COMP 461/561 2009 — Exercises 6-10

Complete by: Noon, Friday, Week 8

These exercises are intended to give you experience writing and running GPSS/H simulation models. For each exercise you should submit the following:

  • a GPSS block diagram model of the system
  • the output report file (.lis) for your simulations
  • observations or answers to any questions as required, and supported by evidence referenced directly in your listing file.
The listing file and answers must be submitted as plaintext attachments to an email, but the GPSS diagrams may be handed in as printed copies if you do not have lectronic versions. Note: Be sure to validate your model is working correctly before assuming your conclusions are correct.

Exercise 6: Cars arrive at a quick service garage every 10 +/-5 minutes. There are five bays at the garage, each with its own mechanic. All cars get an oil change which takes 8 +/-3 minutes and costs $25.00, and half also get a new oil filter for $20.00 which takes 3 +/- 1 minute to install. 40% of all cars get a new air filter which takes 2 +/- 1 minute to put in and costs $15.00. 20% of the cars get a tune-up for $65.00 which takes 35 +/- 10 minutes to do. One quarter of all cars get a brake inspection, which is free but takes 5 +/- 2 minutes to carry out. Of these, one fifth have a full brake service which takes 25 +/- 5 minutes to complete and costs $75.00. Simulate the shop for a six hour day and tabulate the service times and costs for the services provided. Service times should be grouped in five minute intervals in the table and costs should be grouped in multiples of $25.00. How much money does the garage take in for all of its work?

Exercise 7: A grocery store has three cashiers at its checkout: Amy, Ida and Ann. Amy can checkout a customer in 10 +/- 2 minutes, Ida takes 12 +/- 3 minutes and Ann takes 15 +/ 4 minutes. There is a separate queue for each cashier. Customers arrive at the checkout every 5 +/- 2 minutes. 20% of the customers always go to Amy because they know she's fast, and 10% always go to Ann because she's friendly. The rest always join the shortest queue. Model for ten hours of store operation. Whose queue is, on average, the longest?

Exercise 8: Parts arrive at the rate of one every 20 +/- 20 seconds. There are three inspectors working in parallel. Parts form a single line and go to the first available inspector. Inspection takes 55 +/-30 seconds, after which the parts move to a packing station on a conveyor that takes 60 seconds to convey each part. There are four packers working in parallel. Parts form a single line for packing and are processed by the first available packer. Packers take 5 +/- 5 seconds to setup and then 70 +/- 30 seconds to pack one part. Initialise the system by packing 100 parts, then collect statistics for packing the next 250 parts and answer this question: if one new employee is authorized, should we hire another inspector or packer? Defend your answer with your simulation results.

Exercise 9: Parts arrive for inspection according to the following distribution (time expressed in seconds):

interarrival time   probability
10.05
15.11
20.26
25.31
30.17
35.07
40.03
72% of all parts are of Type A and the rest are of Type B. All parts wait in a single FIFO queue for an available inspector. There are three inspectors. Type A parts must be inspected by either Inspector 1 or Inspector 2 and inspection time is exponentially distributed with a mean of 55 seconds. Type B parts must be inspected by Inspector 3, where 50% take between 40 and 60 seconds, 30% take between 60 and 70 seconds and the rest take between 70 and 90 seconds, and all of these distributions are uniform. Simulate for four hours of operation and determine the average waiting time for Inspector 3 in the last two hours.

Exercise 10: A bank has two cash machines which operate after hours. People arrive to use a machine every 5 +/- 2 minutes, forming a single queue for both machines. It takes 4 +/- 2 minutes to use a machine. The first machine goes down every half hour for five minutes, and the second machine goes down every fifteen minutes for two minutes. When a machine goes down, anyone using the machine goes back into the queue, but is the first to use the next machine that comes available. Model the operation of the machines from 4pm to 9am the next day and determine the average amount of time a customer spends in the system.




TCSmith, March, 2009