Can you please help me to get the MMCQ Multiserver Finite queuing validation all pass for the call center $?$ here is the requirements:Key Performance Parameters

$1.$ The call center shall be able to handle on average at least $2$ calls per minute.

$2.$ The call center shall maintain a customer satisfaction score of greater than $5$

$3.$ A customer shall have no more than a $1\%$ chance of the hold lines being full.

$4.$ A customer shall have no more than a $1$ min average hold time.

$5.$ The call center shall have an availability greater than $0\mathrm{.}999$

$6.$ The call center shall average maintenance cost per call shall be less than $$\%$ Part $1$: Define parameters

c $=2$; $\%$ Number of servers

lambda $=2$; $\%$ Average Arrival Rate per minute

mu $=0\mathrm{.}1$; $\%$ Service rate

Nwait $=15$; $\%$ Number of waiting customers

$\%$ Part $2$: Call the MMCQ function and retrieve results

$[$Ws$,$ Wq$,$ c$\_$util, p$\_$drop, p$\_$state$]=$ MMCQ$(1,0\mathrm{.}5,4,5)$;

$\%$ Part $3$: Define a relative error function

rel$\_$error $=$ @$($x$,$ y$)$ abs$($x $-$ y$)/$ y;

$\%$ Part $4$: Validate and print results

fprintf$("$Ws: $\%6\mathrm{.}3$f

$",$ Ws$)$;

fprintf$("$Wq: $\%6\mathrm{.}3$f

$",$ Wq$)$;

fprintf$("$c$\_$util: $\%6\mathrm{.}3$f

$",$ c$\_$util$)$;

fprintf$("$p$\_$drop: $\%8\mathrm{.}5$f

$",$ p$\_$drop$)$;

fprintf$("$State Probabilities: $")$;

for i $=1$:Nwait $+1$

i$=0$:$1$:$10$;

fprintf$("$p$\_$state$(\%$d$)$: $\%$f$,",$ i$,$ p$\_$state$($i$))$;

end

fprintf$("$

$")$;

$\%$ Part $5$: Validate and print "PASS" or "FAIL" for each metric

if rel$\_$error$($Ws$,2\mathrm{.}1557)<0\mathrm{.}005$

fprintf$("$Ws $\%6\mathrm{.}3$f PASS

$",$ Ws$)$;

else

fprintf$("$Ws $\%6\mathrm{.}3$f FAIL

$",$ Ws$)$;

end

if rel$\_$error$($Wq$,0\mathrm{.}1557)<0\mathrm{.}005$

fprintf$("$Wq$=\%6\mathrm{.}3$f PASS

$",$ Wq$)$;

else

fprintf$("$Wq$=\%6\mathrm{.}3$f FAIL

$",$ Wq$)$;

end

if rel$\_$error$($cutil$,0\mathrm{.}4986)<0\mathrm{.}005$

fprintf$("$c$\_$util $\%6\mathrm{.}3$f PASS

$",$ cutil$)$;

else

fprintf$("$c$\_$util $\%6\mathrm{.}3$f FAIL

$",$ cutil$)$;

end

if rel$\_$error$($p$\_$drop, $0\mathrm{.}00272)<0\mathrm{.}005$

fprintf$("$p$\_$drop $=\%8\mathrm{.}5$f PASS

$",$ p$\_$drop$)$;

else

fprintf$("$p$\_$drop $=\%8\mathrm{.}5$f FAIL

$",$ p$\_$drop$)$;

end

$\%$ Part $6$: Corrected p$\_$state initialization

p$\_$state $=[-0\mathrm{.}010609,-0\mathrm{.}021217,-0\mathrm{.}021217,-0\mathrm{.}014145,-0\mathrm{.}0070725,-0\mathrm{.}05658,0\mathrm{.}0,0\mathrm{.}0,0\mathrm{.}0,0\mathrm{.}01]$;

$\%$ Part $7$: Check if the sum of probabilities is close to $1$

if abs$($sum$($p$\_$state$)-1)<1$e$-5$

disp$("$The probabilities sum to $1.$ Test PASSED."$)$;

else

disp$("$The probabilities do not sum to $1.$ Test FAILED."$)$;

end

$\%$ Part $8$: Assuming $10$ states

num$\_$states $=15$;

fprintf$("$The probability of being in state $\%$d is $\%$f$.$

$",$ Nwait, p$\_$state$($Nwait $+1))$;

disp$("$Extra Tests PASSED."$)$;function $[$Ws$,$ Wq$,$ c$\_$util, p$\_$drop, p$\_$state$]=$ MMCQ$($lambda$,$ mu$,$ c$,$ Nwait$)$

$\%$ Calculate the utilization factor

rho $=$ lambda $/$ mu;

$\%$ c$\_$bar $=$ rho $*(1+($c $*$ rho$)^($c $-1)/$ factorial$($c $-1)/(1-$ rho$)^2)$; $\%$ Fix c$\_$bar calculation

$\%$ Calculate p$0($probability of no customers in the system$)$

p$0\_$denom $=$ sum$(($c $*$ rho$).^(0$:$($c $-1))/$ factorial$(0$:$($c $-1)))+($c $*$ rho$)^$c $/$ factorial$($c$)/(1-$ rho$)$; $\%$ Fix p$0\_$denom calculation

p$0=1/$ p$0\_$denom;

p$\_$state $=$ zeros$(1,$ Nwait $+1)$;

p$\_$state$(1)=$ p$0$;

$\%$ Calculate pN $($probability of having N customers in the system$)$

for i $=1$:Nwait

if i $<=$ c

p$\_$state$($i $+1)=($rho$^$i $/$ factorial$($i$))*$ p$0$;

else

p$\_$state$($i $+1)=($rho$^$i $/$ factorial$($c$)*($c$^($i $-$ c$)))*$ p$0$; $\%$ Fix the p$\_$state calculation

end

end

$\%$ Calculate lambda$\_$loss and lambda$\_$eff

lambda$\_$loss $=$ lambda $*$ p$\_$state$($Nwait $+1)$;

lambda$\_$eff $=$ lambda $-$ lambda$\_$loss;

$\%$ Calculate Lq $($average number of customers in the queue$)$

Lq $=$ sum$((0$:Nwait$).*$ p$\_$state$)$;

$\%$ Calculate Ls $($average number of customers in the system$)$

Ls $=$ Lq $+$ lambda$\_$eff $/$ mu;

$\%$ Calculate the utilization

c$\_$bar $=$ Ls $-$ Lq;

c$\_$util $=$ c$\_$bar $/$ c;

$\%$ Calculate p$\_$drop $($probability of a customer being dropped$)$

p$\_$drop $=$ p$\_$state$($Nwait $+1)$;

$\%$ Calculate Ws and Wq

Ws $=$ Ls $/$ lambda$\_$eff;

Wq $=$ Lq $/$ lambda$\_$eff;

end