1,927 research outputs found
Slow transitions, slow mixing and starvation in dense random-access networks
We consider dense wireless random-access networks, modeled as systems of
particles with hard-core interaction. The particles represent the network users
that try to become active after an exponential back-off time, and stay active
for an exponential transmission time. Due to wireless interference, active
users prevent other nearby users from simultaneous activity, which we describe
as hard-core interaction on a conflict graph. We show that dense networks with
aggressive back-off schemes lead to extremely slow transitions between dominant
states, and inevitably cause long mixing times and starvation effects.Comment: 29 pages, 5 figure
Delay performance in random-access grid networks
We examine the impact of torpid mixing and meta-stability issues on the delay
performance in wireless random-access networks. Focusing on regular meshes as
prototypical scenarios, we show that the mean delays in an toric
grid with normalized load are of the order . This
superlinear delay scaling is to be contrasted with the usual linear growth of
the order in conventional queueing networks. The intuitive
explanation for the poor delay characteristics is that (i) high load requires a
high activity factor, (ii) a high activity factor implies extremely slow
transitions between dominant activity states, and (iii) slow transitions cause
starvation and hence excessively long queues and delays. Our proof method
combines both renewal and conductance arguments. A critical ingredient in
quantifying the long transition times is the derivation of the communication
height of the uniformized Markov chain associated with the activity process. We
also discuss connections with Glauber dynamics, conductance and mixing times.
Our proof framework can be applied to other topologies as well, and is also
relevant for the hard-core model in statistical physics and the sampling from
independent sets using single-site update Markov chains
Temporal starvation in multi-channel CSMA networks: an analytical framework
In this paper we consider a stochastic model for a frequency-agile CSMA
protocol for wireless networks where multiple orthogonal frequency channels are
available. Even when the possible interference on the different channels is
described by different conflict graphs, we show that the network dynamics can
be equivalently described as that of a single-channel CSMA algorithm on an
appropriate virtual network. Our focus is on the asymptotic regime in which the
network nodes try to activate aggressively in order to achieve maximum
throughput. Of particular interest is the scenario where the number of
available channels is not sufficient for all nodes of the network to be
simultaneously active and the well-studied temporal starvation issues of the
single-channel CSMA dynamics persist. For most networks we expect that a larger
number of available channels should alleviate these temporal starvation issues.
However, we prove that the aggregate throughput is a non-increasing function of
the number of available channels. To investigate this trade-off that emerges
between aggregate throughput and temporal starvation phenomena, we propose an
analytical framework to study the transient dynamics of multi-channel CSMA
networks by means of first hitting times. Our analysis further reveals that the
mixing time of the activity process does not always correctly characterize the
temporal starvation in the multi-channel scenario and often leads to
pessimistic performance estimates.Comment: 15 pages, 4 figures. Accepted for publication at IFIP Performance
Conference 201
Multipath streaming: fundamental limits and efficient algorithms
We investigate streaming over multiple links. A file is split into small
units called chunks that may be requested on the various links according to
some policy, and received after some random delay. After a start-up time called
pre-buffering time, received chunks are played at a fixed speed. There is
starvation if the chunk to be played has not yet arrived. We provide lower
bounds (fundamental limits) on the starvation probability of any policy. We
further propose simple, order-optimal policies that require no feedback. For
general delay distributions, we provide tractable upper bounds for the
starvation probability of the proposed policies, allowing to select the
pre-buffering time appropriately. We specialize our results to: (i) links that
employ CSMA or opportunistic scheduling at the packet level, (ii) links shared
with a primary user (iii) links that use fair rate sharing at the flow level.
