-geeky version below-
We had heard that the buses in BA are “not always punctual”, but yesterday we had the opportunity to verify this criticism trying to catch #29 from La Boca. Well, probably the only thing that roughly matches the schedule is the total number of bus runs per day. Otherwise, that’s a mess – or a special kind of order, if you want. Indeed, the buses seem to be nicely grouped by numbers and to come in bunches: e.g., 5 times #152, then 3 times #33, next 4 times #64, and #152 again… We were waiting for #29 for more than one hour observing this amazing pattern. And, of course, when our bus finally arrived, it was followed by another #29. Well, at least there is a local transportation, in contrast to most of US, for example.
-geeky version-
The bus arrivals in BA can be modeled by an n-state Markov chain, where each state corresponds to one of n bus lines. The probability of self-transition is 0.9 for every line. The transition probability between any two different buses is 0.1/(n-1). What is the average waiting time (in the number of buses that pass) for #29 ?
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