Answered

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Thanks to a generous and eccentric donor, the school of business has 3 fax machines. The toner in each machine needs to be changed after about 5 hours of use. There is one unit secretary who is responsible for the fax machine maintenance. It takes him 15 minutes to replace the toner cartridge. What is the average number of fax machines in the system

Sagot :

danialamin

Answer:

In the long run there are 0.02647 machines in the system queue.

Step-by-step explanation:

From the equation of the Finite Population Model of form M/M/1 with a finite source ,the average number of fax machines in the system to be maintained is given as :

[tex]L=\dfrac{\lambda^2}{\mu(\mu-\lambda)}[/tex]

Here

  • λ is the arrival rate which is the given as

[tex]\lambda=\dfrac{Number\ of\ machines}{Time\ between\ Service}\\\lambda=\dfrac{3}{5\ hr}\\\lambda=0.6\ hr^{-1}[/tex]

  • μ is the service time which is 15 minutes or 4 per hour

So the equation becomes:

[tex]L=\dfrac{\lambda^2}{\mu(\mu-\lambda)}\\L=\dfrac{0.6^2}{4(4-0.6)}\\L=0.02647[/tex]

So in the long run there are 0.02647 machines in the system queue.

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