We consider a generic model so that our results give insight into the design
and performance of media streaming over (a) wired networks with several paths
between the source and destination, (b) wireless networks featuring spectrum
aggregation and (c) multi-homed wireless networks.Comment: 24 page
Effect of network density and size on the short-term fairness performance of CSMA systems
As the penetration of wireless networks increase, number of neighboring networks contending for the limited unlicensed spectrum band increases. This interference between neighboring networks leads to large systems of locally interacting networks. We investigate whether the short-term fairness of this system of networks degrades with the system size and density if transmitters employ random spectrum access with carrier sensing (CSMA). Our results suggest that (a) short-term fair capacity, which is the throughput region that can be achieved within the acceptable limits of short-term fairness, reduces as the number of contending neighboring networks, i.e., degree of the conflict graph, increases for random regular conflict graphs where each vertex has the same number of neighbors, (b) short-term fair capacity weakly depends on the network size for a random regular conflict graph but a stronger dependence is observed for a grid deployment. We demonstrate the implications of this study on a city-wide Wi-Fi network deployment scenario by relating the short-term fairness to the density of deployment. We also present related results from the statistical physics literature on long-range correlations in large systems and point out the relation between these results and short-term fairness of CSMA systems. © 2012 Koseoglu et al; licensee Springer
Temporal starvation in multi-channel CSMA networks: an analytical framework
In this paper, we consider a stochastic model for a frequency-agile CSMA protocol for wireless networks where multiple orthogonal frequency channels are available. Even when the possible interference on the different channels is described by different conflict graphs, we show that the network dynamics can be equivalently described as that of a single-channel CSMA algorithm on an appropriate virtual network. Our focus is on the asymptotic regime in which the network nodes try to activate aggressively in order to achieve maximum throughput. Of particular interest is the scenario where the number of available channels is not sufficient for all nodes of the network to be simultaneously active and the well-studied temporal starvation issues of the single-channel CSMA dynamics persist. For most networks, we expect that a larger number of available channels should alleviate these temporal starvation issues. However, we prove that the aggregate throughput is a non-increasing function of the number of available channels. To investigate this trade-off that emerges between aggregate throughput and temporal starvation phenomena, we propose an analytic framework to study the transient dynamics of multi-channel CSMA networks by means of first hitting times. Our analysis further reveals that the mixing time of the activity process does not always correctly characterize the temporal starvation in the multi-channel scenario and often leads to pessimistic performance estimates
A parallelized cellular Potts model that enables simulations at tissue scale
The Cellular Potts Model (CPM) is a widely used simulation paradigm for
systems of interacting cells that has been used to study scenarios ranging from
plant development to morphogenesis, tumour growth and cell migration. Despite
their wide use, CPM simulations are considered too computationally intensive
for three-dimensional (3D) models at organ scale. CPMs have been difficult to
parallelise because of their inherently sequential update scheme. Here, we
present a Graphical Processing Unit (GPU)-based parallelisation scheme that
preserves local update statistics and is up to 3-4 orders of magnitude faster
than serial implementations. We show several examples where our scheme
preserves simulation behaviors that are drastically altered by existing
parallelisation methods. We use our framework to construct tissue-scale models
of liver and lymph node environments containing millions of cells that are
directly based on microscopy-imaged tissue structures. Thus, our GPU-based CPM
framework enables in silico studies of multicellular systems of unprecedented
scale.Comment: 29 pages, 11 figures, 3 table
Nonlinearity and stochasticity in biochemical networks
Recent advances in biology have revolutionized our understanding of living systems. For the first time, it is possible to study the behavior of individual cells. This has led to the discovery of many amazing phenomena. For example, cells have developed intelligent mechanisms for foraging, communicating, and responding to environmental changes. These diverse functions in cells are controlled through biochemical networks consisting of many different proteins and signaling molecules. These molecules interact and affect gene expression, which in turn affects protein production. This results in a complex mesh of feedback and feedforward interactions. These complex networks are generally highly nonlinear and stochastic, making them difficult to study quantitatively.
Recent studies have shown that biochemical networks are also highly modular, meaning that different parts of the network do not interact strongly with each other. These modules tend to be conserved across species and serve specific biological functions. However, detect- ing modules and identifying their function tends to be a very difficult task. To overcome some of these complexities, I present an alternative modeling approach that builds quantitative models using coarse-grained biological processes. These coarse-grained models are often stochastic (probabilistic) and highly non-linear.
In this thesis, I focus on modeling biochemical networks in two distinct biological systems: Dictyostelium discoideum and microRNAs. Chapters 2 and 3 focus on cellular communication in the social amoebae Dictyostelium discoideum. Using universality, I propose a stochastic nonlinear model that describes the behavior of individual cells and cellular populations. In chapter 4 I study the interaction between messenger RNAs and noncoding RNAs, using Langevin equations
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