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A taco truck is parked at a local lunch site and customers queue up to buy tacos at a rate of one per minute. The arrivals of customers are completely independent of one another. It takes 40 seconds on average to serve a customer (using a single server), with a standard deviation of 20 seconds. Determine the average time (in seconds) it takes a customer from when they arrive to the truck until they receive their taco. (Enter an integer answer.)

Respuesta :

Answer:2 min

Explanation:

Given

Arrival rate [tex]\lambda =\frac{60}{1}[/tex] per hour

Service rate [tex]\mu =\frac{60\times 60}{40}[/tex] per hour

[tex]\rho =\frac{\lambda }{\mu }=\frac{40}{60}=\frac{2}{3}[/tex]

Now average waiting time in the system  is given by

waiting time [tex]L_s=\frac{1}{\mu -\lambda }[/tex]

[tex]L_s=\frac{1}{90-60}=\frac{1}{30} hr[/tex]

[tex]L_s=\frac{60}{30}=2 min[/tex]

                               

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