Algorithmic aspects of bandwidth trading

We study algorithmic problems that are motivated by bandwidth trading in next-generation networks. Typically, bandwidth trading involves sellers (e.g., network operators) interested in selling bandwidth pipes that offer to buyers a guaranteed level of service for a specified time interval. The buyers (e.g., bandwidth brokers) are looking to procure bandwidth pipes to satisfy the reservation requests of end-users (e.g., Internet subscribers). Depending on what is available in the bandwidth exchange, the goal of a buyer is to either spend the least amount of money so as to satisfy all the reservations made by its customers, or to maximize its revenue from whatever reservations can be satisfied. We model this as a real-time nonpreemptive scheduling problem in which machine types correspond to bandwidth pipes and jobs correspond to end-user reservation requests. Each job specifies a time interval during which it must be processed, and a set of machine types on which it can be executed. If necessary, multiple machines of a given type may be allocated, but each must be paid for. Finally, each job has associated with it a revenue, which is realized if the job is scheduled on some machine. There are two versions of the problem that we consider. In the cost minimization version, the goal is to minimize the total cost incurred for scheduling all jobs, and in the revenue maximization version the goal is to maximize the revenue of the jobs that are scheduled for processing on a given set of machines. We consider several variants of the problems that arise in practical scenarios, and provide constant factor approximations.

[1]  Jan Karel Lenstra,et al.  Combinatorics in operations research , 1996 .

[2]  V VaziraniVijay,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001 .

[3]  David P. Williamson,et al.  A general approximation technique for constrained forest problems , 1992, SODA '92.

[4]  Rafail Ostrovsky,et al.  Approximation algorithms for the job interval selection problem and related scheduling problems , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[5]  Peter Winkler,et al.  Wavelength assignment and generalized interval graph coloring , 2003, SODA '03.

[6]  Giorgos Cheliotis,et al.  Stochastic models for telecom commodity prices , 2001, Comput. Networks.

[7]  F. Spieksma.  On the approximability of an interval scheduling problem , 1999 .

[8]  Gary L. Miller,et al.  The Complexity of Coloring Circular Arcs and Chords , 1980, SIAM J. Algebraic Discret. Methods.

[9]  Leo Kroon,et al.  On the computational complexity of (maximum) class scheduling , 1991 .

[10]  Esther M. Arkin,et al.  Scheduling jobs with fixed start and end times , 1987, Discret. Appl. Math..

[11]  O. Hudry.  R. L. Graham, M. Grötschel, L. Lovasz (sous la direction de), "Handbook of combinatorics", Amsterdam, North-Holland, 1995 (2 volumes) , 2000 .

[12]  Reuven Bar-Yehuda,et al.  A unified approach to approximating resource allocation and scheduling , 2001, JACM.

[13]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[14]  Antoon W.J. Kolen,et al.  An analysis of shift class design problems , 1994 .

[15]  Klaus Jansen,et al.  An approximation algorithm for the license and shift class design problem , 1994 .

[16]  Reuven Bar-Yehuda,et al.  A Linear-Time Approximation Algorithm for the Weighted Vertex Cover Problem , 1981, J. Algorithms.

[17]  Noga Alon,et al.  The Probabilistic Method, Second Edition , 2004 .

[18]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[19]  Sudipto Guha,et al.  Approximating the Throughput of Multiple Machines in Real-Time Scheduling , 2002, SIAM J. Comput..

[20]  Piotr Berman,et al.  Multi-phase Algorithms for Throughput Maximization for Real-Time Scheduling , 2000, J. Comb. Optim..

[21]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[22]  Giorgos Cheliotis,et al.  Bandwidth Trading in the Real World: Findings and Implications for Commodities Brokerage , 2001 .