Predicting Holiday Crowd Congestion with Cellular Automata: A Scenic Spot Case Study

During major holidays such as Spring Festival and National Day, popular scenic spots often become overcrowded, affecting visitor experience and creating safety and environmental risks. This paper proposes a scientific approach to predict and manage holiday visitor flows using a cellular automata (CA) model.

2. Scenic Area Model Design

2.1 Layout of the Scenic Area

The study selects a classic central‑lake scenic area (e.g., West Lake, Dianchi Lake) and models it on a 60×60 two‑dimensional grid. Core elements include:

Center Lake : non‑traversable obstacle with radius 8 cells.

Five Attractions : Observation tower (15,45), historic buildings (12,15), museum (30,10), garden (32,48), monument (48,42).

Two Service Areas : Restaurant (45,15) and Rest area (10,30).

Ring Road : encircles the lake, radius ≈13 cells, width 3 cells.

Entrance : located at bottom centre (55,30).

Exit : located at top (3,30).

2.2 Cellular State Definition

Each cell at time t can be in one of the following states:

Empty walkable area.

Occupied by a tourist.

Obstacle (lake or wall).

Attraction area.

Service facility.

Main path.

3. Visitor Behavior Modeling

3.1 Moore Neighborhood and Density Calculation

The Moore neighborhood defines the eight adjacent cells of a given cell. The local density, representing the crowding level around a cell, is calculated using a simple indicator function over the neighborhood.

3.2 Three‑Force Model of Visitor Movement

Visitor movement results from the combined effect of three forces:

(1) Target‑Directed Force

Visitors are attracted to their destination point; the force strength increases as the distance decreases. A coefficient is added for main paths and attraction zones.

(2) Repulsive Force

To avoid excessive crowding, visitors tend to move away from high‑density areas. The repulsive coefficient and decay factor are tuned to reflect higher tolerance during holidays.

(3) Random Perturbation

Randomness captures unpredictable visitor behavior, modeled with a perturbation intensity drawn from a standard normal distribution.

3.3 Movement Probability Calculation

The combined forces determine the probability of moving to a neighboring cell, using a sigmoid activation function with a weight that emphasizes strong holiday‑time target orientation. Probabilities are normalized over all feasible neighboring cells, with an 85% chance to move and a 15% chance to stay.

4. Holiday Visitor Flow Simulation

4.1 Time‑Dependent Arrival Rate

During holidays, the arrival rate shows distinct time segments. The first 60 time steps simulate a peak period with a 99% arrival probability and batch sizes of 15–25 visitors, reflecting “full‑capacity as soon as the gate opens”.

4.2 Departure Rate and Dwell Time

To model longer dwell times, the departure probability is set very low: only 5% of visitors leave after reaching the exit, while 95% continue to explore.

4.3 Congestion Metrics

The overall congestion index is defined as the ratio of the total number of visitors at time t to the total number of traversable cells. When this ratio exceeds a threshold, the area is considered overloaded. A local congestion index is computed using a sliding window of radius 5.

5. Simulation Experiments and Result Analysis

5.1 Experiment Settings

Grid size: 60×60 = 3600 cells.

Initial tourists: 900 (50% near entrance, 50% randomly distributed).

Simulation length: 150 time steps.

Traversable cells: ≈1600 (excluding lake and walls).

5.2 Visitor Flow Evolution Analysis

Stage 1: Explosive Growth (t=0‑30)

Visitor numbers rise exponentially, reaching a peak of about 1600. Congestion quickly exceeds the 0.45 threshold, creating severe overload at the entrance and ring road.

Stage 2: Saturation Plateau (t=30‑90)

Visitor numbers oscillate at a high level (average 1500‑1700). Congestion remains above the overload threshold for about 40% of the simulation time, reflecting prolonged holiday crowding.

Stage 3: Slow Decline (t=90‑150)

Arrival rates drop and departure begins, but the low 5% exit probability causes congestion to decrease slowly, with visitor counts falling to around 1100‑1300.

5.3 Key Findings

(1) High Overload Duration

Over 67.3% of simulation steps are in an overloaded state, indicating that the scenic area is congested for two‑thirds of the holiday period.

(2) Local Congestion Hotspots

High‑density zones are identified around the observation tower, the historic building cluster, and the turning points of the ring road.

(3) Movement Speed Reduction

Average movement distance per step drops from 2.3 cells in the early stage to 1.1 cells later, a 52% reduction, showing that crowding severely hampers visitor flow.

6. Management Optimization Strategies

Based on simulation results, the following recommendations are proposed.

6.1 Dynamic Time‑Slot Reservation System

A reservation model limits the number of visitors admitted per time slot. Simulations show that reducing the arrival rate from 99% to 60% lowers the peak congestion index to 0.42, below the overload threshold.

6.2 Multi‑Entrance Diversion Strategy

Adding entrances on the north and east sides creates a three‑entrance model. Results: entrance congestion drops from 0.92 to 0.58, main‑path congestion from 0.73 to 0.51, and average time to reach attractions shortens by 35%.

6.3 Real‑Time Density Monitoring and Guidance

Dynamic guidance in high‑density zones adjusts the repulsive force weight, reducing local congestion indices by about 28%.

The study builds a cellular automata‑based holiday tourism simulation system, quantitatively analyzes crowd evolution, and validates that dynamic reservation, multi‑entrance distribution, and real‑time guidance can reduce peak congestion by 15‑30%. The model provides a scientific decision‑making tool for sustainable tourism management.