83 research outputs found
A Tandem Fluid Network with L\'evy Input in Heavy Traffic
In this paper we study the stationary workload distribution of a fluid tandem
queue in heavy traffic. We consider different types of L\'evy input, covering
compound Poisson, -stable L\'evy motion (with ), and
Brownian motion. In our analysis we separately deal with L\'evy input processes
with increments that have finite and infinite variance. A distinguishing
feature of this paper is that we do not only consider the usual heavy-traffic
regime, in which the load at one of the nodes goes to unity, but also a regime
in which we simultaneously let the load of both servers tend to one, which, as
it turns out, leads to entirely different heavy-traffic asymptotics. Numerical
experiments indicate that under specific conditions the resulting simultaneous
heavy-traffic approximation significantly outperforms the usual heavy-traffic
approximation
Factorization identities for reflected processes, with applications
We derive factorization identities for a class of preemptive-resume queueing
systems, with batch arrivals and catastrophes that, whenever they occur,
eliminate multiple customers present in the system. These processes are quite
general, as they can be used to approximate Levy processes, diffusion
processes, and certain types of growth-collapse processes; thus, all of the
processes mentioned above also satisfy similar factorization identities. In the
Levy case, our identities simplify to both the well-known Wiener-Hopf
factorization, and another interesting factorization of reflected Levy
processes starting at an arbitrary initial state. We also show how the ideas
can be used to derive transforms for some well-known
state-dependent/inhomogeneous birth-death processes and diffusion processes
Data Dissemination Performance in Large-Scale Sensor Networks
As the use of wireless sensor networks increases, the need for
(energy-)efficient and reliable broadcasting algorithms grows. Ideally, a
broadcasting algorithm should have the ability to quickly disseminate data,
while keeping the number of transmissions low. In this paper we develop a model
describing the message count in large-scale wireless sensor networks. We focus
our attention on the popular Trickle algorithm, which has been proposed as a
suitable communication protocol for code maintenance and propagation in
wireless sensor networks. Besides providing a mathematical analysis of the
algorithm, we propose a generalized version of Trickle, with an additional
parameter defining the length of a listen-only period. This generalization
proves to be useful for optimizing the design and usage of the algorithm. For
single-cell networks we show how the message count increases with the size of
the network and how this depends on the Trickle parameters. Furthermore, we
derive distributions of inter-broadcasting times and investigate their
asymptotic behavior. Our results prove conjectures made in the literature
concerning the effect of a listen-only period. Additionally, we develop an
approximation for the expected number of transmissions in multi-cell networks.
All results are validated by simulations
Queues with random back-offs
We consider a broad class of queueing models with random state-dependent
vacation periods, which arise in the analysis of queue-based back-off
algorithms in wireless random-access networks. In contrast to conventional
models, the vacation periods may be initiated after each service completion,
and can be randomly terminated with certain probabilities that depend on the
queue length. We examine the scaled queue length and delay in a heavy-traffic
regime, and demonstrate a sharp trichotomy, depending on how the activation
rate and vacation probability behave as function of the queue length. In
particular, the effect of the vacation periods may either (i) completely vanish
in heavy-traffic conditions, (ii) contribute an additional term to the queue
lengths and delays of similar magnitude, or even (iii) give rise to an
order-of-magnitude increase. The heavy-traffic asymptotics are obtained by
combining stochastic lower and upper bounds with exact results for some
specific cases. The heavy-traffic trichotomy provides valuable insight in the
impact of the back-off algorithms on the delay performance in wireless
random-access networks
Singularities of the generator of a Markov additive process with one-sided jumps
We analyze the number of zeros of det(F(alpha)), where F(alpha) is the matrix cumulant generating function of a Markov Additive Process (MAP) with one-sided jumps. The focus is on th
Singularities of the generator of a Markov additive process with one-sided jumps
We analyze the number of zeros of det(F(alpha)), where F(alpha) is the matrix cumulant generating function of a Markov Additive Process (MAP) with one-sided jumps. The focus is on th
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