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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Queuing Model The average length of time that a customer waits in line for service is given by

W ( x , y ) = 1 x y ,   y < x where y is the average arrival rate, written as the number of customers per unit of time, and x is the average service rate, written in the same units. Evaluate each of the following.

(a) W(15, 10) (b) W(12, 9)

(c) W(2, 6) (d) W(4,2)

(a)

To determine

To calculate: The average length of time if the average service rate 15 customer per unit time and the average arrival rate10 customer per unit time.

Explanation

Given information:

The average length of time that customer waits in the line for service,

W(x,y)=1xy,  y<x

Here, the y is the average arrival rate, written as the numbers of customer per unit of time and x is the average service rate, written as the numbers of customer per unit of time.

Calculation:

Consider the written as the numbers of customer per unit of time.

Substitute, 15 for x, 10 for y in profit function,

W(

(b)

To determine

To calculate: The average length of time if the average service rate 12 customer per unit time and the average arrival rate 9 customer per unit time.

(c)

To determine

To calculate: The average length of time if the average service rate 12 number of customer per unit time and the average arrival rate 6 customer per unit time.

(d)

To determine

To calculate: The average length of time if the average service rate 4 number of customer per unit time and the average arrival rate 2 customer per unit time.

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