28,794 research outputs found
Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks
This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc
wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints.
By dual decomposition, the resource allocation problem
naturally decomposes into three subproblems: congestion control,
routing and scheduling that interact through congestion price.
The global convergence property of this algorithm is proved. We
next extend the dual algorithm to handle networks with timevarying
channels and adaptive multi-rate devices. The stability
of the resulting system is established, and its performance is
characterized with respect to an ideal reference system which
has the best feasible rate region at link layer.
We then generalize the aforementioned results to a general
model of queueing network served by a set of interdependent
parallel servers with time-varying service capabilities, which
models many design problems in communication networks. We
show that for a general convex optimization problem where a
subset of variables lie in a polytope and the rest in a convex set,
the dual-based algorithm remains stable and optimal when the
constraint set is modulated by an irreducible finite-state Markov
chain. This paper thus presents a step toward a systematic way
to carry out cross-layer design in the framework of “layering as
optimization decomposition” for time-varying channel models
Cross-layer optimization in TCP/IP networks
TCP-AQM can be interpreted as distributed primal-dual algorithms to maximize aggregate utility over source rates. We show that an equilibrium of TCP/IP, if exists, maximizes aggregate utility over both source rates and routes, provided congestion prices are used as link costs. An equilibrium exists if and only if this utility maximization problem and its Lagrangian dual have no duality gap. In this case, TCP/IP incurs no penalty in not splitting traffic across multiple paths. Such an equilibrium, however, can be unstable. It can be stabilized by adding a static component to link cost, but at the expense of a reduced utility in equilibrium. If link capacities are optimally provisioned, however, pure static routing, which is necessarily stable, is sufficient to maximize utility. Moreover single-path routing again achieves the same utility as multipath routing at optimality
Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks
We consider massively dense ad hoc networks and study their continuum limits
as the node density increases and as the graph providing the available routes
becomes a continuous area with location and congestion dependent costs. We
study both the global optimal solution as well as the non-cooperative routing
problem among a large population of users where each user seeks a path from its
origin to its destination so as to minimize its individual cost. Finally, we
seek for a (continuum version of the) Wardrop equilibrium. We first show how to
derive meaningful cost models as a function of the scaling properties of the
capacity of the network and of the density of nodes. We present various
solution methodologies for the problem: (1) the viscosity solution of the
Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a
method based on Green's Theorem for the least cost problem of an individual,
and (3) a solution of the Wardrop equilibrium problem using a transformation
into an equivalent global optimization problem
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
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