Schips Department Store operates a fleet of 9 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 0.5 trucks per hour. The service rate is 6 trucks per hour. Using the Poisson arrivals and exponential service times model with a finite calling population of 9 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.
What is the hourly cost of operation if the cost is $45 per hour for each truck and $30 per hour for the truck dock? If required, round your answer to two decimal places.
Consider a two-server truck dock operation where the second server could be operated for an additional $30 per hour. How much would the average number of trucks waiting for loading/unloading have to be reduced to make the two-server truck dock economically feasible? If required, round your answer to one decimal place.
The total cost for the two-server truck dock system is? $
The total cost for one-server truck dock system is? $