I am getting the error: "Unrecognized function or variable $\text{'}$p$0\_$denom'.

Error in MMCQ $($line $905)$

p$0=1/$ p$0\_$denom please help me to correct the error and make all the tests passed. $\%\%$ Run this test case to check your code

$\%$ Parameters

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

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

mu $=0\mathrm{.}1$; $\%\%$ The service time should be $1/10$ minutes$($work units$/$time$),10$ minutes per customers. $($it is service time, so the unit should be a time unit$).$

Nwait $=15$;

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

rho $=$ lambda $/$ mu;

$\%$ Call the MMCQ function with the given parameters

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

$\%$ Define a relative error function

$\%$ Validation checks are performed for four key metrics:

$\%$ Ws is compared to p$\_$state$(1)$ with a tolerance of $0\mathrm{.}5\%.$

$\%$ Wq is compared to p$\_$state$(2)$ with the same tolerance.

$\%$ c$\_$util is compared to a predefined value $(0\mathrm{.}4986)$ with a tolerance of $0\mathrm{.}5\%.$

$\%$ p$\_$drop is compared to a predefined value $(0\mathrm{.}00272)$ with a tolerance of $0\mathrm{.}5\%.$

rel$\_$error $=$ @$($x$,$ y$)$ abs$($x $-$ y$)/$ y; $\%$ rel$\_$error calculates relative errors between values $($used for comparisons$).$

$\%$ Validate the results and print "PASS" or "FAIL" for each metric

if rel$\_$error$($Ws$,2\mathrm{.}1557)<0\mathrm{.}005$; $\%$ Ws is compared with p$\_$state$(1).$

fprintf$(\text{'}$Ws $=\%6\mathrm{.}3$f PASS

$\text{'},$ Ws$)$;

else

fprintf$(\text{'}$Ws $=\%6\mathrm{.}3$f FAIL

$\text{'},$ Ws$)$;

end

if rel$\_$error$($Wq$,0\mathrm{.}1557)<0\mathrm{.}005$; $\%$ Wq is compared with $0\mathrm{.}1557.$

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

$\text{'},$ Wq$)$;

else

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

$\text{'},$ Wq$)$;

end

if rel$\_$error$($c$\_$util, $0\mathrm{.}4986)<0\mathrm{.}005$; $\%$ c$\_$util is compared with $0\mathrm{.}4986.$

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

$\text{'},$ c$\_$util$)$;

else

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

$\text{'},$ c$\_$util$)$;

end

if rel$\_$error$($p$\_$drop, $0\mathrm{.}00272)<0\mathrm{.}005$;$\%$ p$\_$drop is compared with $0\mathrm{.}00272.$

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

$\text{'},$ p$\_$drop$)$;

else

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

$\text{'},$ p$\_$drop$)$;

end

fprintf$(\text{'}$p$\_$state: $\%$s

$\text{'},$ p$\_$state$)$;

fprintf$(\text{'}$sum$($p$\_$state$)$: $\%$f

$\text{'},$ sum$($p$\_$state$))$;

fprintf$(\text{'}$p$\_$drop: $\%$s

$\text{'},$ p$\_$drop$)$;

$\%$ Extra Tests:

p$\_$state $\%$ p$\_$state should have $10$ probabilities

sum$($p$\_$state$)\%$ p$\_$state Should be $1$

disp$([\text{'}$The probability of being in state $\text{'},\text{'}$ is $\text{'},$ num$2$str$($p$\_$state$)])$;

$\%$ Check that the probabilities sum to $1$

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

disp$(\text{'}$The probabilities sum to $1.$ Test PASSED.$\text{'})$;

else

disp$(\text{'}$The probabilities do not sum to $1.$ Test FAILED.$\text{'})$;

endfunction $[$Ws$,$ Wq$,$ p$\_$drop, p$\_$state, c$\_$util$]=$ MMCQ$($x$,$ mu$,$ c$,$ Nwait$)$

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

$\%$ rho $=$ lambda$/$mu;

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 $/($factorial$($Nwait$)*(1-$ rho$))))$;

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

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

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

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

lambda$\_$loss $=$ lambda $*$ pN;

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

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

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

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

p$\_$drop $=$ pN $/(1+$ pN$)$;

$\%$ 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$0$;

end

end

$\%$ Calculate Ws and Wq

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

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

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

$\%$ Calculate the utilization factor

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

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

end