Vacation Inns is a chain of hotels operating in the Southwestern part of the Uni

Question

Vacation Inns is a chain of hotels operating in the Southwestern part of the United States. The company uses a toll-free telephone number to take reservations for any of its hotels. The average time to handle each call is 3 minutes, and averages of 12 calls are received per hour. The probability distribution that describes the arrivals is unknown. Over a period of time it is determined that the average caller spends 6 minutes either on hold or receiving service. Find the average time in the queue, the average time in the system, the average number in the queue, and the average number in the system.

Explanation / Answer

Arrival rate , Lamda = 12/60 = .2 / minute

Service rate , Mu = 1/3 = .3333 / minute

Average time in the queue = Wq = Lamda / ( mu(Mu- Lamda))

                                                = .2/ .3333(.3333-.2)

                                                = .2 / 0.0444 = 4.5 minutes

Average time in the system , Ws = 1/( Mu- lamda) = 1/ .1333= 7.5 minutes

Average number in the queue, Lq = Lamda * Wq = .1333 *4.5 = 0.59985

Average number in the system , Ls = Lamda * Ws = .1333*7.5 = 0.99975

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