[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82623-en":3,"doc-seo-82623-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82623,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","A Capacity-Aware Parr Model for Agile Projects","Classical software effort distribution models, including the Putnam–Norden–Rayleigh family and Parr’s alternative curve, were built to describe how development effort unfolds over time under an implied staffing pattern. Direct application to agile settings is constrained when team capacity is fixed, partially fixed, or externally limited. This work refactors Parr’s model into a capacity-aware forecasting layer combining normalized latent effort demand with a capacity trajectory to forecast progress, completion time, capacity deficit, and slack with few parameters.","A Capacity-Aware Parr Model for Agile Projects  \nPedro E. Colla  \nUADER-FCyT  \n[colla.pedro@uader.edu.ar](colla.pedro@uader.edu.ar)  \narXiv :2607 .0 1562v 1 [ cs . SE] 2 Jul 2026  \nAbstract—Classical software effort distribution models, including the Putnam–Norden–Rayleigh family and Parr’s alternative curve, were designed to describe the time distribution of development effort under an implied staffing pattern. Their direct use in agile environments is limited when team capacity is fixed, partially fixed, or externally constrained: the original curve may prescribe a staff demand that the organization cannot allocate. This paper proposes a compact refactoring of Parr’s model as a capacity-aware forecasting layer for agile projects. The contribution is deliberately narrower than a full causal theory of project dynamics. A normalized Parr-shaped latent effort demand is combined with an observed or planned capacity trajectory. The resulting model forecasts aggregate progress, completion time, capacity deficit, and capacity slack without assuming that the same internal activity path is followed under resource restriction. The model uses a small parameter set: total effort K, a Parr shape parameter α, an origin constant c that can match nonzero initial staffing, and the capacity trajectory C (t). A discrete sprint formulation is provided, together with a calibration method from ordinary Scrum records and a rollingorigin validation protocol against simple management baselines.  \nIndex Terms—Parr model, effort forecasting, agile project management, Scrum, staff restriction, capacity planning, effort estimation, rolling forecast.  \nI. INTRODUCTION  \nSoftware effort estimation has long combined two different questions that are often confused in practice: how much effort a project will require, and how that effort will be distributed over time. Parametric models such as COCOMO address the  \nfirst problem through cost drivers and size estimates [1], while effort distribution models such as the Putnam–Norden– Rayleigh model (PNR) describe aggregate staffing or effort profiles over the project life cycle [2] . Parr proposed an alternative to the Rayleigh curve by deriving a symmetric effort density from a logistic view of revealed and unrevealed work [3] . Subsequent analysis observed both the mathematical appeal of the curve and the difficulty of using it as a resource estimation instrument without careful calibration and empirical support [4] .  \nAgile delivery settings make the problem more visible. Scrum teams work in bounded sprints, inspect progress frequently, and select work based on past performance, upcoming capacity, and the ”definition of done” [5] . In such settings, staffing is often not the dependent variable predicted by a curve; rather, capacity is a managerial constraint. A stable team may be assigned to a project before the forecast is produced. A classical Parr curve may therefore prescribe more staff than the  \nR&D effort part of the project UADER-PI/B 230/24 .  \norganization can allocate, or less staff than the team already has available.  \nThis paper proposes a refactored and deliberately parsimonious model. The aim is not to build a complete causal theory of agile project dynamics. The aim is to make a Parr-shaped effort curve usable as an aggregate forecasting component when capacity is externally constrained. The proposed model treats the Parr curve as a latent demand of effort, not asa mandatory staffing policy. Observed or planned capacity controls how fast this latent demand can be consumed. The model therefore supports three management uses: initial duration forecast, sprint-by-sprint reforecast, and scenario analysis for capacity changes.  \nII. BACKGROUND AND POSITIONING  \nThe PNR model represents software effort through a Rayleigh-shaped profile and has been widely used in macrolevel software sizing and estimating [2] . Parr’s model replaces the Rayleigh assumption with a curve derived from a logistic relati","cbCaibrKm4bVzJUs","https://ap.wps.com/l/cbCaibrKm4bVzJUs","pdf",510735,1,10,"English","en",105,"# Abstract\n# Introduction\n# Background and Positioning\n## Agile Estimation Context","[{\"question\":\"Why are classical effort distribution models difficult to use directly in agile projects with capacity constraints?\",\"answer\":\"In agile environments, capacity is often a managerial constraint rather than a variable predicted by a curve. A classical Parr-style profile can imply a staffing level that the organization cannot allocate, or it can conflict with an already assigned team.\"},{\"question\":\"What does the proposed capacity-aware Parr model change in terms of modeling purpose?\",\"answer\":\"It treats the Parr-shaped curve as a latent effort demand that must be consumed according to an observed or planned capacity trajectory. The model focuses on aggregate forecasting rather than building a full causal theory of agile project dynamics.\"},{\"question\":\"What outputs can the model forecast and how is it parameterized?\",\"answer\":\"The model forecasts aggregate progress, completion time, capacity deficit, and capacity slack. It uses a compact parameter set including total effort K, a Parr shape parameter α, an origin constant c, and a capacity trajectory C(t).\"}]",1784181865,25,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"a-capacity-aware-parr-model-for-agile-projects","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/a-capacity-aware-parr-model-for-agile-projects/82623/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are classical effort distribution models difficult to use directly in agile projects with capacity constraints?","Question",{"text":75,"@type":76},"In agile environments, capacity is often a managerial constraint rather than a variable predicted by a curve. A classical Parr-style profile can imply a staffing level that the organization cannot allocate, or it can conflict with an already assigned team.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does the proposed capacity-aware Parr model change in terms of modeling purpose?",{"text":80,"@type":76},"It treats the Parr-shaped curve as a latent effort demand that must be consumed according to an observed or planned capacity trajectory. The model focuses on aggregate forecasting rather than building a full causal theory of agile project dynamics.",{"name":82,"@type":73,"acceptedAnswer":83},"What outputs can the model forecast and how is it parameterized?",{"text":84,"@type":76},"The model forecasts aggregate progress, completion time, capacity deficit, and capacity slack. It uses a compact parameter set including total effort K, a Parr shape parameter α, an origin constant c, and a capacity trajectory C(t).","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]