352 research outputs found
Spatial CSMA: A Distributed Scheduling Algorithm for the SIR Model with Time-varying Channels
Recent work has shown that adaptive CSMA algorithms can achieve throughput
optimality. However, these adaptive CSMA algorithms assume a rather simplistic
model for the wireless medium. Specifically, the interference is typically
modelled by a conflict graph, and the channels are assumed to be static. In
this work, we propose a distributed and adaptive CSMA algorithm under a more
realistic signal-to-interference ratio (SIR) based interference model, with
time-varying channels. We prove that our algorithm is throughput optimal under
this generalized model. Further, we augment our proposed algorithm by using a
parallel update technique. Numerical results show that our algorithm
outperforms the conflict graph based algorithms, in terms of supportable
throughput and the rate of convergence to steady-state.Comment: This work has been presented at National Conference on Communication,
2015, held at IIT Bombay, Mumbai, Indi
Scheduling Storms and Streams in the Cloud
Motivated by emerging big streaming data processing paradigms (e.g., Twitter
Storm, Streaming MapReduce), we investigate the problem of scheduling graphs
over a large cluster of servers. Each graph is a job, where nodes represent
compute tasks and edges indicate data-flows between these compute tasks. Jobs
(graphs) arrive randomly over time, and upon completion, leave the system. When
a job arrives, the scheduler needs to partition the graph and distribute it
over the servers to satisfy load balancing and cost considerations.
Specifically, neighboring compute tasks in the graph that are mapped to
different servers incur load on the network; thus a mapping of the jobs among
the servers incurs a cost that is proportional to the number of "broken edges".
We propose a low complexity randomized scheduling algorithm that, without
service preemptions, stabilizes the system with graph arrivals/departures; more
importantly, it allows a smooth trade-off between minimizing average
partitioning cost and average queue lengths. Interestingly, to avoid service
preemptions, our approach does not rely on a Gibbs sampler; instead, we show
that the corresponding limiting invariant measure has an interpretation
stemming from a loss system.Comment: 14 page
Stochastic switching in biology: from genotype to phenotype
There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1–1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker–Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel–Kramers–Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this review is to provide a self-contained survey of these mathematical methods, mainly within the context of biological switching processes at both the genotypic and phenotypic levels. However, applications to other examples of biological switching are also discussed, including stochastic ion channels, diffusion in randomly switching environments, bacterial chemotaxis, and stochastic neural networks
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
Adaptive access and rate control of CSMA for energy, rate and delay optimization
In this article, we present a cross-layer adaptive algorithm that dynamically maximizes the average utility function. A per stage utility function is defined for each link of a carrier sense multiple access-based wireless network as a weighted concave function of energy consumption, smoothed rate, and smoothed queue size. Hence, by selecting weights we can control the trade-off among them. Using dynamic programming, the utility function is maximized by dynamically adapting channel access, modulation, and coding according to the queue size and quality of the time-varying channel. We show that the optimal transmission policy has a threshold structure versus the channel state where the optimal decision is to transmit when the wireless channel state is better than a threshold. We also provide a queue management scheme where arrival rate is controlled based on the link state. Numerical results show characteristics of the proposed adaptation scheme and highlight the trade-off among energy consumption, smoothed data rate, and link delay.This study was supported in part by the Spanish Government, Ministerio de Ciencia e InnovaciĂłn (MICINN), under projects COMONSENS (CSD2008-00010, CONSOLIDER-INGENIO 2010 program) and COSIMA (TEC2010-19545-C04-03), in part by Iran Telecommunication Research Center under contract 6947/500, and in part by Iran National Science Foundation under grant number 87041174. This study was completed while M. Khodaian was at CEIT and TECNUN (University of Navarra)
- …