relaes o he sae of he projec as follows: remainingrequiremens = RR projecvelociy = RR -1 RR efforremaining = β RR +ϵ β, Where β represens a facor, which is used for convering remaining requiremens ino effor remaining; and inroduces onological uncerainy ϵ β for efforremaining relaed o saus vecor. The onological uncerainy represened by random variable ϵ β, has been modeled wih equaion (7). Assume a review of hisorical daa indicaes ha he organizaional produciviy for produc of his ype is 4 sory-poins/ person-ieraion. Based on a burdened labor rae of $ 2 per person-ieraion, he cos/sory-poins is 2/4 = 5 $/ sory-poins. Then β is calculaed as follows β = (5 $/ sory-poins)/(2 $/ person-ieraion) =1/4 person-ieraion/ sory-poins. eamsrengh = P remainingrequiremens P 1 RR (17) projecvelociy RR 1 RR (18) efforremaining P RR 1 (19) eamsrengh 1 P RR (2) The sofware projec sae ransiion equaion in marix form for sofware projec racking echnique in execuion-space has been derived wih equaions (), and (16); and sofware projec measuremen equaion in marix form for sofware projec racking echnique in execuion-space has been derived wih equaions (17), (19), and (2). Equaion (21) represens a sae space model for sofware projec racking echnique in execuion-space. Sofware Pr ojec Sae Transiion Equaion P 1 1 P p1 RR1 ( 1) ( 1) RR u1 Sofware Pr ojec Measuremen Equaion (21) remainingrequiremens 1 P efforremaining RR eamsrengh 1 P 1 RR 1 P RR 1 p 1 ( 1) P ( 1) RR u 1 ( ) (16 ) Equaions (18) and (21) are used o rack he saus of radiional/hybrid sofware projec in execuion-space. E-ISSN: Issue 11, Volume 1, November 213

6 The sae space models for sofware projec in plan-space and execuion-space differs wih onological uncerainy represened by random variables ɛ p, ɛ β, and ɛ u relaed o eam -capabiliy P, efforremaining, and remaining-requiremens RR respecively. The random variables ɛ p, ɛ β, and ɛ u follow normal probabiliy disribuion. In his paper, we have used he parameer ϒ and ɛ u o classify he racking echniques as follows If ϒ and ɛ u are zero for all ieraions hen he model represens a radiional projec racking echnique. If ϒ is non-zero for all ieraions hen he model represens a hybrid projec racking echnique. 6 Uncerainy Propagaion The sofware projec in execuion-space deviaes from plan-space due o uncerainy involved wih parameers eam capabiliy, efforremaining, and remaining requiremens used for modeling. The uncerainy propagaion is described ieraion-wise, individually and cumulaively, in execuion-space. Wih equaion (21), a ime =, i.e. during firs ieraion P 1 = P + ϵ p1 RR 1 = (ϒ+1) P + (ϒ+1) RR + ϵ u1 Clearly, uncerainy wih eam capabiliy during firs ieraion, IndividualDeviaion_TC 1 = ϵ p1 Deviaion_TC 1 = ϵ p1 Uncerainy wih remaining requiremens during firs ieraion, Deviaion_RR 1 = ϵ u1 CumulaiveDeviaion_RR 1 = Deviaion_RR 1 Wih equaion (21), a ime =1, i.e. during second ieraion P 2 = P 1 + ϵ p2 RR 2 = (ϒ+1) P 1 + (ϒ+1) RR 1 + ϵ u2 By expanding P 1 and RR 1, Uncerainy wih eam capabiliy during second ieraion, Individual Deviaion_TC 2 = ϵ p2 Deviaion_TC 2 = ϵ p1 + ϵ p2 Uncerainy wih remaining requiremens during second ieraion, Deviaion_RR 2 = (ϒ+1) ϵ p1 + (ϒ+1) ϵ u1 + ϵ u2 = (ϒ+1) Deviaion_TC 1 + (ϒ+1) Deviaion_RR 1 +ϵ u2 CumulaiveDeviaion_RR 2 =Deviaion_RR 1 +Deviaion_RR 2 By