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Unformatted text preview: ISEN 316 TEST 1 226 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 workin—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 statespace to represent this system probabilistically. (b) Draw the ratebased statediagram of the system (connecting the system
states). (0) Develop the steadystate 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 workin—process and cycle time. (b) Can the arrival rate be affected by the state of the server system? Explain your
answer! (c) For an Erlang3 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
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 Spring '08
 Staff
 Probability theory, Cycle Time, mean arrival rate, factory cycle time, workstation serial factory

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