Question

Students arrive at the Daz Bog counter to buy frou-frou coffee drinks (with whipped cream) on average every 12 minutes. It takes an average time of 6.5 minutes to serve each customer, with service times following an Exponential distribution. What is the average number of students waiting in line to be served?

Answer 1

the average number of students waiting in line to be served = 0.640 = 16/25 arrivals/min

Explanation:

Explanation:-

Students arrive at the Daz Bog counter to buy frou-frou coffee drinks (with whipped cream) on average every 12 minutes so its means the arrival rate

λ = 1/12minutes

Given an average time of 6.5 minutes to serve each customer, with service times following an Exponential distribution

so given the service rate μ= 1/6.5 per min

The formula of the average number of students waiting in line to be served

that is Average length of the queue

`L_(q) = (λ^2)/(μ (μ -λ))`

`L_(q) = (((1)/(12) )^2)/((1)/(6.5) ((1)/(6.5) -(1)/(12) ))`

on simplification , we get

`L_(q) = 0.640 = (640)/(1000) = (16)/(25)` arrivals/min