Question

1. A Fast Food drive-through Restaurant with a single check-out counter opens six days a week, but its heaviest day of business is on Saturdays. Customers arrive at an average rate of 20 per hour on Saturdays. Customers can be provided service at the rate of one every two minutes. Assuming Poisson arrivals and exponential service times, find:
   1. The average number of customers in line
   2. The average time a car waits before being served
   3. The average time a customer spends in the system
   4. The Utilization rate of the restaurant
   5. The probability that there is no customer in the restaurant

Answer 1

arrivals/time period =			λ=	=20/60=0.33
served/time period=			μ=	=1/2=0.50

1)

average number of customers in system L =

λ/(μ-λ)=

2

2)

average time spend in queue Wq                   =

λ/(μ(μ-λ))=

4.00 minute

3)

average time spend in system W                   =

1/(μ-λ)=

6 minute

4)

utilization factor =      ρ                                        =

λ/μ             =

0.67

5)

probability that there is no customer in the restaurant =1--λ/μ =0.3333