Slide 1overviewLittle’s lawLittle’s lawLittle’s lawLittle’s lawLittle’s lawPROBABILITY AND STATISTICS IN COMPUTER SCIENCE AND SOFTWARE ENGINEERING Chapters 7: Queuing Systems1OVERVIEWWe will now move to study queuing systems, and how they work …This will involve many of the concepts we have looked at earlierFirst we will need to develop some terminology …We’ll see the connection between arrival rate and inter-arrival time …We’ll define response times, service times, and utilization …We’ll see Little’s Law, which relates expected number of jobs, expected response time, and arrival rate …Then we’ll start to look at first model, the Bernoulli single-server queuing process2LITTLE’S LAWSuppose you have a wine rack that holds 240 bottles. You notice that …The rack is typically 2/3 full (160 bottles)You buy on average 8 bottles per monthQuestion: How long (on average) does a bottle of wine stay in the rack?Answer: Apply Little’s Law …In this case, …So we can conclude•E3LITTLE’S LAWA semiconductor factory starts working on 1,000 new wafers each day. On average, there are about 45,000 wafers under development on any given day. Question: On average, how long does it take to complete the wafer?Answer: Apply Little’s Law with . We have•E4LITTLE’S LAWYou receive about 50 e-mail messages per day, and on average you have about 150 unanswered e-mails in your inbox. How long does it take (on average) to answer an e-mail?Solution: Let …Then•E5LITTLE’S LAWCars arrive at a toll booth at a rate of about 3,600 cars per hour. Our tollbooth on average takes 20 seconds to process a car. What is the average length of the waiting line we can expect?Answer: Let and . Then•E6LITTLE’S LAWThere are 250 houses on the market, and new ones are added each month. Using a rolling average of the number of new houses added to the market each month over the last year, we conclude that on average a total of 980 new houses are added to the market each year. What is the average number of days the house stays on the market?Answer: Let .
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