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 inter$-$arrival time of customers are known to be distributed Uniform$(5,15)$ minutes.

The service time for the first server is Uniform$(15,20)$ minutes, and for the second server it is given as:

Service Time $($mins$)$: $515253545$ Probablity: $0\mathrm{.}120\mathrm{.}350\mathrm{.}430\mathrm{.}060\mathrm{.}04$

$1.(50$ pts$)$ Prepare a simulation table and hand$-$simulate the system for one hour exactly. Assume that both servers are busy but the queue is empty initially.

IE $341$ Spring $2024$ Assignment # $12/2$

$2.(25$ pts$)$ Use the sequence of random numbers given below and estimate:

i$)$ Average number of customers in the system ii$)$ Average time spent in the queue

iii$)$ The average utilization of each server iv$)$ Probability of no waiting in the queue

$($Use the following sequence of random numbers: $0\mathrm{.}4970\mathrm{.}3800\mathrm{.}8620\mathrm{.}0200\mathrm{.}3910\mathrm{.}9750\mathrm{.}4800\mathrm{.}9050\mathrm{.}7590\mathrm{.}5600\mathrm{.}5930\mathrm{.}7440\mathrm{.}0690\mathrm{.}3700\mathrm{.}7900\mathrm{.}1760\mathrm{.}0200\mathrm{.}7140\mathrm{.}5390\mathrm{.}9280\mathrm{.}8600\mathrm{.}7170\mathrm{.}8610\mathrm{.}5630\mathrm{.}5430\mathrm{.}8580\mathrm{.}5370\mathrm{.}2070\mathrm{.}5300\mathrm{.}7230\mathrm{.}9230\mathrm{.}1400\mathrm{.}6110\mathrm{.}2250\mathrm{.}3700\mathrm{.}6030\mathrm{.}8700\mathrm{.}132).$

$($Use continuous time. When an arrival and a departure must be simultaneously scheduled, use the convention of scheduling the arrival first$).$