Question

The FastFood restaurant on the Main Street has received a lot of complaints during lunch hour regarding its drive-through service. On average 50 cars arrive at the window according to Poisson distribution. A customer is first served by a clerk who takes the customers’ orders. The customer then drives to the window where another clerk collects payments and passes the order to the customer. Both clerks serve the customers at a rate of 1 customer per minute. Assume service time is exponential distributed. Examine the restaurant’s service performance. Specifically, answer the following questions.
(a) Draw a graph and identify the queue(s), server(s), arrival rate (if you have multiple queues, point out rate for each one) and service rate (for each server if there are multiple servers)?

(b) What’s the utilization of the server(s)?

(c) What’s the average number of cars in the system?

(d) What’s the average number of cars waiting in line?

Answer 1

Answer:(a) 1 customer per 30 minutes (b)0.8 approximately(c) 5 cars (d) 4.2 Approximately

Explanation:

Arrival rate = 50 cars , service rate = 1 customer per minute = 60/ 1 = 60 minutes

Servers = since there are 2 servers 60/2 = 30 minutes

Therefore they service 1 customers per 30 minutes

To calculate the utilization of the servers

= Arrival rate / Service rate

= 50/60

= 0.83

= 0.8 approximately

To calculate the average numbers of cars in the system

ts = Arrival rate /service rate - Arrival rate

= 50 / 60 - 50

= 50 / 10

= 5 cars

To calculate the average numbers of cars waiting in line

ti = Arrival rate ∧2 / service rate ( service rate - Arrival rate )

= 50∧2 / 60 (60 - 50)

= 2,500/ 60 (10)

= 2,500 / 600

= 4.16

= 4.2 cars approximately