Question

vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed. Determine the following: a. The percentage of time the machine is busy b. The average number of customers waiting in line c. The average time customers spend in the system d. The average number in the system

Answer 1

0.667 ;

0.667 customers ;

0.0166708 hour ;

1.334 customers

Explanation:

Given that:

Service time (μ) = 30 seconds ; 2 customers per minute ; 2 * 60 = 120 customers per hour

Arrival time, λ = 80 customers per hour

a.) percentage of time machine is busy (p) ; Utilization factor :

P = λ/ μ = 80 / 120 = 0.667

b.) average number of customers waiting in line Li = p² / 2(1-p)

= 0.667² / 2(1-0.667) = 0.667 customers

c) Average time customer spend in the system = Li/λ + 1/μ

= (0.667 / 80) + (1 / 120)

0.0083375 + 0.0083333

= 0.0166708 hour

= 0.0166708 * 60 = 1.00025 minutes

D) average number in the system ;

Li + p

= 0.667 + 0.667 = 1.334 customers