During peak hours, cars arrive at an entry lane to the car parkof an office building according to a Poisson process with rate of 5cars per 15-minute interval. The lane accepts both ticket-basedentry and ticketless entry. The time taken to “check-in” isexponentially distributed and has mean 2.3 minutes at the lane.
a)Find the probability of observing at most 2 cars arriving atthe lane during a 15-minute interval.
b)Find the probability that the inter-arrival time of cars isless than 1 minute.
c)During peak hours, cars arrive at an entry lane to the carpark of an office building according to a Poisson process with rateof 5 cars per 15-minute interval. The lane accepts bothticket-based entry and ticketless entry. The time taken to“check-in” is exponentially distributed and has mean 2.3 minutes atthe lane. The car park operator opened another entry lane. The newlane accepts only ticketless entry. Cars arrive at this laneaccording to a Poisson process at rate 7 cars per 15-minuteinterval. The time taken to “check-in” at this lane isexponentially distributed with mean 1.5 minutes. What is the meanqueue lengths for these two lanes?
During peak hours, cars arrive at an entry lane to the car park of an office building according to a Poisson process wit
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During peak hours, cars arrive at an entry lane to the car park of an office building according to a Poisson process wit
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