1. Stochastic optimization of service provision with selfish users C.F. Chiasserini, P. Giaccone, E.Leonardi Department of Electronics and Telecommunications F. Altarelli, A. Braunstein, L. Dall’Asta, R. Zecchina – Department of Applied Science and technology

2. Outline NETSTAT - Budapest 20132  Motivational scenario – WiFi green AP  BP-based methodology  Performance evaluation

3. Green AP NETSTAT - Budapest 20133  Scenario: – large WiFi network, with redundant coverage e.g., Politecnico 802.11 campus network – protocol available to turn on/off APs e.g., Energy-wise protocol implemented in Cisco devices – large population of users, each with a given probability of being present  Aim: – reduce power consumption by turning off some APs without affecting (with high probability) the minimum bandwidth of each users

4. Optimization problem NETSTAT - Budapest 20134  given for each user u – position (x u, y u,z u ) – probability of being present and active p u  given the set of possible association rates from users to APs – r ua, between user u and its neighbouring AP a  first criteria: maximize the number of APs to turn off subject to a minimum bandwidth guaranteed for each user  second criteria: maximize the achievable bandwidth

5. Realistic scenario NETSTAT - Budapest 20135  Available data from the network administrators at Politecnico – full control of the WiFI network using Cisco proprietary solutions – position(x,y,floor) and connection log of each AP

6. Aps’ log NETSTAT - Budapest 20136  20/06/2012, from 9:00 to 20:00  33 APs: for each AP, sampled every hour – AP MAC, number of associated clients, number of authenticated clients  1126 users: for each user – AP to which she is associated – association time interval – total data exchanged – average SNR/RSSI

7. User location and presence NETSTAT - Budapest 20137  Assumption: users are located at random around an AP  Assumption: the presence probability p u for user u at time t is evaluated as: number of users connected at time t number of users connected in the whole day

8. Coverage graph NETSTAT - Budapest 20138

9. Rate model NETSTAT - Budapest 20139  given the distance between user u and AP a, we adopt an empirical multifloor propagation model validated in the literature for 802.11 to evaluate the association rate of each user r ua  the bandwidth among users is divided according to a standard 802.11 model taking into account the different association rates and the protocol overheads

10. Methodology for the solver NETSTAT - Budapest 201310  use some classical iterative algorithm to turn OFF the APs – e.g. greedy decimation starting from all APs in ON state  use belief propagation(BP) to evaluate efficiently the cost function

11. Problem definition NETSTAT - Budapest 201311  bipartite graph of users {u 1, …, u U } and APs {s 1, …, s S } – t u = 1 (present), 0 (absent), with probability p u – x s = 1 (AP on), 0 (AP off) – operational cost r s of AP s – w us = payoff of u selecting AP s – w su = load on AP s by user u – capacity c s = maximum load on AP s

12. Factor graph representation NETSTAT - Budapest 201312 Constraints: 1.User connect to at most one AP 2.Capacity constraints 3.Users maximize their payoff

13. Objective function NETSTAT - Budapest 201313  evaluation process of the cost function – fix t (user presence)  selfish behavior of the users induces Nash Equilibrium Points (NEPs)  average across all NEPs – average across all t  novelty: use “mirror messages”

14. Validation NETSTAT - Budapest 201314  mirror approach vs. sampling of NEPs (4 AP, 12 users)  S=number of istances of t (user presence)

15. Optimization result NETSTAT - Budapest 201315  results obtained by switching off the APs in Politecnico scenario

16. Conclusions NETSTAT - Budapest 201316  We propose an novel belief propagation approach to compute the costs of different service configurations – averaging across all the possible Nash Equilibrium Points – more efficient than Montecarlo approaches  Useful for algorithm to solve stochastic allocation problems  Proof of concept – green AP in a corporate WiFI network