Question $1$

Our generic call center system provides a central number in an organization that customers call for technical support, sales information, and order status. Incoming calls arrive with interarrival times being exponentially distributed with a mean of $0\mathrm{.}857$ minute. This central number feeds $26$ trunk lines. If all $26$ lines are in use, a caller gets a busy signal; and he just goes away. An answered caller hears a recording describing three options: transfer to technical support, sales information, or order$-$status inquiry $(76\%,16\%,$ and $8\%,$ respectively$).$ The estimated time for this activity is UNIF$(0\mathrm{.}1,0\mathrm{.}6)$; all times are in minutes.

If the caller chooses technical support, a second recording requests which of three product types the caller is using, which requires UNIF$(0\mathrm{.}1,0\mathrm{.}5)$ minutes. The percentage of requests for product types $1,2,$ and $3$ are $25\%,34\%,$ and $41\%,$ respectively. If a qualified technical support person is available for the selected product type, the call is automatically routed to that person. If none are currently available, the customer is placed in an electronic queue where he is subjected to annoying rock music until a support person is available. The time for all technical support calls is estimated to be TRIA$(3,6,18)$ minutes regardless of the product type. Upon completion of the call, the customer exits the system.

Sales calls are automatically routed to the sales staff. If a salesperson is not available, the caller is treated to soothing new$-$age space music $($after all, we$$re hoping for a sale$).$ Sales calls are estimated to be TRIA$(4,15,45)$sales people tend to talk a lot more than technical support people! Upon completion of the call, the happy customer exits the system. Callers requesting order$-$status information are automatically handled by the phone system, and there is no limit on the number the system can handle $($except that there are only $26$ trunk lines, which is itself a limit$,$ since an ongoing order$-$status call occupies one of these lines$).$ The estimated time for these transactions is TRIA$(2,3,4)$ minutes, with $15\%$ of these callers opting to speak to a real person after they have received their order status.

These calls are routed to the sales staff, where they wait with a lower priority than sales calls. This means that if an order$-$status call is in a queue waiting for a salesperson and a new arriving sales call enters, the sales call will be given priority over the order$-$status call and answered first. These follow$-$up order$-$status calls are estimated to last TRIA$(2,3,4)$ minutes. These callers then exit the system.

The call center hours are from $8$am until $6$pm $,$ with a small proportion of the staff on duty until $7$pm $.$ Although the system closes to new calls at $6$pm$,$ all calls that enter the system by that time are answered and served. Over the course of a day there are eight technical support employees to answer technical support calls. Two are devoted to product Type $1$ calls; three to product Type $2$ calls; and three to product Type $3$ calls. There are four sales employees to answer the sales calls and those order$-$status calls that opt to speak to a real person.

Draw a flowchart diagram for the processes described above.

Question $2$

a$.$ Briefly describe an endogenous system and give an example.

b$.$ State four situations where simulation is not appropriate.

c$.$ What are the components of a system?

Question $3$

a$.$ What are the four items evaluated to ascertain if simulation is the correct approach to solve a particular problem?

b$.$ Briefly explain the term $$simulation$.$

c$.$ What is an event?

d$.$ State five advantages of simulation.