MATH MODELING CLASS USING MATH LAB In the posed elevator problem, your assistant

Question

MATH MODELING CLASS USING MATH LAB

In the posed elevator problem, your assistant notified you that there are 60 workers operating on each of 5 floors atop the ground floor in your office building - 300 in total. The elevator occupancy is 10 people, and there are 3 elevators in total. In the worst-case scenario in terms of total transition time, on each elevator ride at least one person is getting off at each floor. Naturally, we can ask: what is the probability that an elevator with 10 passengers has none of the 5th floor workers? For that trip, it should reduce the elevator travel time by t45 + texit + t54 = 5 + 15 + 5 = 25sec. To see how often this might happen, we can perform random draws of elevator occupants, and average over a long time. This is a way to check the validity of certain modeling assumptions.

Part 1 Write a script which computes random draws for the 10 elevator occupants, and perform this 1000 times. Count the number of times a 5th floor occupant is present, and divide the that count by 1000. A basic structure for this may look like:

N=1000;

f o r . . . % loop ove r a l l N t r i e s

Elev= % g e n e r a t e v al u e s f o r Elev u si ng pseudorandom numbers

i f % put a c o n di ti o n on v al u e s to check f o r a 5 th f l o o r worker

% inc remen t co u n t e r

e l s e

% do no thing ( can l e a v e e l s e s ta temen t blank )

end

% do more t hi n g s i f n e c e s s a r y

end

% output count / N A very useful matlab command to look up would be "randi" or similarly "rand".

Explanation / Answer

%% MATH MODELING CLASS USING MATH LAB - PART1

% initial counter value

counter = 0;

% loop count

n=1000;

% Looping over n times

for k=1:n

% generating random numbers -- randi(numer of floors:300, rows:1, cols:number of occupants:10)

occupants = randi(300, 1, 10);

% calculating number of 5th floor occupants among 10 occupants

% mod(a, m) - function calculates the remainder value when divison happens

% between two numbers

% nnz(v) -- calculates number of ones in the logical array

numberOf5thFloorOccupants = nnz( mod(occupants, 5) == 0) ;

% incrementing the counter value

counter = counter + numberOf5thFloorOccupants;

end

% dividing counter value by number of loop iterations

output = counter / n;

% displaying output

disp(["output : ", output]);

Sample Output:

"output : " "2.027"

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