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# The Little's laws simulation (Essay Sample)

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The Little’s laws simulation
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The little Law’s simulation
Several observations were made when running this simulation. When the simulation begins, the number of people in the room is at zero. If The CV of arrival rate and time of stay is held at zero, the number of the people in the room (I) slowly builds to, time of stay (T) multiplied by the rate of arrival (R) (I=TR). However, the average number of people in the room starts at a zero and builds up at a declining rate, and in the long run gets to the optimum of TR. This happens because at the onset there are no people in the room, thus the system is not stable, however, the system gets to stability in the long run and the average levels at I=TR, see fig 1. This situation is true for all rates of arrival, holding constant CV of rate of arrival and time of stay. The average RT at maximum of expected RT then drops to a minimum because although the arrival rate is constant, the average stay time starts at a minimum when the first person exit. This is because the simulation takes the cumulative total time spent in the room by all persons in the entire simulation and divides this with the expected I to get average T. This gives a minimum at the onset of the simulation as no person has been in the room. Average RT then increases at a constantly reducing rate to level at the expected RT in the long run, see figure 1. This situation is true for all time of stay holding arrival and time of stay CV constant.
Holding all other factors constant, a change in the arrival rate CV, for example from 0 to 1, changes the trend of the average I from rising at a constant reducing rate to rising at an inconstant rate before levelling out at a maximum of TR, see figure 2. The uneven rate of arrival into the room leads to uneven number in the room, thus distorting the constantly reducing rate of rising. Holding all other factors constant, a change in the time of stay CV changes the buildup rate of average RT from even to uneven, see figure 3. This results from the uneven average time spent in the room as some people spends more and others relatively less time in the room. In the long run, however, this levels out at max RT. A change in both arrival and time of stay CV, holding the means constant, results to changes in trends as discussed above. However, it is also noted that the two averages do not just build to a maximum of RT, but at times, the averages exceed RT before levelling off to RT ...
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