# Development Cycle Modeling: Resource Estimation
## 2 Proposed Model  
Figure 1 also illustrates an underlying model candidate: the Statistical Agent-based Model of Development and Evaluation (SAbMDE). SAbMDE joins with those [25] who accept development as an inherently human process and builds on a neuroscience foundation [26; 27; 28] of agent mind, body, and environment interaction. SAbMDE then uses process algebra ideas, such as [PERSON]'s [29; 30], to represent each development phase so that analytical techniques can be uniformly applied across the entire development cycle. [PERSON] has shown [31] that a desired end product (DEP) can be developed by sequentially composing intermediate products (IP) from sets of fundamental composable elements: processes and relations. SAbMDE introduces an agent who decides which elements to compose. A correct decision set produces a sequence of compositions that become an end product, hopefully, the DEP. SAbMDE recognizes (a) that each decision is one of a set of alternatives, (b) that the hierarchical super-set of alternatives forms a development space (DSpace), and (c) that the correct DEP decision  
Figure 1: Development modeling framework. set is the best of many development paths (DPaths) through DSpace. The model's foundation reflects itself in this representation via three inter-related sub-models: Agent, Development, and Evaluation. Model D houses the algorithms and structures that quantitatively define DSpace as well as the tools for DSpace navigation and traversal. Model E contains the testing and evaluation mechanism that informs the decisions that compel DSpace compositions. Model A emulates a development agent's perception, experience, vocabulary, and other human factors needed to create the Model E tests and to evaluate their results. Because each DSpace composition is connected by a decision to an evaluation of test results, there is an ESpace that mirrors DSpace. Because each ESpace test and/or evaluation maps to an agent's perception and vocabulary, there is an ASpace that mirrors ESpace. These spaces, generically XSpaces, have the same form and share a mathematical description. When executed together, Models A, D, and E represent a development cycle quantitatively and flexibly. This capability allows SAbMDE to hypothesize that DSpace characteristics constrain and guide an agent's decision-making in ways that conventional development cycle models can not. SAbMDE constructs DSpace from sets of composable elements: vocabulary items, V, and relations, R. For example, (1) and (2) are the basis of the simple DSpace fragment in Figure 2. Composable elements are supplied directly by an agent or extracted from documents by simple parsing or more sophisticated techniques such as those applied by [PERSON] and [PERSON] (2018). \[V =\{v_{0},v_{1},v_{2},v_{3}\} \tag{1}\] \[R =\{r_{0}\} \tag{2}\]  
The construction begins at composition index 0 (\(l=0\)) with an empty set. Construction continues by enumerating the composable elements at \(l=1\), and then by using the cross-product operator to compose all the combinations of composable elements for \(l>1\). As a result, at every DSpace node (DN Node) for \(l>1\), an agent decision-maker has exactly \(|V||R|\) options from which to choose. Note that at \(l=1\), only the vocabulary items are listed because composition is the same as vocabulary item selection at this composition index; relations have been enumerated but not applied. DSpace is characterized by the choice of composable elements, the numbers of types of composable elements, \(|V|\) and \(|R|\)), and the number of compositions, \(L\), required to produce the DEP. Figure 2: A simple development space (DSpace) excerpt with highlighted development paths (DPaths). A development agent navigates or traverses DSpace by deciding which DNode to compose next. Figure 2 shows a DPath. Note that the DPath is not a direct one. The decision to traverse to DNode e was a mistake that had to be corrected. An evaluation of DNodes f and k confirmed the error. Thus, the actual DPath is contorted.