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Selfish Dynamic Spectrum Access in Multichannel Random Access Networks

Selfish Dynamic Spectrum Access in Multichannel Random Access Networks. Licentiate Seminar Lic. candidate: Ali Özyagci (COS/ICT/KTH) Reviewer: Alexandre Proutiere (Aut. Cont./EES/KTH) Supervisor: Jens Zander (COS/ICT/KTH). Abstract. Why: Centrally managed dynamic spectrum access (DSA)

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Selfish Dynamic Spectrum Access in Multichannel Random Access Networks

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  1. Selfish Dynamic Spectrum Access in Multichannel Random Access Networks Licentiate Seminar Lic. candidate: Ali Özyagci (COS/ICT/KTH) Reviewer: Alexandre Proutiere (Aut. Cont./EES/KTH) Supervisor: Jens Zander (COS/ICT/KTH)

  2. Abstract • Why:Centrally managed dynamic spectrum access (DSA) • May become too complex • May not scale well in large systems Distributed dynamic spectrum access • Users may start acting selfishly • What: How would selfish users access spectrum? • How: • Game theoretic analysis to obtain selfish users’ behavior • Simulations to quantify performance loss

  3. Outline • Motivation • Problem description • Short introduction to game theory • Results • Selfish MRA with complete information • Selfish MRA with incomplete information • Conclusions

  4. DSA enables efficient spectrum use but centrally controlled DSA can become complex. So, distributed mechanisms are interesting. Selfish behavior may prevail in distributed systems and efficiency may degrade We study the performance of a distributed DSA system with selfish users: - Using a Multichannel Random Access (MRA) system as an abstraction Motivation

  5. Problem description • Selfish behavior in DSA schemes with relaxed interference requirements • E.g. open spectrum regime • How do selfish users behave in a distributed DSA system? • How is selfish behavior systematically described? • How does selfish DSA performance compare with cooperative DSA systems? • What is the performance loss?

  6. Selfish behavior • Two users sharing a common channel in 2 time slots

  7. Selfish MRA with incomplete information Selfish MRA with complete information Problem description

  8. Problem description • Represent DSA as MRA system with s-ALOHA as medium access mechanism • Analyze behavior of selfish users (using game theory) • Complete & incomplete information assumptions(systems 3 and 4) • Compare system performance with cooperative systems (1 and 2) • Sum utility of system • Individual utilities of users

  9. Analysis of selfish behavior • Identify users’ mutually “stable” actions • Situations in which users do not want to change their actions • Following previous example: User 1’s actions “Pure strategy Nash equilibria”

  10. Analysis of selfish behavior • Users can behave probabilistically “Mixed strategy Nash equilibrium”

  11. Analysis of selfish behavior • If users know each other’s benefits statistically • User 1 transmits if its current benefit is greater than some threshold. • “threshold strategy”

  12. Game Theory • Systematic study of interactions between independent (rational) decision makers • “Games” are mathematical descriptions of decision makers’ possible actions and their outcomes • One representation is “strategic form” • (Players, Actions, Utilities) • A “solution” is a systematic description of situations that may arise in this interaction • “Nash equilibrium” is a common solution concept • No player has any incentive to change its action. • Pure and mixed Nash equilibria • Threshold strategies

  13. Selfish MRA with complete information N users K channels

  14. Previous work • Selfish, single-channel random access system with complete information • H. Inaltekin and S. Wicker, “The analysis of Nash equilibria of the one-shot random-access game for wireless networks and the behavior of selfish nodes,” Networking, IEEE/ACM Transactions on, vol. 16, no. 5, pp. 1094–1107, Oct. 2008. • Determine Nash equilibria of the system • Show that centrally controlled transmission probabilities are a subset of the game theoretic solution • Analyze throughput • Cooperative, multichannel random access system • W. Szpankowski, “Packet switching in multiple radio channels: Analysis and stability of a random access system,” Computer Networks (1976), vol. 7, no. 1, pp. 17 – 26, 1983. • Throughput, delay, stability analysis with a Markovian model and numerical results

  15. Our contribution [P1] • We extend previous work on selfish systems to a multi-channel random access system • Formulate the MRA system with selfish users as a non-cooperative game where users have complete information • Analytically calculate the transmission strategies at Nash equilibria in the system • Compare the performance of the selfish MRA system with the cooperative system with complete information (scheduling system) in terms of utilities