generalizing, during (+1) h ieraion, Uncerainy wih eam capabiliy, individually and cumulaively IndividualDeviaion _ TC Deviaion _ TC 1 p1 1 p2 p 1... p 1 (22) (23) Uncerainy wih remaining requiremens, individually and cumulaively Deviaion _ RR 1 ( 1) Deviaion _ TC ( 1) Deviaion _ RR u 1 (24 ) Cumulaive Deviaion _ RR 1 Deviaion _ RR Deviaion _ RR (25) 1 7 Simulaion Resuls The projec is iniialized wih he sae vecor [16, 132] T, where T represens marix ranspose operaion. The sofware projec changes is sae because of he requiremens compleed by he developers. And he projec saus, a eiher sar or end of an ieraion, is deermined wih he sae of he projec. The sae is deermined by Team_Capabiliy (sory-poins) represening he workload seleced o be compleed by he developers, and Remaining_Requiremens (sory-poins) represening remaining requiremens o be compleed for projec compleion by developers. The saus is deermined by Effor_Remaining (person-ieraion) effor needed o complee he projec, Team_Srengh (sory-poins/ieraion) represening eam capabiliy o complee requiremens per ieraion, and Projec_Velociy (sory-poins/ieraion) represening compleed requiremens per ieraion, Remaining _ Requiremens (sory-poins) represening remaining requiremens o be compleed for projec compleion by developers. Wih Mone Carlo runs, he deviaion for Remaining_Requiremens and Team_Capabiliy has been shown ieraion-wise, individually and cumulaively respecively; which affecs he saus of he projec in execuion- space. How projec saus, affeced wih uncerainy in remaining requiremens, and Team_Capabiliy is shown wih simulaion. The saus of he projec has been shown wih planned and acual projec execuion a he end of each ieraion. 7.1Tradiional Sofware Projec Tracking Fig. 2 shows he deviaion for Remaining _Requiremens and Team_Capabiliy individually and cumulaively. E-ISSN: Issue 11, Volume 1, November 213

7 Deviaion in Remaining_Requiremens(sory poins) Deviaion in Remaining_Requiremens Individual-Deviaion Cumulaive-Deviaion -2 Time(ieraion) This plo is generaed by Ch Suden Ediion Projec_Velociy(sorypoins/ieraion) Projec_Velociy Acual Time(ieraion) This plo is generaed by Ch Suden Ediion Deviaion in Team_Capabiliy(sory poins) Deviaion in Team_Capabiliy Individual-Deviaion Cumulaive-Deviaion -6 Time(ieraion) This plo is generaed by Ch Suden Ediion Effor_Remaining(person-ieraion) Effor_Remaining Acual -5 Time(ieraion) This plo is generaed by Ch Suden Ediion Fig. 2 Deviaion for Remaining_Requiremens and Team_Capabiliy for Tradiional Projec Fig. 3 shows he projec saus wih Effor _Remaining, Team_Srengh, Remaining _Requiremens and Projec_Velociy curves. The projec has compleed during 1 h ieraion afer planned duraion during 9 h ieraion. Team_Srengh(sorypoins/ieraion) Team_Srengh Acual Remaining_Requiremens(sory poins) Remaining_Requiremens Acual -2 Time(ieraion) This plo is generaed by Ch Suden Ediion 1 Time(ieraion) This plo is generaed by Ch Suden Ediion Fig. 3 Represenaion of Tradiional Projec Saus Table 1 shows he planned and acual projec saus by showing Remaining_Requiremens, Effor_Remaining, Team_ Srengh, and Projec_Velociy a each ieraion. E-ISSN: Issue 11, Volume 1, November 213

