Necessary and sufficient condition for non-concave network utility maximisation

ABSTRACT As the popularity of intellectual-property video services growing, users have raised their expectations on better quality of services. However, the existing traffic engineering solutions are not adequate to provide such desired quality to users. This paper aims to develop the distributed, user-utility-aware and optimisation-based traffic allocation mechanisms for real applications with non-concave utility functions, and then provide a solution to the problem. We formulate the traffic allocation problem as a network utility maximisation problem with link capacity constraints. This optimisation problem is challenging because of the non-concavity of the utility functions and the lack of global information. We overcome the difficulty by designing a class of fully distributed traffic allocation control laws, which requires a minimum communication workload. Moreover, we present a necessary and sufficient condition under which the proposed control laws converge to the globally optimal solution. Finally, we present numerical simulations to illustrate the theoretical results.

[1]  Yu Zhao,et al.  Appointed-time consensus: Accurate and practical designs , 2018, Autom..

[2]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[3]  Kin K. Leung,et al.  A Non-Convex Distributed Optimization Framework and its Application to Wireless Ad-hoc Networks , 2013, IEEE Transactions on Wireless Communications.

[4]  Hao Che,et al.  Adaptive control algorithms for decentralized optimal traffic engineering in the Internet , 2004, IEEE/ACM Transactions on Networking.

[5]  Alexander L. Fradkov,et al.  Shunt Compensation for Indirect Sliding-Mode Adaptive Control , 1996 .

[6]  P. Hande,et al.  Distributed Rate Allocation for Inelastic Flows , 2007, IEEE/ACM Transactions on Networking.

[7]  Bruno Sinopoli,et al.  A Control-Theoretic Approach for Dynamic Adaptive Video Streaming over HTTP , 2015, Comput. Commun. Rev..

[8]  Yugong Luo,et al.  Robust gain-scheduling automatic steering control of unmanned ground vehicles under velocity-varying motion , 2019 .

[9]  Hao Che,et al.  Non-concave network utility maximization in connectionless networks: A fully distributed traffic allocation algorithm , 2017, 2017 American Control Conference (ACC).

[10]  Thomas Voice,et al.  Stability and fairness of explicit congestion control with small buffers , 2008, CCRV.

[11]  W. Zangwill.  Non-Linear Programming Via Penalty Functions , 1967 .

[12]  Tansu Alpcan,et al.  Convergence analysis of quantized primal-dual algorithm in quadratic network utility maximization problems , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[13]  Yugong Luo,et al.  Coordinated path-following and direct yaw-moment control of autonomous electric vehicles with sideslip angle estimation , 2018 .

[14]  Atilla Eryilmaz,et al.  Heavy-ball: A new approach to tame delay and convergence in wireless network optimization , 2016, IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications.

[15]  Hao Zhou,et al.  ADMM based algorithm for eICIC configuration in heterogeneous cellular networks , 2015, 2015 IEEE Conference on Computer Communications (INFOCOM).

[16]  Alexander A. Stotsky,et al.  Combined adaptive and Variable Structure Control , 1994 .

[17]  A. Ozdaglar,et al.  Optimal Distributed Gradient Methods for Network Resource Allocation Problems , 2013 .

[18]  Deep Medhi,et al.  Measurement of Quality of Experience of Video-on-Demand Services: A Survey , 2016, IEEE Communications Surveys & Tutorials.

[19]  Hao Che,et al.  Decentralized optimal traffic engineering in connectionless networks , 2005, IEEE Journal on Selected Areas in Communications.

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

[21]  Cisco Visual Networking Index: Forecast and Methodology 2016-2021.(2017) http://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual- networking-index-vni/complete-white-paper-c11-481360.html. High Efficiency Video Coding (HEVC) Algorithms and Architectures https://jvet.hhi.fraunhofer. , 2017 .

[22]  M. Fazel,et al.  Network Utility Maximization With Nonconcave Utilities Using Sum-of-Squares Method , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[23]  Marc Teboulle,et al.  An $O(1/k)$ Gradient Method for Network Resource Allocation Problems , 2014, IEEE Transactions on Control of Network Systems.

[24]  Guanghui Wen,et al.  Edge-Based Finite-Time Protocol Analysis With Final Consensus Value and Settling Time Estimations , 2020, IEEE Transactions on Cybernetics.

[25]  Thomas Wiegand,et al.  Efficient HTTP-based streaming using Scalable Video Coding , 2012, Signal Process. Image Commun..

[26]  K. K. Ramakrishnan,et al.  Fair and optimal resource allocation for LTE multicast (eMBMS): Group partitioning and dynamics , 2015, 2015 IEEE Conference on Computer Communications (INFOCOM).

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

[28]  Guanghui Wen,et al.  Designing Distributed Specified-Time Consensus Protocols for Linear Multiagent Systems Over Directed Graphs , 2019, IEEE Transactions on Automatic Control.

[29]  Ness B. Shroff,et al.  Non-convex optimization and rate control for multi-class services in the Internet , 2005, IEEE/ACM Transactions on Networking.

[30]  Hao Che,et al.  Non-concave network utility maximization: A distributed optimization approach , 2017, IEEE INFOCOM 2017 - IEEE Conference on Computer Communications.