{
  "annotation_id": "ba8fc7b5-0d97-436a-97f6-d982dbee9048",
  "date_created": "2026-03-02T18:01:00.468000Z",
  "date_modified": "2026-03-02T18:01:00.468000Z",
  "file_hash": "1609ddfcc25470e7f31cc96917b4dece52dff9e75ce54f407a866fbe87c1eee5",
  "private": false,
  "record": {
    "abstract": "In two intersecting many-particle streams, one can often find the emergence\nof oscillatory patterns. Here, we investigate the interaction of pedestrians\nwith vehicles, when they try to cross a road. A numerical study of this coupled\npedestrian-vehicle delay problem has been presented in a previous paper. Here,\nwe focus on the analytical treatment of the problem, which requires to use a\nsimplified car-following model. Our analytical results for the phase transition\nto oscillatory pedestrian and traffic flows and the average waiting times are\nwell supported by numerical evaluations and give a detailed picture of the\ncollective dynamics emerging when pedestrians try to cross a road. The\nmathematical expressions allow one to identify the dependence on model\nparameters such as the vehicle or pedestrian arrival rate, and the safety\nfactor of pedestrian gap acceptance. We also calculate a formula for the\nvehicle time gap distribution, which corresponds to the departure time\ndistribution of a M/D/1 queue.",
    "arxiv_id": "physics/0507178",
    "authors": [
      "Dirk Helbing",
      "Rui Jiang",
      "Martin Treiber"
    ],
    "categories": [
      "physics.soc-ph"
    ],
    "doi": "10.1103/PhysRevE.72.046130",
    "journal_ref": "Physical Review E 72, 046130 (2005)",
    "title": "Analytical investigation of oscillations in intersecting flows of   pedestrian and vehicle traffic",
    "url": "https://arxiv.org/abs/physics/0507178"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "67243f71-2216-4926-bbee-80be7ebe8e19",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}