Breaking into a facility simulation

Finding optimum condition to breaking in

Suppose there is a facility and we have to simulate the time and energy to break into it — in reaching a target in the core of the facility. To simplify the system 2-d space is represented in rectangular grid, where time required and energy spent to pass a cell are assumed through some coefficients.

Compared to previous works (Suheri et al., 2019; Viridi & Haryanto, 2019) what is presented here can be considered as a static case of agent-based model using 2-d grid system.

Rules

A cell in rectangular form might represent different type of physical features as follow.

In the last column of the table there are Coeff which are coefficients of proportional between required time to pass a cell and energy spent to do the activity by an agent.

From start point to end point

Let’s make a simple activity from start point to end point, where there are some empty space between the two points as illustrated below.

Agent start the activity from green cell with value 2, through white cells with value 1, and ends it on blue cell with value 3. Numbers are showing the time required to pass the cells. For this activity total time are simple sum of all displayed numbers, which give 2 + 19 · 1 + 3 = 24.

And for the energy spent during the activity is obtained using Coeff in given table, which give 2 · 2 + 2 · (19 · 1) + 2 · 3 = 48, where all 2s in the beginning of each term are the Coeff. It is not a good example since start point, empty space, and end point have the same value for their Coeff.

Through some walls

Next example is when there are some walls to go through. In order to focus only on going through the walls, the path is chosen to be simply straight.

Total time from start point to end point is 2 + 4 · 1 + 30 + 4 · 1 + 10 + 4 · 1 + 3 = 59, where the first wall contribute 20 for total time, while the second wall contribute 10 for total time. And for energy spent during this activity is 2 · 2 + 2 · (4 · 1) + 6 · 30 + 2 · (4 · 1) + 4 · 10 + 2 · (4 · 1) + 2 · 3 = 254.

Other types

Other possible activities are combination of two previous mentioned activities, where there of them are already given in the beginning of this story.

What about the facility to be broken in?

Well, if you ask which one is the facility, then you are paying attention to what this story is telling. It should be the end point that represents target inside the facility, where start point is located outside the facility. The walls are multi-layered security walls protecting the facility.

Challenges

Notice the first figure with three sub-figures given in the beginning of this story.

• Understand how to obtain the value of total time required and energy spent for the three activities, then explain them a little bit.
• Create at least eight activity from 8 different start point outside the outermost wall targeting end point inside the innermost wall, through various trajectory, which can go through walls or gates / doors.
• Draw the path for all activities with numbers representing time to pass every cell along the path. Show one figure only for one activity.
• Create a graph energy vs time from all eight activities, and find optimum point from previous graph.
• Analyze the results and design a safeguard, e.g. where to put security camera to prevent the intruder.

The spreadsheet file of the figures is available on an issue. And you can also submit you answer of the challenge there.