A Distributed Method for Optimal Capacity Reservation

We consider the problem of reserving link capacity in a network in such a way that any of a given set of flow scenarios can be supported. In the optimal capacity reservation problem, we choose the reserved link capacities to minimize the reservation cost. This problem reduces to a large linear program, with the number of variables and constraints on the order of the number of links times the number of scenarios. We develop a scalable, distributed algorithm for the problem that alternates between solving (in parallel) one-flow problem per scenario, and coordination steps, which connect the individual flows and the reservation capacities.

[1]  T. C. Hu,et al.  Synthesis of a Communication Network , 1964 .

[2]  Walid Ben-Ameur,et al.  Routing of Uncertain Traffic Demands , 2005 .

[3]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[4]  Georgios Petrou,et al.  An approach to robust network design in telecommunications , 2007, RAIRO Oper. Res..

[5]  Stephen P. Boyd,et al.  CVXPY: A Python-Embedded Modeling Language for Convex Optimization , 2016, J. Mach. Learn. Res..

[6]  Michael Poss,et al.  Affine recourse for the robust network design problem: Between static and dynamic routing , 2011, Networks.

[7]  Laurent El Ghaoui,et al.  Robust Optimization , 2021, ICORES.

[8]  M. Minoux.  Optimum Synthesis of a Network with Non-Simultaneous Multicommodity Flow Requirements* , 1981 .

[9]  Martine Labbé,et al.  Network Synthesis with Non-Simultaneous Multicommodity Flow Requirements: Bounds and Heuristics , 1999 .

[10]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[11]  Gianpaolo Oriolo,et al.  Hardness of robust network design , 2007 .

[12]  Stephen P. Boyd,et al.  ECOS: An SOCP solver for embedded systems , 2013, 2013 European Control Conference (ECC).

[13]  Stephen P. Boyd,et al.  Proximal Algorithms , 2013, Found. Trends Optim..

[14]  Walid Ben-Ameur,et al.  NEW ECONOMICAL VIRTUAL PRIVATE NETWORKS , 2003 .

[15]  T. C. Hu,et al.  An Application of Generalized Linear Programming to Network Flows , 1962 .

[16]  Walid Ben-Ameur,et al.  Networks new economical virtual private , 2003, CACM.

[17]  François Laviolette,et al.  Domain-Adversarial Training of Neural Networks , 2015, J. Mach. Learn. Res..