During peak hours, cars arrive at an entry lane to the car park of an office building according to a Poisson process wit
Posted: Tue Jul 12, 2022 11:38 am
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?
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?