Question # $2$

Consider a bank containing $5$ Tellers who serve customers waiting in a single queue. Customers arrive at a rate determined by an exponential inter $-$ arrival time with a mean of $2$ minutes and all customers have a service time which is also exponentially distributed with a mean of $3\mathrm{.}5$ minutes. The bank opens its doors to customers at $9\mathrm{.}00$ a$.$m$.$ and closes its doors to new customers at $5\mathrm{.}00$ p$.$m$..$

Build the arena model for the problem.

Find the best number of replications to achieve a relative error of $0\mathrm{.}08$ at the $95\%$ confidence level $($no $=30$ replications$)$ for average total time in the system.

$\backslash$table$[[$No$.$ of Replication,$\stackrel{}{x}(n),$Half Width $(n,),\frac{(n,)}{(\stackrel{}{x})(n)},\frac{(n,)}{(\stackrel{}{x})(n)}0\mathrm{.}08$