Question
A new salon with a single barber operates near MIT. The salon provides two kinds of services: Quick Barbering (QB) which takes exactly 9 minutes
A new salon with a single barber operates near MIT. The salon provides two kinds of services: Quick Barbering (QB) which takes exactly 9 minutes and Normal Barbering (NB) which takes exactly 15 minutes. On average, the customers who request QB service arrive at a rate of 1 per hour, and the customers who request NB service arrive at a rate of 2 per hour. The two arrival streams follow independent Poisson processes. Because the two arrival streams are independent, the overall arrival process is also a Poisson process, with an average arrival rate of 3 customers per hour, and the probability that a new arrival wants for a QB service is 1/(1+2)=1/3. Assume that the customers are served on a first-in-first-out basis and the salon has unlimited capacity to store waiting customers. What is the expected time spent in the system for a customer who wants for a QB service (including waiting and service time)?
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