CASE

A new car wash center started to give service at one of the most crowded shopping center of

the city. When people come to shop or cinema, they generally want to evaluate this time to give

their automobile to clean. Cleaning process can have different service times depending on the

service the owners want. If the owners want to clean inside of the automobiles, the service times

can increase.

The car wash center is in trouble especially on the weekends because the number of customer

in the shopping center increases on the weekends when compared to working days. The car

wash center has normally two washing area. However, one of the machine was broken and out

of service. Thus, the owner of the center needs to generate a new solution to give better service

to all customers with restricted resources.

As mentioned above, the service times of the automobiles can change. That's why; the owner

of the center wants to learn how the performance measures of his center will change under

different queue disciplines (FIFO and SPT). The probabilities of the time between arrivals and

service times of the automobiles are given in the tables. As an industrial engineer, please help

to the owner to find the answers of his questions listed below.

Time Between Arrivals (min) Prob.

20 0.30

50 0.10

70 0.20

90 0.40

Service Times (min) Prob.

80 0.150

100 0.450

120 0.275

150 0.125

1) Define entities, activities, events, and delays of the system given above.

2) Calculate the interarrival and service times of the first 10 customers respectively using the

given random digit table. You should use the table up to down. Assume there is no customer in

the system when the time shows 0.

3) Prepare the manual simulation tables for 2 different queue disciplines (FIFO and SPT).

4) Calculate the listed performance measures of the center for two different queue disciplines

one by one.

a) What is the average waiting time for a customer?

b) What is the probability of a customer has to wait in the queue?

c) What is the probability of idle server?

d) What is the average service time?

e) What is the average waiting time of those who wait?

f) What is the average time a customer spends in the system?

5) What are your judgments about the performances of the system under different queue

disciplines?

random digits:

69607-24145-73847-64930-73544-26179-35712-63099-40494-21756-12715-77009