2 research outputs found
Stability of Fluid Queuing Systems with Parallel Servers and Stochastic Capacities
This note introduces a piecewise-deterministic queueing (PDQ) model to study
the stability of traffic queues in parallel-link transportation systems facing
stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ
model switches between a finite set of modes according to a Markov chain, and
link inflows are controlled by a state-feedback policy. A PDQ system is stable
only if a lower bound on the time-average link inflows does not exceed the
corresponding time-average saturation rate. Furthermore, a PDQ system is stable
if the following two conditions hold: the nominal mode's saturation rate is
high enough that all queues vanish in this mode, and a bilinear matrix
inequality (BMI) involving an underestimate of the discharge rates of the PDQ
in individual modes is feasible. The stability conditions can be strengthened
for two-mode PDQs. These results can be used for design of routing policies
that guarantee stability of traffic queues under stochastic capacity
fluctuations.Comment: 20 pages, 3 figure
Effects of Information Heterogeneity in Bayesian Routing Games
This article studies the value of information in route choice decisions when
a fraction of players have access to high accuracy information about traffic
incidents relative to others. To model such environments, we introduce a
Bayesian congestion game, in which players have private information about
incidents, and each player chooses her route on a network of parallel links.
The links are prone to incidents that occur with an ex-ante known probability.
The demand is comprised of two player populations: one with access to high
accuracy incident information and another with low accuracy information, i.e.
the populations differ only by their access to information. The common
knowledge includes: (i) the demand and route cost functions, (ii) the fraction
of highly-informed players, (iii) the incident probability, and (iv) the
marginal type distributions induced by the information structure of the game.
We present a full characterization of the Bayesian Wardrop Equilibrium of this
game under the assumption that low information players receive no additional
information beyond common knowledge. We also compute the cost to individual
players and the social cost as a function of the fraction of highly-informed
players when they receive perfectly accurate information. Our first result
suggests that below a certain threshold of highly-informed players, both
populations experience a reduction in individual cost, with the highly-informed
players receiving a greater reduction. However, above this threshold, both
populations realize the same equilibrium cost. Secondly, there exists another
(lower or equal) threshold above which a further increase in the fraction of
highly-informed players does not reduce the expected social costs. Thus, once a
sufficiently large number of players are highly informed, wider distribution of
more accurate information is ineffective at best, and otherwise socially
harmful