  16. Compared systems

  17. Models • Users have different pathgains on different channels • Pathloss model: D+S+R

  18. Models • Transmission cost model: • Utility model:

  19. Game theoretic analysis • Strategic form of the game in selfish MRA system: • Players: All of the N selfish users are players • Actions: To transmit on one of K channels or to wait.Mixed strategies are probability distributions on actions: • Utilities: Utilities are obtained by weighing expected channel utilities with transmit probabilities: • Nash equilibria • Pure-strategy Nash equilibria • Fully mixed Nash equilibria (all users play mixed strategies) • Partially mixed Nash equilibria (some users play pure strategies)

  20. Results • Selfish system performance comparable to cooperative systems for low loads • Not “tragedy of commons” due to pure strategy equilibria • Smaller average utility and larger variation due to multitude of Nash equilibria PDF of sum utilities N=5 K=4

  21. Selfish MRA with incomplete information

  22. Previous work • Johan Hultell, Ömer Ileri, and Jens Zander. Selfish users in energy constrained ALOHA systems with power capture. Wireless Networks, 17:199–212, 2011. 10.1007/s11276-010-0273-z. • Analyzes ALOHA with power capture using game theory under complete, incomplete information assumptions • Derives transmission strategies at Nash equilibria • Single channel analysis • Dandan Wang, C. Comaniciu, Hlaing Minn, and N. Al-Dhahir. A game-theoretic approach for exploiting multiuser diversity in cooperative slotted ALOHA. Wireless Communications, IEEE Transactions on, 7(11):4215–4225, November 2008. • Game theoretic analysis of ALOHA with incomplete info. • Utilizes pricing to improve efficiency of equilibrium • Single channel analysis

  23. Our contribution [P2, P3] • We extend previous work on selfish systems to a multi-channel random access system • Formulate the MRA system with selfish users as a non-cooperative game where users have incomplete information • For homogeneous channels and correlated pathgains we derive transmission probabilities at symmetric Nash equilibrium [P2] • For heterogeneous channels and independent pathgains, we derive transmission probabilities at all equilibria [P3] • Propose an algorithm that converges to transmission probabilities at Nash equilibria • Compare the performance of the selfish MRA system with cooperative systems in terms of utilities

  24. Models • Same as complete information case • Pathloss model: • Transmission cost model:

  25. Game theoretic analysis • Bayesian game formulation of selfish MRA system with incomplete information • Players: All of the N selfish users are players • Actions: To transmit on one of K channels or to wait. • States: All possible pathloss realizations in the MRA system • Types: Pathloss realizations of a given user in a given time slot • Signal function: Gives a player’s type depending on system’s state • Prior belief: Probability distribution assigned by each player to the system’s states • Strategies: A player’s mapping from its types to its actions • Utilities: Utility as a function of a strategy profile and system state can be defined as:

  26. Game theoretic analysis • At Nash equilibrium of a Bayesian game, players will choose strategies such that • A player, depending on its type (pathgains) in a time slot, chooses the action (channel to transmit on) which will maximize its expected utility with respect to all system state realizations (other players possible actions).

  27. DSA with incomplete information • Selfish performance comparable to cooperative distributed system for low loads. • Single selfish user in cooperative system (cheater) has large gain

  28. Heterogeneous channel models [P3] • Heterogeneity could be due to different reasons • interference, frequency dependence, etc. • We take frequency dependent pathloss model • Transmission cost model:

  29. Selfish MRA with incomplete info. and heterogeneous channels • Selfish performance comparable to scheduling system for low loads. • Performance decreases rapidly for high loads

  30. Conclusions • We analyzed selfish users’ behavior in MRA systems using game theory and obtained equilibrium strategies • Complete information: Multiple pure and mixed equilibria exist. Fully mixed equilibrium is unique. • Incomplete information: Threshold strategies. Multiple equilibria exist. Symmetric equilibrium is unique. • Selfish systems perform comparable to cooperative systems for low loads • Performance decreases rapidly for high loads • Strong incentive to act selfishly • Future work • Learning, mechanism design

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