Answered: A vending machine dispenses hot…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 63 per hour, and this rate is Poisson-distributed.

a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)

Average number of customer

b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Average time             minutes

c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Average number             customers

Expert Solution

Step 1

Given Information:

Arrival rate $λ = 63$ per hour

Service rate is calculated as:

$μ = \frac{3600}{20} = 180$ customers per hour.

Then, $ρ = \frac{λ}{μ} = 0.35$

(a) To determine the average number of customers waiting in line:

$\begin{array}{rcl} I_{i} & = & \frac{ρ^{2}}{2 (1 - ρ)} \\ = & \frac{{(0.35)}^{2}}{2 (1 - 0.35)} \\ = & 0.09423076923 \\ \approx & 0.09 \end{array}$

Thsu, the average number of customers waiting in line is 0.09 customers.

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