Question $1$: $(70$ pts$)$ Consider a queuing system with two parallel servers and a single waiting line: customers join a single line if both servers are busy. They are eventually serviced by the first free server. If a customer arrives while both servers are idle, $($s$)$he then prefers server $1,$ who happens to work faster. The interarrival times of the customers are known to be:

$\backslash$table$[[$Interarrival Time $($mins$),$Probability$],[5,0\mathrm{.}35],[10,0\mathrm{.}40],[15,0\mathrm{.}25]]$

The service time for the first server is Uniform $(15,20)$ minutes, and it is Uniform $(14,24)$ minutes for the second server.

$(45$ pts$)$ Prepare a formal "event$-$scheduling" simulation table, hand$-$simulate the system until the $4$th customer departs

$(25$ pts$)$ Report the following statistics:

i$)$ average number of customers in the system

ii$)$ average time spent in the queue

iii$)$ the average utilization of each server

IE $341$

Spring $2024$

Assignment # $2$

$\frac{2}{2}$

Assume that the first server is busy initially. When an arrival and a departure must be simultaneously scheduled, use the convention of scheduling the departure first.

Use the following sequence of random numbers: $0\mathrm{.}4970\mathrm{.}3800\mathrm{.}8620\mathrm{.}0200\mathrm{.}3910\mathrm{.}9750\mathrm{.}4800\mathrm{.}8610\mathrm{.}5630\mathrm{.}5430\mathrm{.}858,0\mathrm{.}537$dots