Wait Line Configuration $[100$ marks$]$

As part of designing a clinic's wait line, we have the option to set up either multiple singleserver queues $($similar to those found in grocery stores$)$ or a single multiple$-$server queue $($similar to those found in banks$)$ with both configurations having the same total arrival and service rates.

"Multiple Single$-$Server Queues"

"A Multiple$-$Server Queue"

For our clinic, we are considering two types of queue configurations as follows:

A$.$ Grocery store queue model: Design three single$-$server queues, where each server has arrival rate $()$ of $5,$ service rate $()$ of $6,$ and number of servers $($s$)$ of $1.$

B$.$ Bank queue model: Design a single three$-$server queue, where arrival rate $()$ is $15,$ service rate $()$ is $6,$ and number of servers $($s$)$ is $3.$

Task $1$: Use the Q$.$xis template to fill the table below $[50$ MARKS$]$:

$\backslash$table$[[\backslash$table$[[$Performance$],[$Measure$]],\backslash$table$[[$Three M$/$M$/1],[$Single$-$Server Queues$],[($Grocery Store$)]],\backslash$table$[[$One M$/$M$/3],[$Three$-$Server Queue $($Bank$)]]],[$Utilization$,,],[L_q,,],[W_q,,],[$W$,,]]$

Hint: for $L_q$ and $L$ of three $\frac{M}{M}\frac{?}{1}$ queue configuration, you need to multiply the result in $Q.x|s||$ by $3$ because there are three independent servers in total.

Task $2$: Discuss which queue configuration you prefer and why $[50$ MARKS$].$

$2$