Stochastic Control of Relay Channels With Cooperative and Strategic Users

This paper studies node cooperation in a wireless network from the MAC layer perspective. A simple relay channel with a source, a relay, and a destination node is considered where the source can transmit a packet directly to the destination or transmit through the relay. The tradeoff between average energy and delay is studied by posing the problem as a stochastic dynamical optimization problem. The following two cases are considered: 1) nodes are cooperative and information is decentralized, and 2) nodes are strategic and information is centralized. With decentralized information and cooperative nodes, a structural result is proven that the optimal policy is the solution of a Bellman-type fixed-point equation over a time invariant state space. For specific cost functions reflecting transmission energy consumption and average delay, numerical results are presented showing that a policy found by solving this fixed-point equation outperforms conventionally used time-division multiple access (TDMA) and random access (RA) policies. When nodes are strategic and information is common knowledge, it is shown that cooperation can be induced by exchange of payments between the nodes, imposed by the network designer such that the socially optimal Markov policy corresponding to the centralized solution is the unique subgame perfect equilibrium of the resulting dynamic game.

[1]  J. Filar,et al.  Competitive Markov Decision Processes , 1996 .

[2]  James E. Smith,et al.  Structural Properties of Stochastic Dynamic Programs , 2002, Oper. Res..

[3]  Refik Molva,et al.  Core: a collaborative reputation mechanism to enforce node cooperation in mobile ad hoc networks , 2002, Communications and Multimedia Security.

[4]  T. Groves,et al.  Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem' , 1977 .

[5]  H. Vincent Poor,et al.  Energy-Efficient Resource Allocation in Wireless Networks , 2007, IEEE Signal Processing Magazine.

[6]  L. Hurwicz.  Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points , 1979 .

[7]  Demosthenis Teneketzis,et al.  Local Public Good Provisioning in Networks: A Nash Implementation Mechanism , 2012, IEEE Journal on Selected Areas in Communications.

[8]  Peter Marbach,et al.  Bandwidth allocation in ad hoc networks: a price-based approach , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[9]  E. Meulen,et al.  Three-terminal communication channels , 1971, Advances in Applied Probability.

[10]  Anthony Ephremides,et al.  A game-theoretic look at simple relay channel , 2006, Wirel. Networks.

[11]  H. Witsenhausen.  A Counterexample in Stochastic Optimum Control , 1968 .

[12]  David Avis,et al.  A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra , 1992, Discret. Comput. Geom..

[13]  Narayan B. Mandayam,et al.  Pricing for enabling forwarding in self-configuring ad hoc networks , 2004, WCNC.

[14]  Demosthenis Teneketzis,et al.  On the design of globally optimal communication strategies for real-time noisy communication systems with noisy feedback , 2008, IEEE Journal on Selected Areas in Communications.

[15]  Tilman Börgers,et al.  An introduction to the theory of mechanism design , 2015 .

[16]  M. Jackson,et al.  Overcoming Incentive Constraints by Linking Decisions , 2007 .

[17]  Matthew O. Jackson,et al.  A crash course in implementation theory , 2001, Soc. Choice Welf..

[18]  D. Teneketzis,et al.  Routing in queueing networks under imperfect information: stochastic dominance and thresholds , 1989 .

[19]  Ashutosh Nayyar,et al.  On globally optimal real-time encoding and decoding strategies in multi-terminal communication systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[20]  Tamer Basar,et al.  Common Information Based Markov Perfect Equilibria for Stochastic Games With Asymmetric Information: Finite Games , 2014, IEEE Transactions on Automatic Control.

[21]  Niki Pissinou,et al.  Mitigating routing misbehavior in multi-hop networks using evolutionary game theory , 2010, 2010 IEEE Globecom Workshops.

[22]  Ashutosh Nayyar,et al.  Optimal Control Strategies in Delayed Sharing Information Structures , 2010, IEEE Transactions on Automatic Control.

[23]  Ali Kakhbod,et al.  An Efficient Game Form for Unicast Service Provisioning , 2009, IEEE Transactions on Automatic Control.

[24]  Mary Baker,et al.  Mitigating routing misbehavior in mobile ad hoc networks , 2000, MobiCom '00.

[25]  Frank H. P. Fitzek,et al.  Cooperation in Wireless Networks: Principles and Applications , 2006 .

[26]  Ali Kakhbod,et al.  An Efficient Game Form for Multi-Rate Multicast Service Provisioning , 2011, IEEE Journal on Selected Areas in Communications.

[27]  Zhu Han,et al.  Auction-Based Resource Allocation for Cooperative Communications , 2008, IEEE Journal on Selected Areas in Communications.

[28]  Pravin Varaiya,et al.  Stochastic Systems: Estimation, Identification, and Adaptive Control , 1986 .

[29]  Jie Yang,et al.  Energy Efficient Relaying Games in Cooperative Wireless Transmission Systems , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[30]  B. Hajek.  Optimal control of two interacting service stations , 1982, 1982 21st IEEE Conference on Decision and Control.

[31]  D. Bertsekas,et al.  Dynamic Programming and Stochastic Control , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[32]  Peter Marbach,et al.  Downlink resource allocation and pricing for wireless networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[33]  Ali Kakhbod,et al.  Power Allocation and Spectrum Sharing in Multi-User, Multi-Channel Systems With Strategic Users , 2010, IEEE Transactions on Automatic Control.

[34]  D. Bergemann,et al.  The Dynamic Pivot Mechanism , 2008 .

[35]  Abbas El Gamal,et al.  Capacity theorems for the relay channel , 1979, IEEE Trans. Inf. Theory.

[36]  Vikram Srinivasan,et al.  Cooperation in wireless ad hoc networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).