Using Excel, do a simulation by hand given the following information. We have

system that has a single server and a single queue $(M/$M$/1),$ interarrival times are exponentially

distributed with a mean of $5$ minutes, and service times are also exponentially distributed with a

mean of $4$ minutes. The sample of the inter$-$arrival and service times are provided in the table

below $($all times are in minutes$).$

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

the lectures.

Additional details

Initially $($at time $0),$ the system is empty and idle.

Base units: Minutes

The simulation length is $30$ minutes.

For each replication, estimate the following key performance indicators.

$(1)$ Total Production.

$(2)$ Average waiting time in queue.

$(3)$ Maximum waiting time in queue.

$(4)$ Average total time in the system.

$(5)$ Maximum total time in the system.

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

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

$(8)$ Server utilization