Homework Fall 2011 Homework due Sept 14 1 To study a modification of a system indicate whether you would use a simulation or not and if a simulation whether the model would be physical or mathematical a a small section of an existing factory b a freeway interchange c an emergency room d a pizza delivery operation e The shuttle bus operation for a rental car agency at an airport f a battlefield communications network g The chemical composition of an optical fiber 2 For the above situations assume they would be studied using a simulation model would the simulation be static or dynamic deterministic or stochastic and continuous or discrete 3 For the above situations name several entities and events 4Go to http www mathworks com academia View the matlab tutorial under learn and follow along with the simulink tutorial doing your own bungee jumping simulation http www mathworks com products demos simulink SimulinkEDU simulinkedu Viewlet simulink edu viewlet swf html For the bungee problem hand in your diagram adding your name to some box Make a table for cord constant k 5 40 500 and m the mass in kilos 25 small child 90 and 250 2 people jumping together indicating an approximate lowest altitude and highest altitude after the fall for each of the 9 combinations Put an X if the lowest point is under ground The company running the jump is thinking of adding a high platform for security For each X in the table indicate how high above the 50 ft mark would this platform have to be so that the person would not hit the ground Sept 19 Project 1 Do Problem 2 page 68 of Barrodale the 2 missile problem print the time of the explosion and which object exploded Plot the trajectories of the three moving bodies You may do this in any language you wish like C and excel x y plot C with your own plotting tools or Matlab by adding a few line to the single missile problem on the class home page Hand in source code output Homework due Sept 21 1 Assume one has the following service times time in minutes Probability 1 25 2 4 3 2 4 15 What are the cumulative probabilities How would you generate them 2 a Generate the arrival Service table for the following data Interarrival 3 6 1 2 4 6 5 1 Service times 2 1 8 5 4 3 2 5 6 b When are the events c Find the following statistics 1 Utilization 2 Average wait time 3 Average time in system 4 average service time 5 expected service time 6 average no of customers waiting Homework due Sept 26 Read section 4 3 of Barrodale Project 2 Do problem 9 page 75 of Barrodale the baseball problem print the time and position of the ball hitting the ground Plot the trajectory of the baseball You may do this in any language you wish like C and excel x y plot C with your own plotting tools or Matlab Hand in source code output Produce the trajectory of the baseball using simulink Oct 3 Quiz Homework for Oct 3 Project 3 In Simulink solve the following problems 1 A damped pendulum with a one kg weight and string of length 1m x cx 9 8 sin x from time 0 to 50 and set c 9 and 10 start with x 1 2 Spread of disease where P represents the percentage of affected population P 2P 2000 P P 0 10 3 Bank balance B with interest at 5 B 0 05B B 0 1000 4 The depth Y of water in a bucket with a whole in it Y Asqrt 2 g sqrt y With g gravity 32 and A is cross sectional area Set A to pi Homework for Oct 5 Project 4 Program a specific probabilistic simulation model the 2 pump gas station problem in Barrodale Cars arrive at a rate of 20 per hour to a gas station with two pumps a single queue If both pumps are busy put the car in the queue Service time 5 minutes per car Run the simulation for 10 000 000 hours Determine and print as output average queue length the average waiting time for a car the percent of the time the pumps are busy both pumps one pump or idle time Hand in source code and the output it produces Use an event driven mode Oct 12 Project 5 Queues On the Unix machine implement the queuing data type using a C class with a linked list a straight array and a circular array see the notes on my website First show it works with 5 items to be queued and then time with 10 000 items Try 3 situations all enqueued and then all dequeued enqueue followed by dequeue so that queue is never longer than 1 randomly enqueue and dequeue if possible with each equally likely Homework for Oct 17 Do one of the questions in the practice midterm Oct 19 Midterm Oct 26 Project 6 Produce phantom data for Positron Emission Tomography and produce images in Matlab Oct 31 Project 7 Implement one of the event simulations on the form that will be given out Nov 7 Random number generator worksheet Nov 9 600 throws determine the frequency of the numbers on the dice for each of the ways the random numbers were generated Nov 14 Project 9 Use the results of project 7 to determine the chi square statistic for each generator Determine the gap frequencies and the Kolmogorov Smirnov statistic Nov 21 Worksheet on queueing analysis Nov 28 take home quiz Dec 5 Project 9 Solving a large queueing problem using SOR