Consider a taxi station where customers arrive in a Poisson
process with rate 1 per minute, and taxis arrive in a Poisson
process with rate 2 per minute. A customer will wait no matter how
many others are present. However, an arriving taxi that does not
find a customer waiting leaves.
Consider A Taxi Station Where Customers Arrive In A Poisson Process With Rate 1 Per Minute And Taxis Arrive In A Poisso 1 (104.69 KiB) Viewed 27 times
Answer: = = a. Average number of taxis waiting = 1. b. the proportion of arriving customers that get taxis = 1/2 Explanation: Let the state be the number of taxis waiting. Then we get a birth-death process with 1= 1 and u= 2. Also, this can be thought of as an M/ M/1 system where being serviced is equivalent to waiting for a customer. Therefore: - = (a) Average number of taxis waiting = 1u-1 = 1 (b) The proportion of arriving customers that get a taxi is the proportion of arriving customers that find at least one taxi waiting. This is equivalent to the proportion of time the system is not in state 0. This is equal to 1-Po = 1 - (1-Au) = 1/2.
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