Is there a "evil" distribution which maximises the waiting time? Or is the Poisson distribution already the theoretical "evil" maximum that a public transport provider can achieve?
Send all buses at once
The Waiting Time Paradox, Or, Why Is My Bus Always Late?
81–90 of 98 posts
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#82> a Poisson process is a memoryless process that assumes the probability of an arrival is entirely independent of the time since the previous arrival. In reality, a well-run bus system will have schedules deliberately structured to avoid this kind of behavior: buses don't begin their routes at random times throughout the day, but rather begin their routes on a schedule chosen to best serve the transit-riding public.…
> Even if the bus system was poorly run, why would it make sense to assume that the expected value of time to arrival doesn't change based on how long you've been waiting? I don't think it's saying anything about how long you've been waiting, and you don't know when was the last arrival. It's saying that if you pick a random point on the timeline, the expected wait time doesn't change. That's because by taking a rand…
> I don't think it's saying anything about how long you've been waiting, and you don't know when was the last arrival.
This is exactly what memorylessness says something about.
Your second paragraph isn't unique to Poisson processes, but the author right at the start says that the expected value of the waiting time is the same as the average interarrival time, which indicates Poisson.
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#83Earlier quoted context omitted.
Same situation with the bus.
Not really. In the son/daughter case, the calculations are: expected daughters: 1 expected sons: 1/2 0 + 1/4 1 + 1/8 2 + 1/16 3 + 1/32 4 + … So number of expected daughters = 1, number of expected sons = 1. In practice since women can't have an infinite number of children, then this wouldn't be an infinite series, so the real number of expected boys would be lower than one, but there you go… Now, for the bus case, yo…
I guess it would be balanced if the rule was,
> 1 when your bus turns up, -1 for every bus going the other way.
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#84Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#85Can't believe no one has yet mentioned the PASTA theorem - Poisson Arrivals See Time Averages (https://en.wikipedia.org/wiki/Arrival_theorem#Theorem_for_ar...).
It is one of the theorems I remember the most from my Queuing Theory classes at the university!
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#86This Wikipedia article seems relevant: https://en.wikipedia.org/wiki/Residual_time
(From reddit - https://www.reddit.com/r/programming/comments/9s4j58/the_wai... )
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#87I've encountered the inspection paradox in debates about factory farming and people talking past each other points. If you take the average farm, chances are that it's doing humane farming. But if you take the average animal, it has an overwhelming chance of being in an industrial farm.
Just like if you pick an average human being she probably is poor and black/indian. But average GDP per capita is pretty high worldwide.
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#88> a Poisson process is a memoryless process that assumes the probability of an arrival is entirely independent of the time since the previous arrival. In reality, a well-run bus system will have schedules deliberately structured to avoid this kind of behavior: buses don't begin their routes at random times throughout the day, but rather begin their routes on a schedule chosen to best serve the transit-riding public.…
> What is an actual phenomenon that is well modeled by a poisson process?
Radioactive decay. Collisions of fluid molecules. Unstimulated (i.e. not in a laser) photon emission due to electron transitions in an atom. Lots of pretty memoryless stuff going on at the microscopic level.
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#89Earlier quoted context omitted.
That's a nice idea but ignores all the people sitting in their offices or homes, choosing to go or not go out of their places down to the bus stop. Better to consider each bus stop as an asset to invest in, the more valuable it is, the more people you can serve.
@mmt to clarify, you seem to be treating bus stops independent of alternative means of transportation. Measuring the average wait time of people at the bus stop is not enough: there are people who chose to ride a bike today instead of waiting at the bus stop, because of what happened to them yesterday at the bus stop.
Wow that is...quite the edit lol. I'm all for small corrections and addendums, but completely changing the meaning of your comment from an attempted callout is something else.
Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?
#90Earlier quoted context omitted.
@mmt to clarify, you seem to be treating bus stops independent of alternative means of transportation. Measuring the average wait time of people at the bus stop is not enough: there are people who chose to ride a bike today instead of waiting at the bus stop, because of what happened to them yesterday at the bus stop.
Wow that is...quite the edit lol. I'm all for small corrections and addendums, but completely changing the meaning of your comment from an attempted callout is something else.
Glad to have impressed you. My edit was intended to bring the comment in line with HN guidelines.