Question

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.)

Answer 1

Answer:2 min

Step-by-step explanation:

Given

Arrival rate
`\lambda =(60)/(1)` per hour

Service rate
`\mu =(60* 60)/(40)` per hour

`\rho =(\lambda )/(\mu )=(40)/(60)=(2)/(3)`

Now average waiting time in the system is given by

waiting time
`L_s=(1)/(\mu -\lambda )`

`L_s=(1)/(90-60)=(1)/(30) hr`

`L_s=(60)/(30)=2 min`