3. An automobile dealer is planning a new custom service center to repair the microcomputer-based engine controls in new-model cars. With the new diag- nostic equipment they are installing, each job should take about 75 minutes to complete. The dealer plans to operate the center 8 hours per day. Preliminary estimates suggest that about 5 customers will bring their cars for repair each day. To analyze this situation, make the following assumptions: The customer arrivals form a Poisson process. Each job requires on average 75 minutes. We can ignore the time that the service center is closed. (That is, no arrivals occur during such gaps, and we don't count them in the total response time.) (a) Measure time in hours. In the terms of queueing theory, what are A, μ, and p? (b) Compute an estimate of the average total response time (which we call Ts). 2 (c) Estimate the average number of cars in the center (including those waiting as well as in service). (d) Suppose the average number of customers arriving turns out to be 6 per day instead of 5. What will be the effect on performance, ás computed in parts (b) and (c)? (e) Comparing the results of parts (b)-(d), you can see that a moderate increase in workload leads to markedly worse performance. Explain briefly why this is so.
3. An automobile dealer is planning a new custom service center to repair the microcomputer-based engine controls in new-model cars. With the new diag- nostic equipment they are installing, each job should take about 75 minutes to complete. The dealer plans to operate the center 8 hours per day. Preliminary estimates suggest that about 5 customers will bring their cars for repair each day. To analyze this situation, make the following assumptions: The customer arrivals form a Poisson process. Each job requires on average 75 minutes. We can ignore the time that the service center is closed. (That is, no arrivals occur during such gaps, and we don't count them in the total response time.) (a) Measure time in hours. In the terms of queueing theory, what are A, μ, and p? (b) Compute an estimate of the average total response time (which we call Ts). 2 (c) Estimate the average number of cars in the center (including those waiting as well as in service). (d) Suppose the average number of customers arriving turns out to be 6 per day instead of 5. What will be the effect on performance, ás computed in parts (b) and (c)? (e) Comparing the results of parts (b)-(d), you can see that a moderate increase in workload leads to markedly worse performance. Explain briefly why this is so.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:3. An automobile dealer is planning a new custom service center to repair the
microcomputer-based engine controls in new-model cars. With the new diag-
nostic equipment they are installing, each job should take about 75 minutes to
complete. The dealer plans to operate the center 8 hours per day. Preliminary
estimates suggest that about 5 customers will bring their cars for repair each day.
To analyze this situation, make the following assumptions: The customer arrivals
form a Poisson process. Each job requires on average 75 minutes. We can ignore
the time that the service center is closed. (That is, no arrivals occur during such
gaps, and we don't count them in the total response time.)
(a) Measure time in hours. In the terms of queueing theory, what are A, μ, and
p?
(b) Compute an estimate of the average total response time (which we call Ts).
2
(c) Estimate the average number of cars in the center (including those waiting
as well as in service).
(d) Suppose the average number of customers arriving turns out to be 6 per day
instead of 5. What will be the effect on performance, ás computed in parts
(b) and (c)?
(e) Comparing the results of parts (b)-(d), you can see that a moderate increase
in workload leads to markedly worse performance. Explain briefly why this
is so.
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