598 research outputs found
Asymptotic Approximations for TCP Compound
In this paper, we derive an approximation for throughput of TCP Compound
connections under random losses. Throughput expressions for TCP Compound under
a deterministic loss model exist in the literature. These are obtained assuming
the window sizes are continuous, i.e., a fluid behaviour is assumed. We
validate this model theoretically. We show that under the deterministic loss
model, the TCP window evolution for TCP Compound is periodic and is independent
of the initial window size. We then consider the case when packets are lost
randomly and independently of each other. We discuss Markov chain models to
analyze performance of TCP in this scenario. We use insights from the
deterministic loss model to get an appropriate scaling for the window size
process and show that these scaled processes, indexed by p, the packet error
rate, converge to a limit Markov chain process as p goes to 0. We show the
existence and uniqueness of the stationary distribution for this limit process.
Using the stationary distribution for the limit process, we obtain
approximations for throughput, under random losses, for TCP Compound when
packet error rates are small. We compare our results with ns2 simulations which
show a good match.Comment: Longer version for NCC 201
Stochastic bounds in fork-join queueing systems under full and partial mapping
In a Fork-Join (FJ) queueing system an upstream fork station splits
incoming jobs into N tasks to be further processed by N parallel servers, each with its own queue; the response time of one job is determined, at a downstream join station, by the maximum of the corresponding tasks’ response times. This queueing system is useful to the modelling of multi-service systems subject to synchronization constraints, such as MapReduce clusters or multipath routing. Despite their apparent simplicity, FJ systems are hard to analyze. This paper provides the first computable stochastic bounds on the waiting and response time distributions in FJ systems under full (bijective) and partial (injective) mapping of tasks to servers. We consider four practical scenarios by combining 1a) renewal and 1b) non-renewal arrivals, and 2a) non-blocking and 2b) blocking servers. In the case of non-blocking servers we prove that delays scale as O(log N), a law which is known for first moments under renewal input only. In the case of blocking servers, we prove that the same factor of log N dictates the stability region of the system. Simulation results indicate that our bounds are tight, especially at high utilizations, in all four scenarios. A remarkable insight gained from our results is that, at moderate to high utilizations, multipath routing “makes sense” from a queueing perspective for two paths only, i.e., response times drop the most when N = 2; the technical explanation is that the resequencing (delay) price starts to quickly dominate the tempting gain due to multipath transmissions
Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields
This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners
Fractional moments of solutions to stochastic recurrence equations
In this paper we study the fractional moments of the stationary
solution to a stochastic recursion.
We derive recursive formulas for the fractional moments of the solution. Special attention is given to the case when
the additive term has an Erlang distribution. We provide various approximations to the
moments and show their performance in a small numerical studyGennady Samorodnitsky's research was
partially supported by the ARO
grant W911NF-07-1-0078, NSF grant DMS-1005903 and NSA grant
H98230-11-1-0154 at Cornell Universit
Renormalization of radiobiological response functions by energy loss fluctuations and complexities in chromosome aberration induction: deactivation theory for proton therapy from cells to tumor control
We employ a multi-scale mechanistic approach to investigate radiation induced
cell toxicities and deactivation mechanisms as a function of linear energy
transfer in hadron therapy. Our theoretical model consists of a system of
Markov chains in microscopic and macroscopic spatio-temporal landscapes, i.e.,
stochastic birth-death processes of cells in millimeter-scale colonies that
incorporates a coarse-grained driving force to account for microscopic
radiation induced damage. The coupling, hence the driving force in this
process, stems from a nano-meter scale radiation induced DNA damage that
incorporates the enzymatic end-joining repair and mis-repair mechanisms. We use
this model for global fitting of the high-throughput and high accuracy
clonogenic cell-survival data acquired under exposure of the therapeutic
scanned proton beams, the experimental design that considers -H2AX as
the biological endpoint and exhibits maximum observed achievable dose and LET,
beyond which the majority of the cells undergo collective biological
deactivation processes. An estimate to optimal dose and LET calculated from
tumor control probability by extension to cells per -size voxels
is presented. We attribute the increase in degree of complexity in chromosome
aberration to variabilities in the observed biological responses as the beam
linear energy transfer (LET) increases, and verify consistency of the predicted
cell death probability with the in-vitro cell survival assay of approximately
100 non-small cell lung cancer (NSCLC) cells
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