THE APPLICATION OF QUEUEING THEORY:Example 2—Which Computer?

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Example 2—Which Computer?

EMERALD UNIVERSITY is making plans to lease a supercomputer to be used for sci- entific research by the faculty and students. Two models are being considered: one from the MBI Corporation and the other from the CRAB Company. The MBI computer costs more but is somewhat faster than the CRAB computer. In particular, if a sequence of typ- ical jobs were run continuously for one 24-hour day, the number completed would have a Poisson distribution with a mean of 30 and 25 for the MBI and the CRAB computers, respectively. It is estimated that an average of 20 jobs will be submitted per day and that the time from one submission to the next will have an exponential distribution with a mean of 0.05 day. The leasing cost per day would be $5,000 for the MBI computer and $3,750 for the CRAB computer.

Thus, the queueing system of concern has the computer as its (single) server and the jobs to be run as its customers. Furthermore, this system fits the M/M/1 model presented at the beginning of Sec. 17.6. With 1 day as the unit of time, A = 20 customers per day, and IL = 30 and 25 customers per day with the MBI and the CRAB computers, respec- tively. You will see in Secs. 26.3 and 26.4 how the decision was made between the two computers.

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