Consider a Poisson queue with random arrivals at the rate of 12 customers per hour and the following steady-state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and p, = 0 for n = 3,4,5, ... . What is the mean (or effective) arrivalrate in customers per hour for this queuing system? Consider drawing a rate diagram to assist in your solution.O 1012O none of the other choicesO 2

The detailed solution to the given question is in Step 2.

Answered: Consider a Poisson queue with random…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.
The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?
Subject - account Please help me. Thankyou.
A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What is the expected average number of snowplows in the garage (waiting for repair and being repaired)? 5 1.04 1.67 8
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A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in…
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