2,816 research outputs found
Network uncertainty in selfish routing
We study the problem of selfish routing in the presence of incomplete network information. Our model consists of a number of users who wish to route their traffic on a network of m parallel links with the objective of minimizing their latency. However, in doing so, they face the challenge of lack of precise information on the capacity of the network links. This uncertainty is modelled via a set of probability distributions over all the possibilities, one for each user. The resulting model is an amalgamation of the KP-model of [13] and the congestion games with user-specific functions of [17]. We embark on a study of Nash equilibria and the price of anarchy in this new model. In particular, we propose polynomial-time algorithms for computing some special cases of pure Nash equilibria and we show that negative results of [17], for the non-existence of pure Nash equilibria in the case of three users, do not apply to our model. Consequently, we propose an interesting open problem in this area, that of the existence of pure Nash equilibria in the general case of our model. Furthermore, we consider appropriate notions for the social cost and the price of anarchy and obtain upper bounds for the latter. With respect to fully mixed Nash equilibria, we propose a method to compute them and show that when they exist they are unique. Finally we prove that the fully mixed Nash equilibrium maximizes the social welfare. 1
Uncertainty in Multi-Commodity Routing Networks: When does it help?
We study the equilibrium behavior in a multi-commodity selfish routing game
with many types of uncertain users where each user over- or under-estimates
their congestion costs by a multiplicative factor. Surprisingly, we find that
uncertainties in different directions have qualitatively distinct impacts on
equilibria. Namely, contrary to the usual notion that uncertainty increases
inefficiencies, network congestion actually decreases when users over-estimate
their costs. On the other hand, under-estimation of costs leads to increased
congestion. We apply these results to urban transportation networks, where
drivers have different estimates about the cost of congestion. In light of the
dynamic pricing policies aimed at tackling congestion, our results indicate
that users' perception of these prices can significantly impact the policy's
efficacy, and "caution in the face of uncertainty" leads to favorable network
conditions.Comment: Currently under revie
Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty
Motivated by the massive deployment of power-hungry data centers for service
provisioning, we examine the problem of routing in optical networks with the
aim of minimizing traffic-driven power consumption. To tackle this issue,
routing must take into account energy efficiency as well as capacity
considerations; moreover, in rapidly-varying network environments, this must be
accomplished in a real-time, distributed manner that remains robust in the
presence of random disturbances and noise. In view of this, we derive a pricing
scheme whose Nash equilibria coincide with the network's socially optimum
states, and we propose a distributed learning method based on the Boltzmann
distribution of statistical mechanics. Using tools from stochastic calculus, we
show that the resulting Boltzmann routing scheme exhibits remarkable
convergence properties under uncertainty: specifically, the long-term average
of the network's power consumption converges within of its
minimum value in time which is at most ,
irrespective of the fluctuations' magnitude; additionally, if the network
admits a strict, non-mixing optimum state, the algorithm converges to it -
again, no matter the noise level. Our analysis is supplemented by extensive
numerical simulations which show that Boltzmann routing can lead to a
significant decrease in power consumption over basic, shortest-path routing
schemes in realistic network conditions.Comment: 24 pages, 4 figure
Price of Anarchy for Non-atomic Congestion Games with Stochastic Demands
We generalize the notions of user equilibrium and system optimum to
non-atomic congestion games with stochastic demands. We establish upper bounds
on the price of anarchy for three different settings of link cost functions and
demand distributions, namely, (a) affine cost functions and general
distributions, (b) polynomial cost functions and general positive-valued
distributions, and (c) polynomial cost functions and the normal distributions.
All the upper bounds are tight in some special cases, including the case of
deterministic demands.Comment: 31 page
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