Bus arrivals independent random variables

In summary, the conversation discusses the use of the Poisson distribution to model bus arrivals and whether there are any mathematical explanations for this approach. The speaker also mentions a study where the Poisson distribution was found to be effective in modeling emergency ward arrivals during high traffic hours.
  • #1
Mark J.
81
0
Hi.
Why in all literature bus arrivals are referred as independent random variables (Poisson as well)?
Is there any reference where there is some math explanation except intuitive approach which of course tell that there is no correlation between 2 bus arrivals?
Best regards
 
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  • #2
Mark J. said:
Hi.
Why in all literature bus arrivals are referred as independent random variables (Poisson as well)?
Is there any reference where there is some math explanation except intuitive approach which of course tell that there is no correlation between 2 bus arrivals?
Best regards

The Poisson distribution is not a good model for vehicle traffic in general, and I wouldn't expect to be very good for scheduled bus service even though the schedule is often just a suggestion. It does work well in a number of applications including time between emergency ward arrivals during high traffic hours.

http://cs.ucsb.edu/~ravenben/classes/276/papers/pf95.pdf
 
Last edited:

What are independent random variables?

Independent random variables are variables that are not affected by each other's values. This means that the outcome of one variable does not have any impact on the outcome of the other variable.

How are bus arrivals considered independent random variables?

Bus arrivals can be considered independent random variables because the arrival time of one bus does not affect the arrival time of another bus. The arrival time of each bus is completely independent of the others.

What is the significance of considering bus arrivals as independent random variables?

The significance of considering bus arrivals as independent random variables is that it allows for more accurate predictions and analysis of bus schedules. By assuming independence, we can use statistical methods to analyze the arrival times and make better predictions for future arrivals.

Can the independence assumption of bus arrivals be violated?

Yes, the independence assumption of bus arrivals can be violated if there are external factors that affect the arrival times, such as traffic or weather conditions. In these cases, the arrivals may not be completely independent, and the analysis may need to be adjusted to account for these factors.

How can the independence assumption of bus arrivals be tested?

The independence assumption of bus arrivals can be tested using statistical methods such as correlation analysis. If there is a significant correlation between the arrival times of different buses, then the independence assumption is violated.

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