Tính toán Cân bằng Người Dùng Động trên Các Mạng Quy Mô Lớn Mà Không Cần Biết Các Thông Số Toàn Cục

Duong Viet Thong1, Aviv Gibali2, Mathias Staudigl3, Phan Tu Vuong4
1Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Vietnam
2Department of Mathematics, ORT Braude College, Karmiel, Israel
3Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
4Mathematical Sciences, University of Southampton, Southampton, UK

Tóm tắt

Cân bằng người dùng động (DUE) là một khái niệm giải pháp giống như Nash mô tả một trạng thái cân bằng trong các hệ thống giao thông động trong một khoảng thời gian lập kế hoạch cố định. DUE là một loại bài toán cân bằng thách thức, kết nối các mô hình tải mạng và các khái niệm về trạng thái cân bằng hệ thống trong một khung toán học ngắn gọn. Gần đây, Friesz và Han đã giới thiệu một khung tích hợp cho việc tính toán DUE trên các mạng quy mô lớn, với một thuật toán điểm cố định cơ bản để tính toán DUE hiệu quả. Trong cùng công trình đó, họ trình bày một bộ công cụ MATLAB mã nguồn mở cho phép các nhà nghiên cứu kiểm tra và xác thực các bộ giải số mới. Bài báo này dựa trên đóng góp tiên phong đó và mở rộng nó theo nhiều cách quan trọng. Ở cấp độ khái niệm, chúng tôi cung cấp các thuật toán hội tụ mạnh mẽ mới được thiết kế để tính toán một DUE trực tiếp trong không gian vô hạn chiều của các dòng đường đi. Một đặc điểm quan trọng của các thuật toán của chúng tôi là chúng cung cấp các đảm bảo hội tụ có thể chứng minh mà không cần biết các thông số toàn cục. Thực tế, các thuật toán mà chúng tôi đề xuất là thích ứng, theo nghĩa là chúng không cần kiến thức a priori về các thông số toàn cục của toán tử trễ, và có thể hội tụ được ngay cả đối với các toán tử trễ không đơn điệu. Chúng tôi thực hiện các sơ đồ số của mình trên các ví dụ thử nghiệm tiêu chuẩn và so sánh chúng với chiến lược giải số mà Friesz và Han đã sử dụng.

Từ khóa

#Cân bằng người dùng động #DUE #mạng quy mô lớn #thuật toán hội tụ #toán tử trễ

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