8 Ierai -on# Projec Execuion(Tradiional Projec) Remaining_ Requiremens (sory poins) Effor_Remai -ning (person ieraion) Team_Sr -engh (sory poins/ier aion) Projec_Ve -lociy (sory poins/iera ion) Acual Projec Execuion(Tradiional Projec) Table 1 Represenaion of and Acual Tradiional Projec Saus 7.2 Hybrid Sofware Projec Tracking Fig. 4 shows he deviaion for Remaining _Requiremens and Team_Capabiliy individually and cumulaively. Deviaion in Team_Capabiliy(sory poins) Fig. 4 Deviaion for Remaining_Requiremens and Team_Capabiliy for Hybrid Projec Fig. 5 shows he projec saus wih Effor _Remaining, Team_Srengh, Remaining _ Requiremens and Projec_Velociy curves. The projec has compleed during 8 h ieraion before planned duraion during 1 h ieraion. Remaining_Requiremens(sory poins) Time(ieraion) This plo is generaed by Ch Suden Ediion Deviaion in Team_Capabiliy Remaining_Requiremens Individual-Deviaion Cumulaive-Deviaion Acual -2 Time(ieraion) This plo is generaed by Ch Suden Ediion Deviaion in Remaining_Requiremens(sory poins) Deviaion in Remaining_Requiremens Individual-Deviaion Cumulaive-Deviaion Time(ieraion) This plo is generaed by Ch Suden Ediion Projec_Velociy(sorypoins/ieraion) Projec_Velociy Acual Time(ieraion) This plo is generaed by Ch Suden Ediion E-ISSN: Issue 11, Volume 1, November 213

9 Effor_Remaining(person-ieraion) Team_Srengh(sorypoins/ieraion) Fig. 5 Represenaion of Hybrid Projec Saus Table 2 shows he planned and acual projec saus by showing Remaining_Requiremens, Effor_ Remaining, Team_Srengh, and Projec_Velociy a each ieraion. Noe ha, during he las ieraion, Remaining_Requiremens and Effor_Remaining are negaive. As RR ( 1) P ( 1) RR u 1 1 (26) Depending on RR, P, and ϵ u+1 ; RR +1 becomes negaive. Effor _ Remaining Remaining_ Requiremens (27) -5 Time(ieraion) This plo is generaed by Ch Suden Ediion Effor_Remaining Team_Srengh Acual Acual Time(ieraion) This plo is generaed by Ch Suden Ediion Effor_Remaining as well become negaive. Tha means projec acually compleed somewhere during he las ieraion. Ier ai on # Projec Execuion (Hybrid Projec) Effor_Rem Team_Sr aining engh (person (sory ieraion) poins/ier Remaining _Requirem ens (sory poins) Projec_Veloci y (sory poins/ieraion) aion) Acual Projec Execuion (Hybrid Projec) Ier ai on # Remaining _Requirem ens (sory poins) Effor_Rem aining (person ieraion) Team_Sr engh (sory poins/ier aion) Projec_Veloci y (sory poins/ieraion) Table 2 Represenaion of and Acual Hybrid Projec Saus Remarks: Wih simulaion resuls for radiional/hybrid projec racking following observaions are o be noed- The Projec_Velociy is varying for hybrid projec due o requiremens volailiy phenomena, while uniform for radiional projec in plan-space. Remaining_Requiremens decreases wih ieraion. Team-srengh is uniform in plan-space and varying in execuion-space. The projec is compleed before or afer he planned duraion as Team_Srengh in execuion- space, on an average, is more or less han plan- space. E-ISSN: Issue 11, Volume 1, November 213

