6. Movies Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evenings, customers arrive at Movies Tonight with an arrival rate of 1.25 customers per minute. The checkout clerk has a service rate of 2 customers per minute. Assume Poisson arrivals and exponential service times. Arrival rate (?) = 1.25 custs/min Service rate (?) = 2 custs/min a) What is the probability that no customers are in the system? P0 = 1 – ? / ? = 1- 1.25 / 2 = 0.375 b) What is the average number of customers waiting for service? Lq = (?)2 / ? (? – ?) = (1.25)2 / 2(2-1.25) = 1.0417 customers c) What is the average time a customer waits for service to begin? Wq = Lq / ? = 1.0417 / 1.25 = 0.8333 minutes (x 60 seconds = 50 seconds) d) What is the probability that an arriving customer will have to wait for service? Pw = ? / ? = 1.25 / 2 = 0.625 e) Do the operating characteristics indicate that the one-clerk checkout system provides an acceptable level of service? - Yes
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We are given the arrival rate (λ) = 1.25 customers per minute and the service rate (μ) = 2 customers per minute. Show more…
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