A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds
ID: 379877 • Letter: A
Question
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 69 per hour, and this rate is Poisson-distributed.
Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)
Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Determine the average number of customers in the system. (Do not round intermediate calculations.Round your answer to 2 decimal places.)
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 69 per hour, and this rate is Poisson-distributed.
Explanation / Answer
= 75 69 customers per hour
=60*60/30 = 120 customers per hour
= / = 7/120 = 0.625 69/120=0.575
the average number of customers waiting in line
Ii = 2 / 2(1- ) = 0.5752 / 2(1-0.575) = 0.33/0.8= 0.39 customers
the average time customers spend in the system
Ti = Ii / =0.39/69=0.00565 hours
T = Ti + 1/ =0.00565+1/120=0.01239hours =0.839 minutes
average number of customers in the system
I = Ii + =0.39+0.575 =0.965 customers