Cars arrive at a gas station located at a busy intersection at the rate of 30 per hour, Poisson distributed. Arriving ca

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Cars arrive at a gas station located at a busy intersection at
the rate of 30 per hour, Poisson distributed. Arriving cars will
form a FCFS line in the parking area that can hold only 4 cars. Any
car that arrives when this area is full will drive on and find gas
elsewhere. The station has 6 pumps; the time to fill gas (including
driving up to the pump, filling gas, paying, and driving away) is
exponentially distributed with a mean of 10 minutes. a. How many
minutes does a car spend at this station on average – waiting and
getting gas? b. What percent of the time are cars able to get into
the station? c. On average what percent of the time are the pumps
busy – what is their utilization? d. What is the probability that
an arriving car has to wait? e. What is the probability at least
two pumps are idle? f. During the 8-hour period between noon and 8
pm, how many cars (on average) drive on to find gas elsewhere?