$(75$ points$)$ Using Excel, do a simulation by hand given the following information. We have system that has a single server and a single quaue $($M$/$M$/1),$ interarrival times are exponentially distributed with a mean of $5$ minutes, and service times are also exponentally distributed with a mean of $4$ minutes. The sample of the inter$-$arrival and service times are providad in the table below $($all times are in minutes$).$

$\backslash$table$[[,$Replication $1,$Replication $2,$Replication $3],[$Entity$,\backslash$table$[[$Inter Arrival$],[$Time$]],\backslash$table$[[$Procesaing$],[$Time$.]],\backslash$table$[[$Inter Arrival$],[$Time$]],\backslash$table$[[$Processing$],[$Time$]],\backslash$table$[[$Inter Arrival$],[$Time$]],\backslash$table$[[$Processing$],[$Time$]]],[1,1085,0\mathrm{.}74,8\mathrm{.}75,3\mathrm{.}05,1\mathrm{.}28,0\mathrm{.}50],[2,5\mathrm{.}67,1\mathrm{.}15,7\mathrm{.}53,1\mathrm{.}33,1\mathrm{.}39,1\mathrm{.}31],[3,4\mathrm{.}98,2\mathrm{.}31,1\mathrm{.}88,2\mathrm{.}32,1\mathrm{.}77,0\mathrm{.}41],[4,4\mathrm{.}57,1\mathrm{.}28,4\mathrm{.}52,4\mathrm{.}84,1\mathrm{.}31,4\mathrm{.}71],[5,2\mathrm{.}36,5\mathrm{.}89,3\mathrm{.}93,3\mathrm{.}64,5\mathrm{.}58,1\mathrm{.}01],[6,,4\mathrm{.}36,,1\mathrm{.}14,,2\mathrm{.}73]]$

For each replication, complate the simulation by hand, you may use any of the two methods shown in the lectures.

Additional details

Initially $($at time O$),$ the system is empty and idla.

Base units: Minutes

The simulation length is $30$ minutes.

For each replication, estimate the fol owing key performance indicators.

$(1)$ Total Production.

$(2)$ Average waiting time in queue.

$(3)$ Maximum waiting time in queue.

$(4)$ Average total time in wytem.

$(5)$ Maximum total time in system.

$(6)$ Time$-$average number of parts in queue.

$(7)$ Maximum number of parts in queue.

$(8)$ Server utilization