Rosanna Manzo

This paper analyzes a infinite-capacity queueing system operating with multiple distinct servers. Phase-type distributions with different irreducible representations characterize the service times. The servers are indexed in a fixed order. The entry of customers is modeled according to a Markovian arrival process. Upon arrival, a customer is placed in the infinite-capacity buffer if all servers are busy. Conversely, if multiple servers are idle, the arriving customer occupies the free server with the lowest index. Jockeying between servers during service is prohibited. This system is a natural generalization of the classical system with Markovian arrival process, phase-type service distribution and N servers (MAP/PH/N) to the case where the servers can be distinct. Such a system frequently arises as a model for various real-world systems with heterogeneous equipment. A multidimensional Markov chain with an infinitesimal generator having a special block structure characterizes the state dynamics of the system. We present an explicit expression for the generator and derive the tractable ergodicity condition. The system states exhibit a matrix-geometric stationary distribution. Additionally, analytical expressions to evaluate the core system performance metrics are established. Closed-form formulations for the Laplace–Stieltjes transforms and the initial moments of the distribution regarding both sojourn and waiting times of a generic customer are derived. Finally, numerical examples are presented. These examples illustrate the dependence of the system's key performance measures on the arrival rate and the service rate of the slowest server. They also confirm the importance of accounting for correlation in the arrival process and volatility of service times and demonstrate how the results can be used for optimization purposes.

In this paper we develop a novel approach to the analysis and study of one class optimization problems with non-coercive objective functionals. With this in mind we introduce a special class fo anisotropic functional spaces. We give a precise definition of such spaces and show that they can be considered as a natural generalization of the standard Sobolev spaces. Bases on this concept, we relax of a special class of non-coercive minimization problems in Sobolev spaces W 1,2 (Ω), provide a rigorous mathematical analysis of the proposed relaxed version, establish sufficient conditions of its solvability, show that the objective functional is coercive, and derive the corresponding optimality conditions. To demonstrate the validity of the obtained results, we apply the proposed approach to the relaxation of the well-know variational model for removing multiplicative noise in image processing.

This paper focuses on differential inclusions for measures, that are differential relations whose solutions are time-evolving measures. The definition of evolution equations for measures attracted a lot of attention recently. We start by recalling the main concepts developed in the latest literature and comparing them. In particular, we show how the definition of Measure Differential Inclusion is the most general allowing to model phenomena as diffusion from a Dirac delta. Then we pass to Lyapunov-type stability proposing two concepts of stability, based on the measure support and first moment, and show relationships between such definitions depending on the assumptions on the evolution equation used.

In this paper, we analyze the numerical aspects of the practical implementation of the generalized active contour model, that has been recently proposed in the literature, for extracting agricultural crop fields with a high level of inhomogeneity from satellite data. We also derive the corresponding Euler–Lagrange equation and discuss its relaxation method.

Mostly motivated by the crop field classification problem and the automated computational methodology for extracting agricultural crop fields from satellite data, we proposed in a bounded variation (BV) space a new approach to the piecewise smooth approximation of the slope-based vegetation indices and the closely related crop field segmentation problem of multi-band satellite images.

Semi-open queueing networks are suitable for modeling complex manufacturing, health care, and logistics systems. Such networks are different from more well-known open queueing networks because the number of users, that can be serviced in the network simultaneously is restricted by a finite constant. The network loses customers who arrive when its capacity reaches its limit. This paper examined an analytical model characterized by features like the possibility to capture potential correlations in the arrival process by assuming the marked Markov arrival process and modify service rates in the network's nodes depending on the number of users currently processed in the network. A hysteresis strategy for dynamic service rate selection was assumed. Fixing the thresholds of this strategy, the behavior of the network was determined by a continuous-time multidimensional Markov chain with a finite state that is a quasi-birth-and-death process. An explicit formula for the generator of this process was obtained. Expressions for the computation of network performance measures were derived. Numerical results highlight the dependence of some measures on thresholds defining the control policy, and their use to optimize the system is illustrated.

We propose a new variational model in Sobolev-Orlicz spaces with non-standard growth conditions of the objective functional and discuss its applications to the simultaneous contrast enhancement and denoising of color images. The characteristic feature of the proposed model is that we deal with a constrained non-convex minimization problem that lives in variable Sobolev-Orlicz spaces where the variable exponent is unknown a priori and it depends on a particular function that belongs to the domain of the objective functional. In contrast to the standard approach, we do not apply any spatial regularization to the image gradient. We discuss the consistency of the variational model, give the scheme for its regularization, derive the corresponding optimality system, and propose an iterative algorithm for practical implementations.

We consider a multi-server queueing system with a visible queue and an arrival flow that is dynamically dependent on the system’s rating. This rating reflects the level of customer satisfaction with the quality and price of the provided service. A higher rating implies a higher arrival rate, which motivates the service provider to increase the price of the service. A steady-state analysis of this system using the proposed mechanism for changing the rating and a threshold strategy for changing the price is performed. This is carried out via the consideration of a suitably constructed multidimensional Markov chain. The impact of the variation in the threshold defining the strategy for changing the price on the key performance indicators is numerically illustrated. The results can be used to make managerial decisions, leading to an increase in the effectiveness of system operations.