# University of Twente Student Theses

## A mathematical model for the occupation rate in a neighborhood

Nijman, C.C.
(2019)
*A mathematical model for the occupation rate in a neighborhood.*

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Abstract: | Now a days both the population and the number of cars in the Netherlands is growing fast such that finding an empty parking space is hard. Lack of enough parking spaces leads to cruising, a time-consuming phenomenon that is bad for the environment and also for the health of people. Digital information about the number of empty parking space close by would be helpful for drivers especially during rush hour. Therefore ARS TT&T wants a model to predict the occupancy rate in a neighborhood such that information could be given to drivers who are looking for a single parking space. The main question of this research is about: To what extend can a Markov chain prediction model be used to predict the distribution of the occupancy rate of a parking lot in a neighborhood based on the ARS data files? This question was explored based on the following sub questions: How important is knowledge about the distribution of parking times for visitors and for permit holders? What is the optimum fraction of parking spaces that should be equipped with a sensor? What is the sensitivity of the fraction of with a sensor-equipped parking space? What is the sensitivity of the number of scans per day and the distribution of the scans over the day? Are there other data sources that can provide extra information? The number of cars for every minute between 9.00am and 21.00pm for 500 days on PARK200 is deduced from the data. Each minute a single parking space can be either empty or not. As it is not clear what happens with parkers at the last minute of the day it is assumed that these cars stay overnight such that the parking time of these cars is at least 720 minutes. The short- and long-term parkers are found with the distribution of the parking time. The parking process can be described as a two-dimensional Markov process with Poisson arrivals, general service or parking time, c servers or parking spaces and maximum c cars in the system. An important assumption in this process is that parkers do decide independent from each other how long they will stay at the parking place. This idea suggests that the short-term parkers in the system only influences the maximum number of long-term parkers that can enter the system at time t. The actual number of cars that enters the system depends on the parking demand and the available parking space. The situation at the parking place can be modeled as a non-homogeneous two-dimensional Markov chain. Predictions were done for each dimension separately with the first and higher order Markov chain prediction model. The transition probabilities were determined with the arrival-departure behavior and with the fit distribution of the transitions. The non-homogeneity of the chain was tackled by estimating the transition probabilities with data coming from a time interval containing time t. In this time interval it is assumed that the Markov chain is homogeneous. The research reveals that the higher order models as proposed by Chin was the best mathematical model in combination with some mathematical techniques. These techniques do take care of the two-dimensionality of the process and the non-homogeneity of the chain. There were also mathematical techniques used to correct for prediction flaws. This report starts with a section that describes the magnitude of the parking problem, followed by the problem description and a discussion of the research variables. Section two zooms in on the data sets. The next section addresses the assumptions and restrictions needed to make this study operational, followed by a mathematical problem description. Section 4 contains the mathematical concepts used in this report and section 5 a discussion of the way the model will be applied together with techniques. The next section in this report highlights some interesting results. The last section in this report regards conclusions and recommendations. |

Item Type: | Essay (Master) |

Clients: | ARS T&TT, Denhaag, Nederland |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 31 mathematics |

Programme: | Applied Mathematics MSc (60348) |

Link to this item: | https://purl.utwente.nl/essays/77279 |

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