171,248 research outputs found
Stochastic decomposition in discrete-time queues with generalized vacations and applications
For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a rantdom slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive proirity systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this property
Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices
Approximating the set of reachable states of a dynamical system is an
algorithmic yet mathematically rigorous way to reason about its safety.
Although progress has been made in the development of efficient algorithms for
affine dynamical systems, available algorithms still lack scalability to ensure
their wide adoption in the industrial setting. While modern linear algebra
packages are efficient for matrices with tens of thousands of dimensions,
set-based image computations are limited to a few hundred. We propose to
decompose reach set computations such that set operations are performed in low
dimensions, while matrix operations like exponentiation are carried out in the
full dimension. Our method is applicable both in dense- and discrete-time
settings. For a set of standard benchmarks, it shows a speed-up of up to two
orders of magnitude compared to the respective state-of-the art tools, with
only modest losses in accuracy. For the dense-time case, we show an experiment
with more than 10.000 variables, roughly two orders of magnitude higher than
possible with previous approaches
Decentralized Abstractions for Feedback Interconnected Multi-Agent Systems
The purpose of this report is to define abstractions for multi-agent systems
under coupled constraints. In the proposed decentralized framework, we specify
a finite or countable transition system for each agent which only takes into
account the discrete positions of its neighbors. The dynamics of the considered
systems consist of two components. An appropriate feedback law which guarantees
that certain performance requirements (eg. connectivity) are preserved and
induces the coupled constraints and additional free inputs which we exploit in
order to accomplish high level tasks. In this work we provide sufficient
conditions on the space and time discretization of the system which ensure that
we can extract a well posed and hence meaningful finite transition system.Comment: 15 page
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