Ships Department Store operates a fleet of 12 trucks. The trucks arrive at rando

Question

Ships Department Store operates a fleet of 12 trucks. The trucks arrive at random times throughout the day at the store's truck dock to be loaded with new deliveries or to have incoming shipments from the regional warehouse unloaded. Each truck returns to the truck dock for service two times per 8-hour day. Thus, the arrival rate per truck is 0.2 trucks per hour. The service rate is 4 trucks per hour. Using the Poisson arrivals and exponential service times model with a finite calling population of 12 trucks, determine the following operating characteristics: The probability that no trucks are at the truck dock. If required, round your answer to four decimal places. The average number of trucks waiting for loading/unloading. If required, round your answer to four decimal places. The average number of trucks in the truck dock area. If required, round your answer to four decimal places. The average waiting time before loading/unloading begins. If required, round your answer to four decimal places. The average waiting time in the system. If required, round your answer to four decimal places.

Explanation / Answer

Answer:

Here in the question lambda = 0.2 trucks per hour

and mu = 4 trucks per hour

therefore P0 = 1 - 0.2/4 = 95%

Ls= average number of units (trucks) in the system = 0.2 / (4-0.2) = 0.0526

Ws= average time a unit spends in the system = 1 / (4-0.2) = 0.263

Lq= average number of units waiting in the queue = 0.2^2 / 4*(4-0.2) = 0.000263

Wq= average time a unit spends waiting in the queue = 0.2 / 4*(4-0.2) = 0.013

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