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?

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 =

mean number  for arrivals = 0.4

and  

now we will get here mean number of served that is

mean number of served =

mean number of served = 0.5

so now utilization factor will be as

utilization factor =    ...................1

put here value we get

utilization factor =

utilization factor = 0.80

utilization factor = 80%

and

average time in the queue will be

average time in the queue =

average time in the queue = 8 minutes