10 8 Conclusion Tradiional/Hybrid sofware projec racking echnique has been developed wih sae-space approach o rack sofware projec in plan-space and execuion-space. This consiss of projec sae ransiion equaion and projec measuremen equaion. The projec measuremen equaion is used o derive projec saus as a funcion of he projec sae. The projec sae is derived wih projec sae ransiion equaion. The radiional/hybrid sofware projec racking echnique is shown o be able o represen he saus of sofware projec in plan-space and execuion-space a macro-level, i.e., he projec saus is checked a he end of each ieraion by measuring he effor needed o complee he projec, remaining requiremens o complee he projec, eam srengh represening he eam velociy and he projec progress wih projec velociy. The projecsae is described wih sae-variables as requiremens seleced o be compleed during an ieraion, and remaining requiremens o be compleed for projec compleion respecively. The effec of uncerainy on projec saus, and he projec ends during he las ieraion, has shown wih simulaion. The onological uncerainy has been modelled wih a Normal- Disribuion by using an approximaion mehod. The onological uncerainy has shown graphically wih ieraion, individually and cumulaively during projec execuion. References: [1] Roger Akinson, Lynn Crawford, and Sephen Ward, Fundamenal Uncerainies in Projecs and The Scope of Projec Managemen, Inernaional Journal of Projec Managemen,Volume 24, Issue 8, November 26, pp [2] Ahmed Al-Emran, Punee Kapur, Diemar Pfahl, Guenher Ruhe, Sudying he Impac of Uncerainy in Operaional Release Planning An Inegraed Mehod and Is Iniial Evaluaion, Informaion and Sofware Technology, Vol.52, 21, pp [3] Nozer D. Singpurwalla, Simon P. Wilson, Saisical Mehods in Sofware Engineering Reliabiliy and Risk, Springer Series in Saisics, May [4] T. Dyba, Improvisaion in Small Sofware Organizaions, IEEE Sofware, Vol. 17, No. 5, 2, pp [5] S. Nerur, R. Mahapara, G. Mangalaraj, Challenges of Migraing o Agile Mehodologies, Communicaions of he ACM, May 25, pp [6] B. Boehm, Ge ready for Agile Mehods, wih care, IEEE Compuer, Vol. 35, No.1, 22, pp [7] Boehm, B. and Turner, R., Balancing Agiliy and Discipline: A Guide for he Perplexed, Addison-Wesley, Boson, MA, 24. [8] Barry W. Boehm, Sofware Engineering Economics, IEEE Transacions on Sofware Engineering, Volume SE-1, Number 1, January1984,pp [9] Lung Chun Liu, Ellis Horowiz, A Formal Model for Sofware Projec Managemen, IEEE Transacions on Sofware Engineering, Vol.. No. 1, Ocober 1989, pp [1] Olga Perminova, Magnus Gusafsson,and Kim Wiksröm, Defining Uncerainy in Projecs A New Perspecive, Iinernaional Journal of Projec Managemen,Vol.26, Issue 1, January 28, pp [11] Anders Soderholm, Projec Managemen of Unexpeced Evens, Inernaional Journal of Projec Managemen, Volume 26, Issue 1, January 28, pp [12] E. Kusch, M. Hall, Inervening Condiions on he Managemen of Projec Risk: Dealing wih Uncerainy in Informaion Technology Projecs, Inernaional Journal of Projec Managemen, Volume 23, Issue 8, November 25, pp [13] Saisical Sofware Engineering, Panel on Saisical Mehods in Sofware Engineering, Naional Research Council, Naional Academy Press, Washingon, D.C [14] Walker Royce, Successful Sofware Managemen Syle: Seering and Balnce, IEEE Sofware Published by he IEEE Compuer Sociey, Sepember/ Ocober 25, pp [] Lee G., Muraa T., A β -Disribued Sochasic Peri Ne Model for Sofware Developmen Time/Cos Managemen, Journal of Sysems and Sofware, Vol. 26, 1994,pp [16] Marius Verici, Sofware Projec Duraion Esimaion Using Merix Model, Revisa Informaica Economicănr.3 (47)/28, pp [17] Masaeru Tsunoda, Tomoko Masumura, and Ken-Ichi Masumoo, Modeling Sofware Projec Monioring wih Sakeholders, 9 h IEEE/ACIS Inernaional Conference on Compuer and Informaion Science, 21, pp [18] Dimirios Seas, Samaia Bibi, Panagiois Sfesos, Ioannis Samelos, Vassilis Gerogiannis, Using Bayesian Belief Neworks o Model Sofware Projec Managemen Anipaerns, E-ISSN: Issue 11, Volume 1, November 213

