I am still getting error message and we could not make the MMCQ Validation tests passed with the optimal values for lambda and mu for the trade studies results. $\%$ 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 cfunction $[$Ws$,$ Wq$,$ c$\_$util, p$\_$drop, p$\_$state$]=$ MMCQ$($lambda$,$ mu$,$ c$,$ Nwait$)$

$\%$ INPUTS:

$\%$ lambda $=$ arrival rate

$\%$ mu $=$ service rate

$\%$ Nwait $=$ Number of queue elements, not including servers

$\%$ c $=$ Number of servers

$\%$ OUTPUTS:

$\%$ Ws $=$ Average wait in the system

$\%$ Wq $=$ Average wait in the queue

$\%$ c$\_$util $=$ Average percentage of servers busy

$\%$ p$\_$drop $=$ probability the queue is full

$\%$ p$\_$state $=$ probability of each state

$\%$ INSERT YOUR CODE HERE

$\%$ Calculate traffic intensity

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

$\%\%$ Compute the Erlang B formula to calculate the probability of blocking

$\%$ p$\_$block $=$ erlangb$($c$,$ rho$)$;

$\%$ Calculate the utilization factor

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

$\%$ Calculate the probability of blocking

p$\_$block $=$ erlangb$($c$,$ rho$)$;

$\%$ Display the result

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

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

p$0\_$denom $=$ p$0\_$denom $+(($c$*$rho$)^$c $/($factorial$($c$)*(1-$rho$)))*(1-($rho$^$Nwait $/(1-$ rho$)))$;

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

fprintf$(\text{'}$p$0$: $\%\mathrm{.}4$f

$\text{'},$ p$0)$;

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

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

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$0$;

end

end

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

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

p$\_$drop $=$ pN;

$\%$ Calculate c$\_$util $($utilization of the servers$)$

c$\_$util $=($rho$^$c $*$ p$0)/($factorial$($c$)*(1-$ rho$))*(1-$ rho$^($Nwait $-$ c $+1))$;

$\%$ Calculate Wq $($average waiting time in the queue$)$

Wq $=(($rho$^($c$+1))*$ p$0)/($factorial$($c$)*(1-$ rho$/$Nwait$)^2)$; $\%$ Average waiting time in the queue

$\%$ Print the result

fprintf$(\text{'}$Average waiting time in the queue $($Wq$)$: $\%\mathrm{.}2$f$\text{'},$ Wq$)$;

$\%$ Calculate Ws $($average time spent in the system$)$

Ws $=$ Wq $+(1/$ mu$)$;

$\%$ Print the results

fprintf$(\text{'}$p$0$: $\%\mathrm{.}4$f $\text{'},$ p$0)$; fprintf$(\text{'}$pN: $\%\mathrm{.}2$f$\text{'},$ p$0)$;

end