a friend of mine has asked me to help him with predictive modelling of car traffic in a medium sized parking garage. The garage has its busy and easy days, its peak hours, dead hours opening hours (it is opened during 12 hours during weekdays and during 8 hours during weekends).

The goal is to predict how many cars will enter the garage during a given day (say, tomorrow) and how are these cars supposed to be distributed over the day.

Please point me to general references (preferably, publicly available) to strategies and techniques.

Thank you

  • $\begingroup$ What exactly are you trying to model/predict here? $\endgroup$ – Nick Feb 13 '11 at 21:52
  • $\begingroup$ Thank you. I've edited the question. Hope it is now more clear $\endgroup$ – David D Feb 14 '11 at 5:12
  • $\begingroup$ Sounds like a Poisson Process problem to me. Let me see what do others think about it. $\endgroup$ – suncoolsu Feb 14 '11 at 5:18
  • $\begingroup$ See my comment to Dmitrij Celov's answer and clarify your question. $\endgroup$ – Boris Gorelik Feb 14 '11 at 12:53

The field that is relevant to the problem is the Queuing theory, a particular sub-field is a Birth-death processes. An article that in my opinion is helpful to your task is R.C. Larson and K.Satsunama (2010) Congestion Pricing: A Parking Queue Model, following the links in references would give more ideas on where to proceed.

Note, that recently R package queueing has been released (with misprint in the title however). Finally, I think, that this link for queuing software could be helpful.

  • 2
    $\begingroup$ Birth-death process attempts to analyze the throughput of the process (here, the parking garage clerk, or similar). I have a feeling that DavidD is looking for a method to predict the amount of cars that will try to check in the garage (not the queue, but the demand). $\endgroup$ – Boris Gorelik Feb 14 '11 at 12:52
  • $\begingroup$ @bgbg, the problem with parking is that cars in the garage are not staying for the whole time, when you drive into the city, you see how many free places are in a particular garage, so you decide either to occupy it or search for free of charge place somewhere else (I assume that it is a kind of the parking lot, but just underground, here I agree that more details would be useful).Since cars in the garage are not staying fro the whole day(s) so you DO need a Birth-death process to describe if a particular place is free or occupied,this time of a day and of a week. Waiting for David's comments. $\endgroup$ – Dmitrij Celov Feb 15 '11 at 9:11

Predicting hourly data has become my main interest. This problem arises normally in Call Center Forecasting. One needs to be concerned with hourly patterns within the day , different daily patterns across the week and seasonal patterns across the year ( Monthly indicators/Weekly Indicators. In addition there can be and I have seen interaction between hourly patterns and daily patterns. Transfer Function ( a generalization/super-set of Regression for time series data ) can easily accommodate the mentioned structures. Additionally events during the year (Xmas, Easter etc) need to be possibly included using lead, contemporaneous and/or lag structures. In time series analysis we need to validate via Intervention Detection schemes that there are no Pulses, Level/Step Shifts , Seasonal Pulses and/or Local Time Trends remaining in the error process suggesting an augmentation to the model. If the residual series suggests autotregressive structure then one simply adds a suitable ARIMA structure. Care should be taken when selecting a resource to deal with this problem. I recently analyzed and developed forecasts for a similar problem: the number of passengers in the Paris Subway System by hour and by day. IMHO this is a problem of constructing a useful equation from the data which can then be used to simulate possible scenarios which can then be used to evaluate queue length etc.

  • $\begingroup$ +1 Interesting examples. Are any of them accessible on the Web? $\endgroup$ – whuber Apr 1 '11 at 20:32

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