Wq $=($rho $^2)/($mu $*(1-$rho$))$;

rho $=$ lambda $/($mu$)$;

Lq $=$ lambda $*$ Wq;

Ws $=$ Wq $+1/$mu; $\%$ Average time in System

Ls $=$ Ws $*$ lambda;

plot$(1$:$21,$ Wq$)\%$ Probability that arrival must wait against thd number of servers

xlabel$(\text{'}$Number of Servers $($c$)\text{'})$

ylabel$(\text{'}$Average hold Lines$($Wq$)\text{'})$

xlim$([1\mathrm{.}522\mathrm{.}1])$

ylim$([-211\mathrm{.}87-209\mathrm{.}80])$ Assignment $(5$ pts$).$ Create a plot of the probability of dropping a customer vs$.$ the number of call hold lines. The number of call hold lines should range from $1$ to $20.$ Set the number of customer service agents to the smallest value that meets requirements, see above. Assignment $(5$ pts$).$ What is the smallest number of hold lines that meet the system requirements? Using the fprintf command to display your results. Assignment $(5$ pts$).$ Characterize the interplay of hold lines and customer service agents by computing a contour plot of customer wait time in the queue and overlay a contour plot of probability of drop. Make the contour lines more readable by multiplying the drop probabilities by $100.$ Hint: Look at the example code in the MATLAB contour function documentation. Assignment $(5$ pts$).$ Use the contour plot above to refine your design point for the number of customer service agents $($c$\_$design$)$ and the number of hold lines $($N$\_$hold$\_$design$).$ Report c$\_$design and N$\_$hold$\_$design below using the fprintf command. Hint: The contours pointing upward $($left$-$to$-$right$)$ correspond to the probability of being dropped. Conversely, the contour lines pointing downward are the probability of drop. Assignment $(5$ pts$).$ Use the MMCQ function you created to compute the expected performance for your system. Report the average wait time, average time in the queue, the probability of a dropped call, and the average agent utilization. Make sure each result is labeled with the correct Assignment $(5$ pts$).$ Create a bar chart of the state probabilities. Multiply the state probabilities by $100$ to make the result easier to read. Make sure to properly label the states and the axis on the graph. Hint: Lookup the bar command in the MATLAB documentation.