The interest in retrial queueing systems mainly lies in their application to telephone systems. This paper studies multiserver retrial queueing systems with n servers. The arrival process is a quite general point process. An arriving customer occupies one of the free servers. If upon arrival all servers are busy, then the customer waits for his service in orbit, and after a random time retries in order to occupy a server. The orbit has one waiting space only, and an arriving customer, who finds all servers busy and the waiting space occupied, is lost from the system. Time intervals between possible retrials are assumed to have arbitrary distribution (the retrial scheme is explained more precisely in the paper). The paper provides analysis of this system. Specifically the paper studies the optimal number of servers to decrease the loss proportion to a given value. The representation obtained for the loss proportion enables us to solve the problem numerically. The algorithm for numerical solution includes effective simulation, which meets the challenge of a rare events problem in simulation.

Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines theuse of a global optimization method—AGOP—for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design.

The Faà di Bruno formulæ for higher-order derivatives of a composite function are important in analysis for a variety of applications. There is a substantial literature on the univariate case, but despite significant applications the multivariate case has until recently received limited study. We present a succinct result which is a natural generalization of the univariate version. The derivation makes use of an explicit integralform of the remainder term for multivariate Taylor expansions.

We study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halleyroot-finding algorithms, as well as the so-called c-methods. The conjugacy classes of theseiterative methods are found explicitly.

It is well known that spectral methods (tau, Galerkin, collocation) have a condition number of O(N4) where N is the number of retained modes of polynomial approximations. This paper presents some efficient spectral algorithms, which have a condition number of O(N2), based on the ultraspherical-Galerkin methods for the integrated forms of second-order elliptic equations in one and two space variables. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. The complexities of the algorithms are a small multiple of Nd+1 operations for a d-dimensional domain with (N – 1)d unknowns, while the convergence rates of the algorithms are exponentials with smooth solutions.

We present a general closed 4-point quadrature rule based on Euler-type identities. We use this rule to prove a generalization of Hadamard's inequalities for (2r)-convex functions (r ≥ 1).

A recent paper by Leipnik and Pearce introduced the gamma Weibull distribution. One of the main properties given is its characteristic function, which is expressed as an infinite sum. In this note, we provide a simpler representation in terms of the well-known hypergeometric functions in some special cases. We also derive expressions for moments of the distribution.

Three stochastic processes, the birth, death and birth-death processes, subject to immigration can be decomposed into the sum of each process in the absence of immigration and anindependent process. We examine these independent processes through their probability generating functions (pgfs) and derive their expectations.

We obtain a generalized discrete Hilbert and Hardy-Hilbert inequality with non-conjugate parameters by means of an Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our findings with existing results. We improve some earlier results and apply the results to some special homogeneous functions.

The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved to show the existence of four plane waves in a two-dimensional model. The expressions for velocities of these plane waves are obtained. The boundary conditions at the free surface are used to obtain a system of four nonhomogeneous equations. These equations are solved numerically for a particular model to obtain reflection coefficients for the incidence of coupled longitudinal displacement and coupled transverse microrotational waves. These reflection coefficients as well as the energy ratios are computed and are shown graphically with the angle of incidence in the presence and absence of thermal effects.