Assignment1
IE3110 Assignment 1 Due Date:14 Sep 2021
Question 1
Jessica is building a simulation model for the emergency department of a local hospital.
The hospital categorizes the patients into type A1 and type A2, where A1 refers to the
critically ill patient, and A2 refers to the non-critically ill patient. The arrival process for
A1 and A2 are Poisson process with rates equal to 1 per hour and 8 per hour respectively.
There are two doctors serving in the emergency department. The first doctor is a senior
consultant who can serve both types of patients, while the second doctor is a junior doctor
who can only serve A2. As A1 is critically ill, when the patient arrives, he will be
attended immediately if the first doctor is free or if the first doctor is attending an A2
patient. For the later case, the A2 patient has to rejoin the queue, and when he is attended
by another doctor, his treatment has to restart again. Assume that the treatment times for
both types of patient are exponentially distributed with average treatment time equal to
10 minutes.
Define the states and events for this system. Draw the flow chart for executing the events.
Question 2
Consider a single station assembly and test system, orders are released to the system with
a rate of 3 units per hour (Poisson process). We assume that there is only a single station
which can perform both the assembly and testing functions. The processing time of the
station (when performing both functions together) follows exponential distribution with a
rate of 8 units per hour. There is a probability of 0.5 that finished products are of bad
quality. These poor quality products need to be disassembled by an operator before re-
channeling back to the same station for assembly again. The time spent for disassembling
also follows exponential distribution at a rate of 6 units per hour and there are more than
enough operators who can perform disassembly tasks (we can assume that the number of
operators is infinite). It is possible that an order will visit the station several times before
finally passing the quality check.
(a) Define the events and the states.
(b) Draw a flow chart for each event to show how the event updates the states and the
future event list.
Question 3
In a manufacturing plant, there are N identical machines. The distribution of the time to
failure for all the machines follows exponential distribution with rate . There is one
repair man who can repair the machine with rate of (exponential distribution). A
simulation model will be build to estimate the average number of machines which are
down.
(a) Define the state and Event.
(b) For each arrival event, what is the flow chart of executing the events?
Question 4
Consider the following two servers tandem queuing system in which the buffer size for
the queue1 is infinite but the buffer size for the queue2 is 1. Blocking occurs whenever
there is a unit waiting at the queue2 as unit at the server1 cannot move to queue 2 even
after it has completed its service at server 1.
Define the states and events for this system. Draw the flow chart for executing these
events.
Question 5
A supermarket has two checkout stations, regular and express. Customers come with a
constant arrival rate of 30 per hour (poisson arrival). A customer arriving will join the
express queue if he finds that the number of people queued at the express queue is not
more than the number of people queued at the regular queue. Assume that the customers
cannot switch the queue after he has joined the queue. On the other hand, the servers
(express or regular) will serve the customers from their respective queue if the queue is
not empty, but if the queue is empty, they will help to serve the customers from the other
queue. The express server has an average processing time of 3 minutes (exponential
distributed), and the regular server has an average processing time of 4 minutes
(exponential distributed).
(a) Define the events set and the state space.
(b) Draw flow charts for the respective events to show how the events update the states
and the future event list.
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