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Travka [436]
3 years ago
14

Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate

follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what proportion of the time is the serverbusy?A) 0.43B) 0.57C) 0.75D) 0.25E) 0.33
Mathematics
1 answer:
Elan Coil [88]3 years ago
3 0

Answer:

The answer is B) 0.57.

Step-by-step explanation:

In this problem we have to apply queueing theory.

It is a single server queueing problem.

The arrival rate is  \lambda=4 and the service rate is \mu=7.

The proportion of time that the server is busy is now as the "server utilization"and can be calculated as:

p=\frac{\lambda}{c\mu} =\frac{4}{1*7}=0.57

where c is the number of server (in this case, one server).

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Step-by-step explanation:

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Please go back to the source of  your question and describe the other graphs that were given to you.

The graph that shows a straight line is the linear function.

4 0
3 years ago
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gregori [183]

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Step-by-step explanation:

7 0
2 years ago
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3 years ago
logan trades 50 pennies for nickels he gets a nickel for each group of 5 pennies what equation can be used to find how many nick
V125BC [204]

The  equation  that can be used to find how many nickels logan uses is: 50÷5.

<h3>Equation to find the number of nickels</h3>

Given:

Total pennies=50

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Hence:

Number of nickels=1÷5×50

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Number of nickels=10 nickels

Therefore the  equation  that can be used to find how many nickels logan uses is: 50÷5.

Learn more about Equation to find the number of nickels here:brainly.com/question/10704332

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4 0
2 years ago
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gregori [183]

Answer:

Option C.

Step-by-step explanation:

This is a function because all of the numbers have a partner, and none of them have more than one.

                                    Example of Not a Function

Function                                Not a Function

-4 to 5                                      <em> -4 to 5</em>                             <

9 to 7                                       <em> -4 to 3    </em>                          <

13 to 3                                       13 to 3                              ^

-7 to 5                                        9 to 7                               ^

                                                 -7 to 5                               ^

                                           Not a Function because of this

8 0
3 years ago
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