There are 3 parking places outside apartment. Prob. That car seeking parking in short time dt. Adt+o(dt) Prob owner drives away in short time dt is Bdt+o(dt) State space {0,1,2,3} transitions are from 0 to 1 to 2 to 3 and vice versa Then how the rate from 0 to 1 is 3B, from 1 to 2 is 2B
From state 0 to 1, any of the three cars that are parked there can drive away, so the transition rate from 0 to 1 (or from three cars parked to two cars parked) is the sum of the transition rates of any of the three cars moving away; i.e 3 * B. Similar logic applies for the transition from 1 to 2 etc.
