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lect0409

# lect0409 - IEOR 4106 Spring 2009 Professor Whitt...

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IEOR 4106, Spring 2009, Professor Whitt Introduction to Renewal Theory: Thursday, April 9 1. Speeding Ticket Revenue A policeman spends his entire day on the lookout for speeders. The policeman cruises on average approximately 10 minutes before stopping a car for some offense. Of the cars he stops, 90% of the drivers are given speeding tickets with an \$80 fine. It takes the policeman an average of 5 minutes to write such a ticket. The other 10% of the stops are for more serious offenses, leading to an average fine of \$300. These more serious charges take an average of 30 minutes to process. In the long run what is the rate of money brought in by fines? ——————————————————————— ANSWER The average time between successive stops is 10 + (0 . 9 × 5) + (0 . 1 × 30) = 10 + 4 . 5 + 3 . 0 = 17 . 5 minutes . The average fine revenue per stop is 0 . 9 × 80 + 0 . 1 × 300 = 72 + 30 = 102 Hence, by the renewal reward theorem, the long-run average rate fine revenue is accrued is E [fine per stop] E [time per stop] = \$102 17 . 5 minutes = \$5 . 28
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• Spring '08
• Whitt
• Probability theory, Ri, long-run average rate, renewal reward theorem, long-run average reward, renewal reward processes

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