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#### SE3250 Capability Engineering Homework 3 1) (5 points) Below is an adoption model of a new software capability, where the simulation time is measured in months

###### Computer Science

SE3250 Capability Engineering Homework 3

1) (5 points) Below is an adoption model of a new software capability, where the simulation time is measured in months.

Equations adoption constant = 1.3 software adoption rate = adoption constant * software users (a) Fill in the blank: The model above is an example of feedback. (b) The software users level starts with a small initial base and reaches 1000 at 3 months. Manually calculate the value of software users at 4 months showing all your calculations. Approximate the value with Euler’s method of integration by 1) computing using one time increment of 1 month (DT = 1), and then 2) use two time increments of .5 months each (DT = .5). Is either a more accurate approximation and why?

2. (10 points) A model of the base-wide adoption of a new app for military and civilian personnel is shown below. Due to its high utility, the app is expected to be adopted by nearly nearly everyone topping off at 35,000. A small number of initial adopters (2000) were the beta testers. Its adoption rate is controlled by the word-of-mouth effect, whereby current users influence some of their colleagues to adopt. Initially the number of users multiply this way. As the users increase however, there are less available people to be influenced as a fraction of people’s contacts. It becomes more difficult to meet someone who isn’t already a user. See the model and equations below. What kind of dynamics behavior(s) do you expect for the number of users and why? Would your answer be different if only the word-of-mouth effect was modeled (bottom portion) without the population availability effects (top portion)? Which alternative behavior and why? Simulate the users over at least a 10 month time period. You may use a time interval (DT) of 1 month (or less) for your computations. Does the output resemble your expected reference behavior? You may plot it on the provided grid.

Equations app users (initial value) = 2000 user adoption rate = app users * word of mouth effect * fraction of non-users word of mouth effect = 0.8 total population = 35000 people not using = total population - app users fraction of non-users = people not using / total population

3. (15 points) You are working on a capability engineering project for the Army evaluating battle effectiveness options. You have agreed to begin by developing a simple continuous battle simulation based on Lanchester’s Law for aimed fire. It assumes two opposing forces are firing continuously at each other. The attrition of each side is proportional to the opposing side troop level and it’s lethality of firing according to:

Where x and y are the troop levels of opposing sides, α and β are their respective lethality coefficients. The model assumes attrition to each side is proportional to the number of units remaining on the other, and there are no reinforcements. Each unit has a fixed rate of fire, with each shot having a certain probability of eliminating the opposing unit at which it is aimed. Develop a continuous battle simulation model. The program shall have parameter inputs for the troop starting levels, x0 and y0, and the lethality coefficients α and β. The inputs can be manually set for each run, varied across runs in the model, elicited from an interactive user, or file input. It shall output a time history of the remaining troops for each side. This will require a numerical integration of the differential equations over time. Output graphics of individual runs is highly desirable but not required. An example test case with expected results for x0 = 1000, y0 = 800, α = .8, and β = .9 is shown in Figure 1. Supplementary information can be found in Alan Washburn, Lanchester Systems, 2000 (see Sakai Resources – References and Supplements). This test example is described in section 2.2 on p. 7.

The Army stakeholders are also interested in extensions to the model for probabilistic inputs, force reinforcement policies, technology options, Monte-Carlo analysis with multiple runs, output analysis, and potentially more. Consider these for future iterations of your model. Show your model diagram and simulation outputs as evidence of successful execution. If you have no visual model then briefly describe the model structure. Submit any model files, programs written or output files generated.