3044sample1f11

# Use the following uniform 0 1 observations to

• Notes
• 5

This preview shows page 2 - 4 out of 5 pages.

Use the following uniform .0; 1/ observations to generate the interarrival times .53 .37 .08 .62 .53 .56 .14 .67 .82 .68 and the following N.0; 1/ numbers to generate the respective processing times 0:23 0:17 0:43 0:02 2:13 0:04 0:18 0:42 0:24 1:17 Round each service time to the nearest integer. In both cases, read from left to right. (a) What is the average time in queue for the 10 new jobs? (b) What is the (average) utilization of the machine? 6. Short questions. (a) The discrete random variable X has probability (mass) function Pr .X D 1/ D 0:45 , and Pr .X D 2/ D 0:55 . Give the Simio expression that generates realizations of X . (b) Which distribution does the Simio expression Random.Exponential(2) generate data from? Give its parameter(s). (c) Suppose X is geometric .0:8/ . Find P.X > 5 j X > 3/ . (d) Suppose X 1 ; X 2 ; : : : ; X 8 are i.i.d. uniform .0; 2/ . Use the central limit theorem to approxi- mate P.5 < P 8 i D 1 X i < 11/ . (e) Suppose X binomial .3; 0:75/ and Y binomial .2; 0:75/ are independent. Find P.X C Y 3/ . 7. Consider a single-server queuing system with FIFO service discipline and let X.t/ be the number of customers in the system (including the customer in service). A simulation run for 180 minutes produced the following sample path (output) t -interval OE0; 40/ OE40; 72/ OE72; 83/ OE83; 96/ OE96; 129/ OE129; 136/ O X.t/ 0 1 2 1 2 1 t -interval OE136; 148/ OE148; 165/ OE165; 175/ OE175; 180/ OE180; 1 / O X.t/ 2 3 2 1 0 (a) Compute an estimate of the mean number of customers in the system during OE0; 180Ł .

Subscribe to view the full document.

3 (b) Compute an estimate of the mean server utilization during OE0; 180Ł . (c) Compute an estimate of the mean customer delay in queue during OE0; 180Ł . 8. Parts at a machine (with an infinite-capacity buffer) according to a Poisson process at the rate of 2 parts per minute. They are processed one-at-a-time by the machine. The processing times are i.i.d. uniform between 20 and 30 seconds.
You've reached the end of this preview.
• Spring '08
• ALEXOPOULOS
• Probability theory, discrete random variable, mean customer delay

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern