Customers arriving at a service center are assigned to one of three categories, with category 1given the highest priority. Records indicate that an average of nine customers arrive per hour andthat one-third are assigned to each category. There are two servers, and each can process customers at the rate of five per hour. Arrival and service rates can be described by Poisson distributions.a. What is the utilization rate for this system?b. Determine the average waiting time for units in each class.c. Find the average number of customers in each class that are waiting for service

Customers arriving at a service center are assigned to one of three categories, with category 1given the highest priority. Records indicate that an average of nine customers arrive per hour andthat one-third are assigned to each category. There are two servers, and each can process customers at the rate of five per hour. Arrival and service rates can be described by Poisson distributions.a. What is the utilization rate for this system?b. Determine the average waiting time for units in each class.c. Find the average number of customers in each class that are waiting for service

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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A priority waiting system assigns arriving customers to one of four classes. Arrival rates (Poisson) of the classes are shown in the following table. Five servers process the customers, and eachcan handle three customers per hour.a. What is the system utilization?b. What is the average wait for service by customers in the various classes? How many are waiting in each class, on average?c. If the arrival rate of the second priority class could be reduced to three units per hour by shifting some arrivals into the third priority class, how would your answers to part b change?d. What observations can you make based on your answers to part c?
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