Chapter 11 Homework - The reference desk of a university...

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A: what is the probabilty that no (0) requests are in the system B: what is the average number of requests that will be waiting for service C: What is the average waiting time in minutes before service begins E: what is the probabilyt that a new arrival has to wait for service σ σ Σ Σ λ the MEAN number of arrials per time period λ 10/hr .17/min μ the mean number of services per time period μ 12/hr .2/min X the number of arrivals in the time period X e 2.71828 e A: B: C: D: E: The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arival pattern and that the service times follow an expoential probabilty disribution with a service rate of 12 requests per hour. D: What is the average time at the reference desk in miutes (waiting time plus service time) ( 〖 ^ 〖〖 ^ 〖 )/ P(0)= ( 〖 .17 〖 ^0 ^(−.17))/0! ? =? ^( −.17 ) =.8437 L=4.82+.17/.2=5.67 ? = _? 〖 .17 〖 ^2/(.2(.2−.17))=4.82 ? _〖=4.82/.17=28.35 _ W = 28.35+1/.2=33.35 ? =.17/.2=.85 _?
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Poisson Arrival Rate λ 10 Exponential Service Rate μ 12 Probability of no orders in the system P(0) 0.1666667 Average number of orders waiting L(g) 4.1666667 Average number of orders in the system L 3.3333333 Average time an order waits W(q) 0.4166667 Average time an order is in the system W 0.5 Probability an order must wait P(w) 0.8333333
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σ Σ λ 2.5/hr .04/min μ 10/hr .17/min X e A: B: there is a .9932 probabilty that the customers don’t wait for over 5 minutes C: new μ: 8/hr = .13/min Agan Interior Design provides home and office decorating assistance to its customers. In normal operation an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questios and make product recommenatios The consultant averages 10 minutes with each customer. A: Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and expotential service times B: Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal bing met? If not what actions do you recommend?
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