Question

At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. It takes an average of 2 min to serve each arrival. What is the utilization factor? Given same problem, what is the average time in the queue for each arrival?

Answer 1

Answer:

utilization factor = 80%

average time in the queue = 8 minutes

Explanation:

given data

arrive randomly rate = 12 every 30 minutes

average time serve = 2 min

to find out

utilization factor and average time in the queue

solution

first we get here mean number for arrivals that is

mean number  for arrivals = $\frac{12}{30}$

mean number  for arrivals = 0.4

and  

now we will get here mean number of served that is

mean number of served = $\frac{1}{2}$

mean number of served = 0.5

so now utilization factor will be as

utilization factor = $\frac{mean\ number\ for\ arrivals}{mean\ number\ of\ served}$    ...................1

put here value we get

utilization factor = $\frac{0.4}{0.5}$

utilization factor = 0.80

utilization factor = 80%

and

average time in the queue will be

average time in the queue = $\frac{0.4}{0.5(0.5-0.4)}$

average time in the queue = 8 minutes