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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. Outline.

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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


NETSTAT - Budapest 2013

  • Motivational scenario
    • WiFigreen AP
  • BP-basedmethodology
  • Performance evaluation
green ap
Green AP

NETSTAT - Budapest 2013

  • 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
optimization problem
Optimization problem

NETSTAT - Budapest 2013

  • given for each user u
    • position (xu, yu,zu)
    • probability of being present and active pu
  • given the set of possible association rates from users to APs
    • rua, 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
realistic scenario
Realistic scenario

NETSTAT - Budapest 2013

  • 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
aps log
Aps’ log

NETSTAT - Budapest 2013

  • 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
user location and presence
User location and presence

number of users connected at time t

number of users connected in the whole day

NETSTAT - Budapest 2013

Assumption: users are located at random around an AP

Assumption: the presence probability pu for user u at time t is evaluated as:

coverage graph
Coverage graph

NETSTAT - Budapest 2013

rate model
Rate model

NETSTAT - Budapest 2013

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 rua

the bandwidth among users is divided according to a standard 802.11 model taking into account the different association rates and the protocol overheads

methodology for the solver
Methodology for the solver

NETSTAT - Budapest 2013

  • 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
problem definition
Problem definition

NETSTAT - Budapest 2013

  • bipartite graph of users {u1, …, uU} and APs {s1, …, sS}
    • tu = 1 (present), 0 (absent), with probability pu
    • xs = 1 (AP on), 0 (AP off)
    • operational cost rs of AP s
    • wus = payoff of u selecting AP s
    • wsu = load on AP s by user u
    • capacity cs = maximum load on AP s
factor graph representation
Factor graph representation
  • Constraints:

User connect to atmostone AP


Usersmaximizetheir payoff

NETSTAT - Budapest 2013

objective function
Objective function

NETSTAT - Budapest 2013

  • 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”

NETSTAT - Budapest 2013

  • mirror approach vs. sampling of NEPs (4 AP, 12 users)
    • S=number of istances of t (user presence)
optimization result
Optimization result

NETSTAT - Budapest 2013

results obtained by switching off the APs in Politecnico scenario


NETSTAT - Budapest 2013

  • 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