The average number of arrivals during an average service period is also reflected in the relationship between customer arrival rate and customer service rate, x = a/h.
The percentage of time the customer server is busy can also be shown to be represented by this formula. Simply said, the arrival rate is the number of arrivals within a certain period of time (e.g., per hour, day etc.). The formula arrival rate = 1/inter-arrival time can be used to calculate it. What is the likelihood that a customer will stay in the bank longer than 15 minutes? P(X>15) = e –15λ = e –3/2 . service According to Little's Law, the average length of a line (L) is equal to the sum of the system's throughput times the amount of time people spend waiting in line (W) (Lambda). So, L is equal to Lambda*W.
We are aware that our relationship is sinusoidal, with minimal values at 9:00 am and 9:00 pm.
The maximum time, at 3:00 pm, is at t = 6 hours if we define 9:00 am as our t = 0.
the second minimum, service which occurs at 9:00 p.m., is at t = 12 hours.
The next step is to identify a trigonometric function that is minimum at time t = 0, which can be done as follows: customer
-Cos(c*t)
when t = 0
-cos(0) = - 1
there comes a purpose:
A*cos(c*t) = -C(t) + B
the constants A, c, and B.
Knowing that we have no clients at time t = 0 and a maximum of 875 customers at time t = 6h.
then: C(0) = 0 = -A + B
Consequently, A = B.
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