The study examines the accuracy of analytical results for a call center model represented as a retrial queueing network with impatient customers. A discrete-event simulation algorithm was developed that explicitly incorporates the structural specifics of the model, including a loss-type distributor, retrial orbit, and finite-capacity queues. Through simulation experiments, we identified the optimal number of model replications that provide sufficiently accurate approximations of the mean values of the network performance characteristics while maintaining an acceptable computational time. To enable an adequate comparison between the analytical and simulation results, the times required for both models to reach the stationary regime were analyzed. Subsequently, the accuracy of the analytical results was evaluated for the selected performance characteristics of the call center model over the stationary interval of the network. Comparative analysis revealed close agreement between simulation and analytical results in steady state, particularly under heavy load conditions. These results confirm that the asymptotic approach, based on the diffusion approximation and Fokker–Planck–Kolmogorov equation, provides accurate predictions under high load.
In the present study, we develop a novel mathematical model for COVID-19 transmission by explicitly incorporating the influence of viruses in the environment. Epidemiological evidence suggests that regions with high environmental viral concentration tend to exhibit higher infection rates, although this factor is often neglected in classical transmission models. To address this limitation, we propose a compartmental model consisting of susceptible individuals, symptomatic infected individuals, asymptomatic infected individuals, recovered individuals, and a distinct compartment representing viruses in the environment. The system dynamics are formulated using ordinary differential equations. The dynamical behavior of the model is investigated by analyzing the equilibrium points and deriving the basic reproduction number R0. Using Lyapunov’s direct method and LaSalle’s invariance principle, sufficient conditions for the local and global stability of both disease-free and endemic equilibria are established. Conditions for disease extinction and persistence are also derived. Similarly, it is inferred that the presence of viruses in the environment is responsible for disease occurrence and is associated with infection severity and threshold levels. Numerical simulations are performed to validate the analytical results and to illustrate the impact of environmental viral concentration on disease transmission.
Using only elementary facts about conditional independence, a simple proof of the Hammersley–Clifford theorem is given.
T-matrices are singular n×n real matrices, with n=2k+1, k∈N, in which apart from the elements of the first row and the middle column, all other elements are zero. We construct Drazin’s pseudo-inverse for each T-matrix.
The authors attempt here to exercise an efficient approximation scheme for obtaining highly accurate approximate solutions to Bratu-type and Troesch’s problems. The underlying mathematical ingredients of the scheme are the double exponential transformation followed by the finite Whittaker cardinal function approximation of functions in the basis generating Shannon–Kotelnikov multiresolution analysis of L2(Ω)(Ω=[a,b]⊂R). We provide a formula relating the exponent n in the desired order (O(10−n)) of accuracy and the resolution J of the approximation space (Paley–Wiener space of bandwidth [−2Jπ,2Jπ]) of multiresolution analysis of L2(R), the lower and upper limits in the finite sum in the approximation of the solution, and a formula for the a posteriori error. A comparison of the accuracy of the approximate solutions obtained with that of other results in the literature confirms the better efficiency of the present scheme.
In [Croatian Oper. Res. Rev. 13 (2022), 131–135], it was shown that the Lipschitz continuity condition with respect to the first and/or second variable has been misapplied in prior literature on systems of variational inequalities. This paper corrects errors in previous work by M. A. Noor and K. I. Noor by introducing a new iterative method.
A new class of positive linear operators is constructed by incorporating an exponential weight function with the aim of enhancing approximation performance. The convergence behavior of the proposed operators is examined using Korovkin’s theorem, and a Voronovskaja-type asymptotic formula is derived to assess the convergence rate. Comparative numerical experiments with classical operators, including Baskakov and Bernstein operators, are conducted. The results indicate that the proposed operators provide significantly improved approximation accuracy over a wider range of test functions.
The aim of this work is to improve the complexity result for the large-update method. First, we present a new 2-parameter kernel function with a hyperbolic barrier term. Then, using simple tools, we show that the complexity bound of the algorithm based on the proposed kernel function for the large-update method is O(n√lnnlnnϵ) iterations. This result matches the best-known iteration bounds for interior-point methods based on all existing types of kernel functions. Finally, to illustrate the effectiveness of the algorithm, we provide numerical tests.
We obtain an extension of multiple Markov Gaussian processes with discrete parameters to Gaussian semiflows with multiple Markov property.
In this article we concern ourselves with the study of the parallel Schwarz algorithms employed for solving advection-diffusion type partial differential equations. Schwarz algorithms, very popular in the literature as efficient methods for solving partial differential equations, were pioneered by the mathematical analyst Hermann Schwarz back in 1870. The technology behind these algorithms is that they divide the global problem into a collection of smaller subproblems, and these local problems are solved in an iterative fashion. In this study we use Fourier analysis techniques to obtain the contraction factor of the algorithms for two overlapping unbounded subdomains, by modifying the outer boundary conditions of the global domain.
This study develops an exponential inequality for widely orthant dependent random variables. We establish complete convergence and derive a convergence rate of O(1)(log2n)α1+αn−α1+α for the strong law of large numbers, where 0<α≤1. As an application to a linear model, we obtain the strong law of large numbers with a convergence rate of O(1)(log2n)2α1+αn−2α1+α, where 0<α<1. Numerical simulations are provided to illustrate and support the theoretical results.
We investigate some harmonic problems on the tangent bundle with a deformed Sasaki metric. Firstly, we study the harmonicity of a vector field with respect to this metric, and we construct some examples of harmonic vector fields. Secondly, we study the harmonicity of a vector field along a map between Riemannian manifolds, where the tangent bundle of the target manifold is equipped with a deformed Sasaki metric. Finally, we discuss the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, where the tangent bundle of the first manifold is equipped with a deformed Sasaki metric.
We consider the problem of portfolio optimization for an infinite discrete time horizon under transaction costs. We study Bellman equations for this problem. The main goal of this article is to construct a shadow price, i.e. to prove the existence of an equivalent market without transaction costs for which the optimal strategy is the same as in the market with transaction costs.
This article presents and analyzes a finite element approach for the 2D-viscoelastic wave equation with dynamic boundary conditions and strong damping. We use the Faedo–Galerkin method to prove the global existence of solutions and the multiplier approach to determine the asymptotic behavior in a bounded domain. We show and analyze typical semi-discrete systems as well as an implicit fully discrete scheme. For both semi-discrete and fully discrete methods, optimal a priori error estimates are demonstrated. Finally, some numerical findings and a priori error estimate are derived.
This paper presents an improved method for selecting the best features for data, based on the combination of the mutual information (MI) method and the chaotic binary bat algorithm (CBBA). The proposed method, named MI-CBBA, is based on three stages: (1) MI is used to rank the most relevant features in order of importance from the highest to the lowest importance, (2) a chaotic sine map is used to generate the initial population parameters for the binary bat algorithm, and (3) the binary bat algorithm is applied as an additional stage to reduce the dimensionality of the data and obtain the best features. The results obtained through application to biological data show that the proposed MI-CBBA algorithm has higher classification accuracy with a smaller number of selected features compared to the standard bat algorithm.
