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

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Outline

Motivational scenario– WiFi green AP

BP-based methodology Performance evaluation

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Green AP

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

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Optimization problem

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

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Realistic scenario

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

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Aps’ log

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

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User location and presence

Assumption: users are located at random around an AP Assumption: the presence probability pu for user u at time t is

evaluated as:

number of users connected at time t

number of users connected in the whole day

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Coverage graph

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Rate model

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

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Methodology for the solver

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

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Problem definition

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

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Factor graph representation

Constraints:1. User connect to at most

one AP

2. Capacity constraints

3. Users maximize their payoff

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Objective function

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”

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Validation

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

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Optimization result

results obtained by switching off the APs in Politecnico scenario

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Conclusions

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