A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds
ID: 379863 • 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.)
Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)
Explanation / Answer
We have following information,
Customers arrive at a mean rate of 69 per hour; Arrival rate = 69 customers per hour
Service time is 30 seconds per cup; Service rate µ = one hour / 30 seconds = 60 * 60 seconds / 30 seconds = 120 customer per hour
a. Determine the average number of customers waiting in line.
The average number of customers waiting in line Lq = ^2 / [µ (µ-)]
Lq = 69^2 / [120 *(120-69)]
Lq = 4761 / (120 *51)
Lq = 0.78 customers
Average number of customer 0.78
b. Determine the average time customers spend in the system.
The average time customers spend in the system W = Wq + 1/µ
Where Wq = /µ * (µ - ) = 69 / 120 * (120 -69) = 69/ 120 * 51 = 0.01127 hour or 0.68 minutes
Therefore,
The average time customers spend in the system W = Wq + 1/µ
W = 0.01127 +1/120
= 0.0196 hours or 1.18 minutes
Average time is 1.18 minutes
c. Determine the average number of customers in the system
Average number of customers in the system = Lq + /µ
= 0.78 + 69/120
= 1.35 customers
Average number 1.35 customers