91影视

Average number of customers waiting in the system, ${\mathrm{L}}_{\mathrm{s}}=鈥�\frac{\mathrm{位}}{\mathrm{渭}-\mathrm{位}}$

$位$= Rate of customers' arrival

$渭$= Service Rate

Now, putting these values in the following results

$\begin{array}{l}{L}_s=鈥�\frac{6}{10-6}\\ 鈥�鈥�鈥�鈥�鈥�鈥�=1.5\end{array}$

Hence, the average number of customers in the camera department is 1.5.

Now, calculate the average time spent by a customer in the camera department, with the help of the given formula;

Here,

Average time spent by a customer in the camera department

${\mathrm{W}}_{\mathrm{s}}鈥�=鈥�\frac{{\mathrm{L}}_{\mathrm{s}}}{\mathrm{位}}$

${\mathrm{L}}_{\mathrm{s}}$= the average number of customers waiting in line

$位$= Rate of customers' arrival

Now, putting the values in equation (2), obtain the following results:

role="math" localid="1650533370151" $\begin{array}{l}{\mathrm{W}}_{\mathrm{s}}=鈥�\frac{15}{6}\\ =0.25鈥�鈥�\mathrm{hour}鈥�\mathrm{or}鈥�15鈥�鈥�\mathrm{minutes}\end{array}$

Hence, the average time spent by a customer in the camera department is 15 minutes

Average time utilization Where,$\left(\mathrm{蚁}\right)=\frac{\mathrm{位}}{\mathrm{渭}}$

$蚁$= Average time utilization

$渭$= Service Rate

$位$= Rate of customers' arrival

Now, putting these values in the following results:

$\begin{array}{l}蚁=\frac{6}{10}\\ 鈥�鈥�鈥�鈥�鈥�=鈥�0.6鈥�鈥�\mathrm{or}鈥�鈥�60\%\\ 鈥�\end{array}$

Hence, the average time utilization of the clerk is 60%.

P = 1- (Probability that less than 2 people are in the camera department )

$=1-\left(P_0+鈥�P_1+P_2\right)$

${\mathrm{P}}_{\mathrm{n}}=\left(1-\frac{\mathrm{位}}{\mathrm{渭}}\right){\left(\frac{\mathrm{位}}{\mathrm{渭}}\right)}^{\mathrm{n}}$

Therefore;

$\begin{array}{l}{\mathrm{P}}_0=鈥�\left(1-\frac{6}{10}\right)鈥�脳{\frac{6}{10}}^0\\ 鈥�鈥�鈥�鈥�=0.4脳0.1\\ 鈥�鈥�鈥�鈥�=鈥�鈥�鈥�0.4\end{array}$

$\begin{array}{l}{\mathrm{P}}_1=鈥�\left(1-\frac{6}{10}\right)鈥�脳{\frac{6}{10}}^1\\ 鈥�鈥�鈥�鈥�=0.4脳0.6\\ 鈥�鈥�鈥�鈥�=鈥�鈥�鈥�0.24\end{array}$

$\begin{array}{l}{\mathrm{P}}_2=鈥�\left(1-\frac{6}{10}\right)鈥�脳{\frac{6}{10}}^2\\ 鈥�鈥�鈥�鈥�=0.4脳0.36\\ 鈥�鈥�鈥�鈥�=鈥�鈥�鈥�0.144\end{array}$

Now, putting these values in the following results

role="math" localid="1650533896293" $\begin{array}{l}\mathrm{P}\left(\mathrm{more}鈥�\mathrm{than}鈥�2鈥�\mathrm{customer}\right)鈥�\\ =1-\left(0.4+0.24+0.144\right)\\ 鈥�=0.216\end{array}$

Hence, the probability that more than 2 people are in the camera department is

0.216 or 21.6%

Number of clerks (S) = 2

Time utilization$蚁$= 0.6

Determine the value of${\mathrm{L}}_{\mathrm{q}}$the expected number of customers Waiting in the Line corresponding to S = 2 and$蚁$= 0.6.

The value of = 0.0593 Now, calculate the average number of customers in the department with the help of the given formula:

${\mathrm{L}}_{\mathrm{s}}={\mathrm{L}}_{\mathrm{q}}+\frac{\mathrm{位}}{\mathrm{渭}}$

${\mathrm{L}}_{\mathrm{q}}$= Expected number of customers spending time in the store

$渭$= Service Rate

$位$= Rate of customers' arrival

Calculate the average total time spent by a consumer in the camera department with the help of the given formula:

Average time spent by a customer in the camera department $\left(W_s\right)鈥�=鈥�\frac{L_s}{位}$

Putting these values in the following result

$\begin{array}{l}{\mathrm{W}}_{\mathrm{s}}鈥�=鈥�\frac{0.6593}{6}\\ 鈥�鈥�鈥�鈥�鈥�鈥�=鈥�0.1099鈥�\mathrm{hour}鈥�\mathrm{or}鈥�6.594鈥�\mathrm{minutes}\end{array}$

Hence, the average total time spent by a consumer in the camera department is

6.594 minutes.