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Test 1 Yellow Sol 2010

Test 1 Yellow Sol 2010 - ISEN 316 TEST 1 2-26 YELLOW...

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Unformatted text preview: ISEN 316 TEST 1 2-26 YELLOW Instructions: Use the fiont of your solutiOns papers only. Place the exam on top of your answers and staple them together in the left top corner. Write your name and UIN on the top of this sheet. 28 points . 1. Consider two workstation serial factory as depicted by the diagram below: w Compute the factory cycle time, throughput and work-in—process. Assume the following data is known: 21 = 4jobs/hr C50) = 1.5 E[Sl]=1/6hrs C2[Sl] =2 ELSE] :12 min CZ[SZ]=4 36 points 2. Consider a M IE2 l2 / 4 system, with a mean arrival rate of 27. and a mean service rate per machine of p . (a) Define a state-space to represent this system probabilistically. (b) Draw the rate-based state-diagram of the system (connecting the system states). (0) Develop the steady-state equation relating the state probabilities by isolating on the state Where the system is full and the arrival process is in the second phase. (d) Write the equation (using the state probabilities) for the WI? in the queue. 36 points 3. Consider an experiment where two die (a pair of dice) (red and blue) are tossed simultaneously. Both dies are 6 sided with equal areas (equal probabilities of each side ending up on the top). The red die, however, is unusual in that it has two sides with 1’s and two sides with 4’s, one side with a 2 and one side with a 3 (these are numbers or dots, whichever you want to consider). (a) What is a sample space for this experiment (define it, since there is more than one way of doing this!). List all the outcomes. (b) How many events are there for this experiment. (c) What is the event that the sum of the top 'faces equals 5. That is, what are the outcomes that make up this event? ' (d) What is the probability of the event of (c) occurring? 10 points bonus 4. Define the following terms or answer the questions: (a) What is the relationship between work-in—process and cycle time. (b) Can the arrival rate be affected by the state of the server system? Explain your answer! (c) For an Erlang-3 phased service system, what is service rate per phase for an overall rate of 5 jobs per hour. Explain this answer in terms of service time! @ 51% (4: m) M M 5‘ $322+ 1“ 72:14" 2&4— ga 3" 4/” r312, (33 “£3 We?“ Hpazfl’fsz; #72917.) "VZ'OfiM +‘flm *fiax *‘yfi'flzwj :3 E =3 <z,4,>,<23>, Camgm'i _ Q) fifthfigztflf) : 3-- PW%(222))§:(D&—) :_ J... Fr -— §C3,Z)§ w :: A_.._,—_._... . ...
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