Fall 2008 Instructor: Vlad Wojcik
Assignment # 1: Due 14 Oct 2008, 4 PM.
PROBLEM 1: Gas station simulation [45 marks]
Consider a gas station that has two service lanes. Each lane has room for two cars, but only one car can be serviced at any one time in a given lane. Assume that potential customers arrive at the station site with a mean interarrival time of 5 min, exponentially distributed. If no lane is empty, 25% of potential customers will bypass the station; if both lanes are filled, all potential customers will bypass the station.
The service times for all customers are approximately normally distributed, with a mean value of 6 min and standard deviation of 1.5 min., but no service times of less than 3 min nor more than 9 min occur.
Simulate this system to determine what percentage of customers is actually lost and the percentage of service time is actually being provided in each lane.
PROBLEM 2: Mixing concrete [45 marks]
Consider a small mixed concrete plant which can produce a batch of concrete, 25 cu meters in volume, in a period of 30 min. After the concrete is produced, it is placed in 50 cu meters capacity hopper. The plant can start producing another batch after this operation, but only if the hopper contains less than 25 cu meters of concrete.
Also assume that there are 10 trucks of 10 cu meters capacity each which are to be loaded from the hopper. The time to load each truck is 5 min. The trucks deliver the concrete to various sites, and the travel times correspond to the frequency distribution depicted beside.
At the site the truck must wait to unload. This waiting time is exponentially distributed with with a mean of 10 min. Unloading time is uniformly distributed in a range from 5 min to 15 min. The return trip requires the same amount of time as the outbound trip.
Operations of this system start at 8 AM each day, with 50 cu meters of concrete in the hopper and all trucks at the plant, empty and ready to load. No new batch of concrete can be started after 2:30 PM, and no truck can leave the plant after 3:20 PM.
Simulate this system to determine the average amount of concrete which can be delivered in a day and the amount of time after 4 PM trucks will require to complete the last trip. Include the overtime for each truck in this last amount.
Both hardcopy (paper) and electronic submission is required.
Hardcopy submission: Your submission envelope with the standard Cover Page should contain all relevant printouts and supporting documentation, demonstrating your design and flawless behaviour of your program. The envelope should be dropped in the submission box on or before deadline date / time.
Electronic submission: Please create a directory on Sandcastle and place within it all the files (and only the files) to be submitted. To submit issue the command submit4p94, which is interactive in its nature. Obviously, you are allowed to submit your assignment only once. Should you encounter difficulties, please report them to Mr. Cale Fairchild.
Similarly, the electronic submission should be performed on or before deadline date / time.
Possible lateness in assignment submission is counted in days, each period of a day ending at 4 PM. The penalty for late submission of assignments is 25% up to three days (or a part of a day). After that period the penalty is 100%.
While honest cooperation between students is considered appropriate, the Department considers plagiarism a serious offense. For clarification on these issues you are directed to the statement of Departmental Policies and Procedures.
Instructor: Vlad Wojcik
Revised: 7 October, 2008 11:13 AM
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