QUESTION 5A post office has a counter for customers' drive-through to get the services. The design of thedrive-through lane allows for unlimited queue length. The arrival and service rate are Poissondistributed with A= 20 customers per hour arriving on average and u=25 customers per hour canbe served on average.a) Compute the average number of arrivals.b) Compute the average time a customer waits.c) Compute the average number of arrivals in the system.d) Compute the average time a customer is in the system.e) Compute the probability that less than or equal to 3 customers are in the system.f) If the single counter for the customer drive-through has been replaced with the automaticoperation, service rates are constant with A= 20 and u =25. Compute (a), (b), (c) and (d).

Let, Arrival rate, λ = 20 per hour Service rate, μ = 25 customers per hour The average number of…

Answered: A post office has a counter for…

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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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) arrival rate in customers per hour for this queuing system? Consider drawing a rate diagram to assist in your solution. O 10 12 O none of the other choices O 2
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please dont answer in image format. Do type Thnks
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