Empty taxis arrive at an airport at a rate of 3 per minute and passengers arrive at
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Question:
Empty taxis arrive at an airport at a rate of 3 per minute and passengers arrive at pickup at a rate of 2 per minute. Taxis pick up a single passenger at a time and passengers only wait for a taxi if there are less than 4 people waiting ahead of them. This is a Poisson process.
a. What is the expected time for a passenger to be picked up?
b. model this using the continuous-time Markov chain {0,1,2,3,4} denoting by the number of people waiting at the waiting area. Show that the steady-state probabilities are πo= 81/211, π1=54/211,π2=36/211,π3=24/211,π416/211
Related Book For
Applied Physics
ISBN: 978-0132109277
10th Edition
Authors: Dale ewen, Neill schurter, P. erik gundersen
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