Greedy primal-dual algorithm for dynamic resource allocation in complex networks

In Stolyar (Queueing Systems 50 (2005) 401–457) a dynamic control strategy, called greedy primal-dual (GPD) algorithm, was introduced for the problem of maximizing queueing network utility subject to stability of the queues, and was proved to be (asymptotically) optimal. (The network utility is a concave function of the average rates at which the network generates several “commodities.”) Underlying the control problem of Stolyar (Queueing Systems 50 (2005) 401–457) is a convex optimization problem subject to a set of linear constraints.In this paper we introduce a generalized GPD algorithm, which applies to the network control problem with additional convex (possibly non-linear) constraints on the average commodity rates. The underlying optimization problem in this case is a convex problem subject to convex constraints. We prove asymptotic optimality of the generalized GPD algorithm. We illustrate key features and applications of the algorithm on simple examples.

[1]  B. V. Dean,et al.  Studies in Linear and Non-Linear Programming. , 1959 .

[2]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[3]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[4]  Matthew S. Grob,et al.  CDMA/HDR: a bandwidth-efficient high-speed wireless data service for nomadic users , 2000, IEEE Commun. Mag..

[5]  Matthew Andrews,et al.  Providing quality of service over a shared wireless link , 2001, IEEE Commun. Mag..

[6]  David Tse,et al.  Opportunistic beamforming using dumb antennas , 2002, IEEE Trans. Inf. Theory.

[7]  Frank Kelly,et al.  Fairness and Stability of End-to-End Congestion Control , 2003, Eur. J. Control.

[8]  Steven H. Low,et al.  A duality model of TCP and queue management algorithms , 2003, TNET.

[9]  A. Stolyar.  MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic , 2004 .

[10]  Eytan Modiano,et al.  Fairness and Optimal Stochastic Control for Heterogeneous Networks , 2005, IEEE/ACM Transactions on Networking.

[11]  Ness B. Shroff,et al.  The impact of imperfect scheduling on cross-layer rate control in wireless networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[12]  Alexander L. Stolyar,et al.  On the Asymptotic Optimality of the Gradient Scheduling Algorithm for Multiuser Throughput Allocation , 2005, Oper. Res..

[13]  Alexander L. Stolyar,et al.  Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm , 2005, Queueing Syst. Theory Appl..

[14]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[15]  Alexander L. Stolyar,et al.  Greedy primal-dual algorithm for dynamic resource allocation in complex networks , 2006, Queueing Syst. Theory Appl..

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

[17]  R. Srikant,et al.  Fair Resource Allocation in Wireless Networks Using Queue-Length-Based Scheduling and Congestion Control , 2005, IEEE/ACM Transactions on Networking.