I am trying to model the arrival rate (delay between the arrivals) of the cars in my city. I have some real data with the resolution of one minute. For example, Number of counted cars at position x at time 00:01 am=>5 Number of counted cars at position x at time 00:02 am=>3 ... ..
I tried to distribute the number of cars in 60 seconds randomly, but it seems that this kind of randomly distributing cars in a minute inherits the random number generator's characteristics. I tried a couple of random number functions such as Poission, but each time I got a different plot. I tried to distribute cars manually in a minute, but I got a zig-zagaed plot like "/|_/_/|".
I was wondering if you could kindly suggest any academic approach which can help me to model the arrival rates.
Kind regards
Mohsen
Hi Alex
Thanks for your reply and sorry for my slow response. I tested some theories on my dataset.
As I mentioned, I have some real data with the resolution of one minute. For example, Number of counted cars at position x at time 00:01 am=>1 Number of counted cars at position x at time 00:02 am=>2
I tried to distribute cars randomly in a minute. This is my algorithm. I used the first random number as the arrival rate and the rest as delta. ( Number of cars are measured per min, I am converting them to seconds). For example, if I have one car at 00:01 => arrival time would be a random number such as 20. two cars at 00:02 => I will generate two Rand numbers such as 24, and 30 (sum of these two should be less that 60 as we only have 60 sec in a min) hence , the first arrival time would be 24 and the second arrival time would be 54 (24+30) then I will have this
first car at 00:01:20, second car at 00:02:24 Third car ar 00:02:54
I also tested this algorithm with random data (Instead of using the actual (real) number of cars per min, I used random numbers as the number of cars per min) and distribute these events ( number of cars which generated randomly) randomly in a minute, but I got very similar plot to the plot that I got from the actual number of cars which were distributed randomly in a min. This is the point that worried me. Maybe my algorithm (using delta) is not good enough.
I found out that the total number of cars for all of the street, and for all the measured period follows Weibul distribution. In other words for all of the street and for the whole of periods:total number of cars at 00:01 , total number of cars at 00:02,..,total number of cars at 23:59 folows Weibul distribution.
I am really concerned about the accuracy of my algorithm.
Many thanks Mohsen