1,721,249 research outputs found
Weakly perturbed Schwarzschild lens in the strong deflection limit
No full textWe investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang and Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining pointlike to the lowest order
GSPN Semantics for Queueing Networks with Blocking
No full textQueueing network models with finite capacity queues and blocking are used to represent systems with finite capacity resource constraints, such as production, communication and computer systems. Various blocking mechanisms have been defined in the literature to represent the different behaviours of real systems with limited resources. In this paper we propose a technique that allows to represent this type of queueing networks by means of generalized stochastic Petri nets. The method allows to obtain several benefits both for the qualitative and the quantitative analysis of these queueing networks. In particular it offers the possibility of using results and tools developed within the framework of the Petri nets. In the paper some of these potentialities are presented
On the use of structural Petri net analysis for studying product form equilibrium distributions of queueing networks with blocking
No full textIn this paper we investigate some relations between the Petri net formalism and the queueing networks with blocking. This type of queueing network models are used to represent systems with finite capacity resource constraints, such as production, communication and computer systems. Various blocking mechanisms have been defined in the literature to represent the different behaviours of real systems with limited resources. We show that the representation of these queueing networks by means of Generalized Stochastic Petri Nets offers the possibility of using results developed within the Petri net framework. In particular, we investigate product form equilibrium distributions for queueing networks with blocking by means of structural Petri net results. More precisely, we use the notion of implicit places. With this concept we characterise a class of queueing networks with blocking having interesting properties. For each queueing network of this class there exists another model with the same performance measures and exhibiting product form equilibrium distribution
Simulation of Fluid Stochastic Petri Nets
No full textThis paper describes a method for the simulation of Fluid Stochastic Petri Nets (FSPNs). The FSPNs are a promising formalism for modeling hybrid dynamic systems, that is, systems having both discrete and continuous components that evolve over time. Unfortunately analytical evaluation of performance measures of such nets requires the solution of a complex system of integro-differential equations whose numerical analysis often becomes a formidable task. One of the possible ways for computing performance measures is the use of simulative approaches. Because of the mixed (discrete and continuous) state space, simulation of FSPNs models poses some interesting challenges, which are addressed in the paper. This paper provides a simulative approach for deriving performance measures for a class of FSPNs. The techniques described in the present paper are included in a simulation tool for this class of FSPNs
An Efficient Algorithm for the Transient Analysis of a Class of Deterministic Stochastic Petri Nets
No full textIn this paper a new algorithm for the transient solution of a sub-class of Deterministic Stochastic Petri Nets (DSPN) is proposed. The technique can be applied to DSPNs comprising only deterministic and immediate transitions and such that in each tangible marking only one deterministic transition is enabled. The algorithm does not require any additional restriction on the deterministic transition delays that can have any positive real value. Most of the optimized algorithms presented in the literature are based on an efficient solution of the equations governing the stochastic process associated with the DSPN; the new algorithm we propose is based on an efficient combinatorial analysis of the paths within the state space underlying the DSPN, instead
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