585 research outputs found
Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space
In asymptotic regimes, both in time and space (network size), the derivation
of network capacity results is grossly simplified by brushing aside queueing
behavior in non-Jackson networks. This simplifying double-limit model, however,
lends itself to conservative numerical results in finite regimes. To properly
account for queueing behavior beyond a simple calculus based on average rates,
we advocate a system theoretic methodology for the capacity problem in finite
time and space regimes. This methodology also accounts for spatial correlations
arising in networks with CSMA/CA scheduling and it delivers rigorous
closed-form capacity results in terms of probability distributions. Unlike
numerous existing asymptotic results, subject to anecdotal practical concerns,
our transient one can be used in practical settings: for example, to compute
the time scales at which multi-hop routing is more advantageous than single-hop
routing
Large deviations of an infinite-server system with a linearly scaled background process
This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates ¿i¿i by a factor NN and the transition rates ¿ij¿ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where NN tends to 88). The paper also presents qualitative properties of the system’s behavior conditional on the rare event under consideration happening. Keywords: Queues; Infinite-server systems; Markov modulation; Large deviation
Sharp Bounds in Stochastic Network Calculus
The practicality of the stochastic network calculus (SNC) is often questioned
on grounds of potential looseness of its performance bounds. In this paper it
is uncovered that for bursty arrival processes (specifically Markov-Modulated
On-Off (MMOO)), whose amenability to \textit{per-flow} analysis is typically
proclaimed as a highlight of SNC, the bounds can unfortunately indeed be very
loose (e.g., by several orders of magnitude off). In response to this uncovered
weakness of SNC, the (Standard) per-flow bounds are herein improved by deriving
a general sample-path bound, using martingale based techniques, which
accommodates FIFO, SP, EDF, and GPS scheduling. The obtained (Martingale)
bounds gain an exponential decay factor of in
the number of flows . Moreover, numerical comparisons against simulations
show that the Martingale bounds are remarkably accurate for FIFO, SP, and EDF
scheduling; for GPS scheduling, although the Martingale bounds substantially
improve the Standard bounds, they are numerically loose, demanding for
improvements in the core SNC analysis of GPS
Two-dimensional fluid queues with temporary assistance
We consider a two-dimensional stochastic fluid model with ON-OFF inputs
and temporary assistance, which is an extension of the same model with
in Mahabhashyam et al. (2008). The rates of change of both buffers are
piecewise constant and dependent on the underlying Markovian phase of the
model, and the rates of change for Buffer 2 are also dependent on the specific
level of Buffer 1. This is because both buffers share a fixed output capacity,
the precise proportion of which depends on Buffer 1. The generalization of the
number of ON-OFF inputs necessitates modifications in the original rules of
output-capacity sharing from Mahabhashyam et al. (2008) and considerably
complicates both the theoretical analysis and the numerical computation of
various performance measures
Two extensions of Kingman's GI/G/1 bound
A simple bound in GI/G/1 queues was obtained by Kingman using a discrete martingale transform. We extend this technique to 1) multiclass queues and 2) Markov Additive Processes (MAPs) whose background processes can be time-inhomogeneous or have an uncountable state-space. Both extensions are facilitated by a necessary and sufficient ordinary differential equation (ODE) condition for MAPs to admit continuous martingale transforms. Simulations show that the bounds on waiting time distributions are almost exact in heavy-traffic, including the cases of 1) heterogeneous input, e.g., mixing Weibull and Erlang-k classes and 2) Generalized Markovian Arrival Processes, a new class extending the Batch Markovian Arrival Processes to continuous batch sizes
Fluid flow models in performance analysis
We review several developments in fluid flow models: feedback fluid models, linear stochastic fluid networks and bandwidth sharing networks. We also mention some promising new research directions
Asymptotic analysis by the saddle point method of the Anick-Mitra-Sondhi model
We consider a fluid queue where the input process consists of N identical
sources that turn on and off at exponential waiting times. The server works at
the constant rate c and an on source generates fluid at unit rate. This model
was first formulated and analyzed by Anick, Mitra and Sondhi. We obtain an
alternate representation of the joint steady state distribution of the buffer
content and the number of on sources. This is given as a contour integral that
we then analyze for large N. We give detailed asymptotic results for the joint
distribution, as well as the associated marginal and conditional distributions.
In particular, simple conditional limits laws are obtained. These shows how the
buffer content behaves conditioned on the number of active sources and vice
versa. Numerical comparisons show that our asymptotic results are very accurate
even for N=20
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
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