ANALYSIS OF URBAN PUBLIC TRANSPORT NEURAL NETWORK

ABSTRACT

This thesis explores the use of neural networks to optimize urban public transport systems. By analyzing historical transit data and real-time traffic patterns, the model predicts passenger demand and enhances route planning. Various neural network architectures are tested for their accuracy and efficiency in handling transport-related data. Results show that AI-driven models can significantly improve public transport scheduling, reduce delays, and support smart city development.

АННОТАЦИЯ

Данная работа посвящена применению нейронных сетей для оптимизации систем городского общественного транспорта. Модель анализирует исторические данные о перевозках и текущие транспортные потоки, предсказывая пассажирский спрос и улучшая планирование маршрутов. Исследуются различные архитектуры нейронных сетей на предмет их точности и эффективности при работе с транспортными данными. Результаты показывают, что модели на основе ИИ способны существенно повысить эффективность расписаний, сократить задержки и способствовать развитию умных городов.

Keywords: urban public transport, neural networks, artificial intelligence, passenger flow prediction, intelligent transportation systems.

Ключевые слова: городской общественный транспорт, нейронные сети, искусственный интеллект, прогнозирование пассажиропотока, интеллектуальные транспортные системы

Introduction

Creating a formula for an Urban Public Transport Neural Network (UPTNN) involves incorporating key variables that represent various components of the urban transport system. While neural networks don’t typically work with explicit formulas in the same way traditional mathematical models do, we can break down the underlying components and represent them through mathematical expressions.

In general, neural networks work by learning patterns from data, with the architecture involving layers of neurons (nodes), weights, and biases. For a formula or mathematical framework, we can think of how neural networks might be structured for specific tasks, such as demand prediction, route optimization, or congestion prediction.

Analysis of existing formulas for the public transport equation

General Neural Network Formula:

A neural network, in its simplest form, can be represented as follows:

Where:

y = output (predictions, decisions, etc., such as number of passengers, optimal routes, etc.)

x = input vector (features like time of day, traffic data, weather, etc.)

W = weight matrix (learned parameters that transform the input data)

b = bias vector (adjustment factor for each node)

f= activation function (e.g., ReLU, sigmoid, or tanh) that determines the output of each neuron

For a single neuron:

Where:

x_i: input features, w_i: weights, b: bias, z: linear combination of weights and inputs, ϕ(z): activation function (e.g., sigmoid, ReLU, tanh), a: output of the neuron.

Now, let’s break this down for different tasks in an urban public transport neural network.

Demand Prediction Formula (Passenger Count Prediction)

Let’s say we want to predict passenger demand for a specific route at a given time.

-Inputs (x): Time of day, historical ridership, weather, special events, day of the week, etc.

-Output (y): Predicted passenger count for a given route at a specific time.

Where:

-W₁ and b₁ are weights and biases learned from historical ridership data.

- might be an activation function like ReLU or sigmoid, depending on the nature of the output (continuous or binary).

Main Body

Simple Neural Network (1 hidden layer)

Let’s consider a neural network with:

• 2 input neurons;
• 1 hidden layer with 2 neurons;
• 1 output neuron.

Assume:

• Inputs: x=[1,2];
• Hidden layer weights:   
• Hidden layer biases:

b1=[0.1,0.2]

• Activation function: ReLU, ReLU(z)=max(0,z);
• Output layer weights: W₂=[0.5,0.6];
• Output bias: b₂=0.3;

Step-by-Step calculation

Hidden layer output:

Do the dot product:

Apply ReLU:

Output layer:

The final activation is a sigmoid:

Conclusion.

The formulas above represent a high-level view of how neural networks could be applied to various aspects of an urban public transport system. The actual implementation would involve detailed training and optimization based on real-world data, making use of neural network architectures such as feedforward networks, recurrent networks, and reinforcement learning depending on the specific task.

References:

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