Question

For the Starbucks Coffee Company stores in Beijing, China, using the Poisson distribution, corporate management back in Seattle forecasts that Western and Chinese customer demand will be only 10 customers arriving per hour (60 minutes). A detailed review of corporate training procedures and Chinese associate capabilities suggest that the mean service time during this period will be 4 minutes per customer. Based upon this queuing data, what is the average time that a customer spends in the queue (Wo) in minutes? 0 10.2 minutes O 8.00 minutes 0 12.00 minutes 9.80 minutes

Answer 1

Answer : 8 minutes

As 10 customer arrive per hour the arrival rate is 10 cars per hour. As each customer takes 4 minutes to be serves, in each hour 60/4 = 15 customers can be served.

Hence = 10 and = 15

Average time a customer spends in the waiting line, Wq is given as below

$W_q = \frac{\lambda}{\mu(\mu-\lambda)} = \frac{10}{15*(15-10)} = \frac{10}{75} = 0.1333$

Hence waiting time in queue is 0.1333 hours or 0.1333*60 = 8 minutes