Question

During busy periods, a new customer walks into WHS every 15 minutes on average, with a standard deviation of 15 minutes. At PHS, a customer walks in every hour on average, with a standard deviation of 1 hour. WHS has a staff of 4 stylists, while PHS has 1 stylist. The average service time at both salons is 30 minutes, with a standard deviation of 30 minutes.

1.If Alice goes to PHS, how long (in minutes) must she wait in line before her haircut starts?

2.WHS will buy out PHS. WHS will then close PHS’s operations and serve all customers, including existing PHS customers, at the WHS location only. Assuming that the previous traffic of PHS customers now flows to the WHS location, what is the new inter-arrival time (in minutes) at WHS?

Answer 1

WHS

Inter-Arrival time = 15 minutes

Standard deviation = 15 minutes

Stylists = 4

Average service time = 30 minutes

Standard deviation of Service time = 30 minutes

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PHS

Inter-Arrival time = 60 minutes

Standard deviation = 60 minutes

Stylists = 1

Average service time = 30 minutes

Standard deviation of Service time = 30 minutes

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1)

PHS

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2)

WHS

After buyout, Arrival rate = 60*(1/Interarrival time of WHS + 1/Interarrival time of PHS)

= 60/15+1/1

= 5 per hour

New inter-arrival time at WHS = 60/arrival rate

= 60/5

= 12 minutes