11 Dep. of Informaics, Arisole Universiy of Thessaloniki, Thessaloniki, Greece. [19] Bob Hughes, Mike Coerell, Rajib Mall, Sofware Projec Managemen, Taa McGraw Hill Educaion Privae limied, New Delhi, 5h Ediion, 211. [2] Gabrial A. Barraza, W. Adward Back, and Fernando Maa, Probabilisic Monioring of Projec Performance using SS- Curves, Journal of Consrucion Engineering and Managemen, ASCE, March/April 2, pp [21] Roland S. Burns, Advanced Conrol Engineering, Buerworh-Heinemann, 1 s Ediion, 21, pp [22] Greg Welch, and Gary Bishop, An Inroducion o he Kalman Filer, SIGGRAPH 21, Los Angeles, CA, Augus 12-17, 21, pp.-16. [23] Mike Cohn, Agile Esimaing and Planning, Pearson, Third Impression 212, pp [24] D.J.C. Mackay, Inroducion o Mone Carlo Mehods, Deparmen of Physics, Cambridge Universiy, Cavendish Laboraory, Madingley Road, Cambridge, CB3HE, Unied Kingdom. [25] B. Brehmer, Dynamic Decision Making: The Conrol of Complex Sysems, Aca Psychol., Vol. 81, pp , [26] Peer S. Maybeck, Sochasic Models, Esimaion, and Conrol, Volume 1, Academic Press, Inc.(London) Ld,pp.1-3. [27] Seiner, I.D., Models for inferring Relaionships beween Group size and Poenial Group Produciviy, Behavioral Science, 1966, pp [28] Claudia de O. Melo, Daniela S. Cruzes, Fabio Kon, and, Reidar Conradi, Inerpreaive Case Sudies on Agile Team Produciviy and Managemen, Informaion and Sofware Technology, Vol.55, 213,pp [29] B Lakhanpal, Undersanding he Facors influencing he Performance of Sofware Developmen Groups: An Exploraory Group- Level Analysis, Informaion and Sofware Technology, Volume 35, Issue 8, Augus 1993, pp [3] D. Rodriguez, M.A. Sicilia, E. Garcíaa, and R. Harrison, Empirical Findings on Team Size and Produciviy in Sofware Developmen, The Journal of Sysems and Sofware,Vol. 85,March 212,pp [31] Chrisof Ebar, Jozef De Man, Requiremens Uncerainy: Influencing Facors and Concree Improvemens, ICSE, 5, S. Louis, Missouri,USA, May -21,25, pp [32] D. Pfahl, and K. Lebsanf Using Simulaion o Analyse he Impac of Sofware Requiremen Volailiy on Projec Performance, Informaion and Sofware Technology, Vol. 42, 2, pp [33] Tony Moynihan, Coping wih Requiremens- Uncerainy, : The Theories-of-Acion of Experienced IS/Sofware Projec Managers, The Journal of Sysems and Sofware, Vol. 53,Augus 2,pp [34] Susan Ferreira, James Collofello, Dan Shunk, and Gerald Mackulak, Undersanding he Effecs of Requiremens Volailiy in Sofware Engineering by using Analyical Modeling and Sofware Process Simulaion, The Journal of Sysems and Sofware,Vol. 82,Ocober 29,pp [35] kim Bang Salling, Risk Analysis and Mone Carlo Simulaion wihin Transpor Appraisal, Cenre for Traffic and Transpor, CTT-DTU, Build. 1, Technical Universiy of Denmark DK- 28 Lyngby, Denmark, pp.3-5. [36] Marin Hilber, Toward a Synhesis of Cogniive Biases: How Noisy Informaion Processing can bias Human Decision Making, Psychological Bullein, Vol.138, Issue 2, March 212, pp [37] Geoffrey Gordon, Sysem Simulaion, Second Ediion, Pearson -Prenice Hall, pp.4-41, 8. E-ISSN: Issue 11, Volume 1, November 213