2,371 research outputs found
Selfish Routing on Dynamic Flows
Selfish routing on dynamic flows over time is used to model scenarios that
vary with time in which individual agents act in their best interest. In this
paper we provide a survey of a particular dynamic model, the deterministic
queuing model, and discuss how the model can be adjusted and applied to
different real-life scenarios. We then examine how these adjustments affect the
computability, optimality, and existence of selfish routings.Comment: Oberlin College Computer Science Honors Thesis. Supervisor: Alexa
Sharp, Oberlin Colleg
The Price of Anarchy for Selfish Ring Routing is Two
We analyze the network congestion game with atomic players, asymmetric
strategies, and the maximum latency among all players as social cost. This
important social cost function is much less understood than the average
latency. We show that the price of anarchy is at most two, when the network is
a ring and the link latencies are linear. Our bound is tight. This is the first
sharp bound for the maximum latency objective.Comment: Full version of WINE 2012 paper, 24 page
Price and Capacity Competition
We study the efficiency of oligopoly equilibria in a model where firms compete over capacities and prices. The motivating example is a communication network where service providers invest in capacities and then compete in prices. Our model economy corresponds to a two-stage game. First, firms (service providers) independently choose their capacity levels. Second, after the capacity levels are observed, they set prices. Given the capacities and prices, users (consumers) allocate their demands across the firms. We first establish the existence of pure strategy subgame perfect equilibria (oligopoly equilibria) and characterize the set of equilibria. These equilibria feature pure strategies along the equilibrium path, but off-the-equilibrium path they are supported by mixed strategies. We then investigate the efficiency properties of these equilibria, where "efficiency" is defined as the ratio of surplus in equilibrium relative to the first best. We show that efficiency in the worst oligopoly equilibria of this game can be arbitrarily low. However, if the best oligopoly equilibrium is selected (among multiple equilibria), the worst-case efficiency loss has a tight bound, approximately equal to 5/6 with 2 firms. This bound monotonically decreases towards zero when the number of firms increases. We also suggest a simple way of implementing the best oligopoly equilibrium. With two firms, this involves the lower-cost firm acting as a Stackelberg leader and choosing its capacity first. We show that in this Stackelberg game form, there exists a unique equilibrium corresponding to the best oligopoly equilibrium. We also show that an alternative game form where capacities and prices are chosen simultaneously always fails to have a pure strategy equilibrium. These results suggest that the timing of capacity and price choices in oligopolistic environments is important both for the existence of equilibrium and for the extent of efficiency losses in equilibrium.
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
Mean-Field Stochastic Differential Game for Fine Alignment Control of Cooperative Optical Beam Systems
The deployment of autonomous optical link communication platforms that
benefit from mobility and optical data rates is essential in public safety
communications. However, maintaining an accurate line-of-sight and perfect
tracking between mobile platforms or unmanned aerial vehicles (UAVs) in
free-space remains challenging for cooperative optical communication due to the
underlying mechanical vibration and accidental shocks. Indeed, a misalignment
can result in optical channel disconnection, leading to connectivity loss. To
address this challenge, we propose a two-way optical link that coordinates
mobile UAVs' closed-loop fine beam tracking operation in a swarm architecture
to enhance terrestrial public safety communication systems. We study a dynamic
of the optical beam tracking games in which each agent's dynamic and cost
function are coupled with the other optical beam transceiver agents' states via
a mean-field term. We describe a line-of-sight stochastic cooperative beam
tracking communication through a mean field game paradigm that can provide
reliable network structure and persistent distributed connectivity and
communicability. We derive two optimal mean-field beam tracking control
frameworks through decentralized and centralized strategies. The solutions of
these strategies are derived from forward-backward ordinary differential
equations and rely on the linearity Hamilton-Jacobi-Bellman Fokker-Planck
(HJB-FP) equations and stochastic maximum principle. Furthermore, we
numerically compute the solution pair to the two joint equations using Newton
and fixed point iterations methods to verify the existence and uniqueness of
the equilibrium that drives the control to a Nash equilibrium for both
differential games
Equilibrium of Heterogeneous Congestion Control: Optimality and Stability
When heterogeneous congestion control protocols
that react to different pricing signals share the same network,
the current theory based on utility maximization fails to predict
the network behavior. The pricing signals can be different types
of signals such as packet loss, queueing delay, etc, or different
values of the same type of signal such as different ECN marking
values based on the same actual link congestion level. Unlike in a
homogeneous network, the bandwidth allocation now depends on
router parameters and flow arrival patterns. It can be non-unique,
suboptimal and unstable. In Tang et al. (“Equilibrium of heterogeneous
congestion control: Existence and uniqueness,” IEEE/ACM
Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and
uniqueness of equilibrium of heterogeneous protocols are investigated.
This paper extends the study with two objectives: analyzing
the optimality and stability of such networks and designing control
schemes to improve those properties. First, we demonstrate the
intricate behavior of a heterogeneous network through simulations
and present a framework to help understand its equilibrium
properties. Second, we propose a simple source-based algorithm
to decouple bandwidth allocation from router parameters and
flow arrival patterns by only updating a linear parameter in the
sources’ algorithms on a slow timescale. It steers a network to
the unique optimal equilibrium. The scheme can be deployed
incrementally as the existing protocol needs no change and only
new protocols need to adopt the slow timescale adaptation
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