Approximate analytic solution for critical parameters in a thermal explosion problem

In this paper, a new approximate analytical solution based on the homotopy perturbation method (HPM) is applied to predict critical conditions for a thermal explosion problem. Apart from the conceptual simplicity and flexibility, the method gives rise to an easy converging solution leading to the predictions of critical parameters for thermal explosion.     

Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse

Certain diffusion processes known as semimartingale reflecting Brownian motions (SRBMs) have been shown to approximate many single class and some multiclass open queueing networks under conditions of heavy traffic. While it is known that not all multiclass networks with feedback can be approximated in heavy traffic by SRBMs, one of the outstanding challenges in contemporary research on queueing networks is to identify broad categories of networks that can be so approximated and to prove a heavy traffic limit theorem justifying the approximation. In this paper, general sufficient conditions are given under which a heavy traffic limit theorem holds for open multiclass queueing networks with head-of-the-line (HL) service disciplines, which, in particular, require that service within each class is on a first-in-first-out (FIFO) basis. The two main conditions that need to be verified are that (a) the reflection matrix for the SRBM is well defined and completely- S, and (b) a form of state space collapse holds. A result of Dai and Harrison shows that condition (a) holds for FIFO networks of Kelly type and their proof is extended here to cover networks with the HLPPS (head-of-the-line proportional processor sharing) service discipline. In a companion work, Bramson shows that a multiplicative form of state space collapse holds for these two families of networks. These results, when combined with the main theorem of this paper, yield new heavy traffic limit theorems for FIFO networks of Kelly type and networks with the HLPPS service discipline. This revised version was published online in June 2006 with corrections to the Cover Date.     

Ground state solution for a problem with mean curvature operator in Minkowski space

In this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in Minkowski space.     

Secure state estimation for complex networks with multi-channel oriented round robin protocol

This paper focuses on the secure state estimation problem for complex networks (CNs) which are compromised by deception attack and constrained with limited communication resource. Firstly, a multi-channel oriented round robin (RR) protocol is proposed to schedule the data transferred over the communication network consisting of multiple transmission channels. The extended RR protocol can not only avoid the data collision caused by limited communication resource, but also fully utilize the sliced network bandwidth. Then, a state estimation error model is constructed by further considering the influence of deception attack. Following the model, efficient state estimators are designed based on analyzing the sufficient conditions that assuring the stability of the formulated state estimation error system. Finally, numerical results are presented to validate the theoretical outcomes.     

A simulated annealing based solution approach for the two-layered location registration and paging areas partitioning problem in cellular mobile networks

This paper presents a mathematical model and simulated annealing based solution approach for finding optimal location updates and paging area configuration for mobile communication networks. We use a two-layered zone-based location registration and paging scheme in which the costs of location updates and paging signaling traffic are reduced by introducing a two-step paging process. The location updates and paging procedures in a two-layered scheme are first described, and an approximation of the measure required for calculating the paging-related signaling volume is provided based on assumptions of cell shapes and mobile stations’ movement patterns. A simulated annealing (SA)-based solution method is devised along with a greedy heuristic, and computational experiments are conducted to illustrate the superiority of the proposed SA-based method over other solution methods.     

Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

The paper is devoted to solving the two‐stage problem of stochastic programming with quantile criterion. It is assumed that the loss function is bilinear in random parameters and strategies, and the random vector has a normal distribution. Two algorithms are suggested to solve the problem, and they are compared. The first algorithm is based on the reduction of the original stochastic problem to a mixed integer linear programming problem. The second algorithm is based on the reduction of the problem to a sequence of convex programming problems. Performance characteristics of both the algorithms are illustrated by an example. A modification of both the algorithms is suggested to reduce the computing time. The new algorithm uses the solution obtained by the second algorithm as a starting point for the first algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks

In real road networks, the presence of no-left, no-right or no U-turn signs, restricts the movement of vehicles at intersections. These turn prohibitions must be considered when calculating the shortest path between a starting and an ending point in a road network. We propose an extension of Dijkstra’s algorithm to solve the shortest path problem with turn prohibitions. The method uses arc labeling and a network structure with low memory requirements. We compare the proposed method with the dual graph approach in a set of randomly generated networks and Bogotá’s large-scale road network. Our computational experiments show that the performance of the proposed method is better than that of the dual graph approach, both in terms of computing time and memory requirements. We co-developed a Web-based decision support system for computing shortest paths with turn prohibitions that uses the proposed method as the core engine.     

Existence of least energy nodal solution with two nodal domains for a generalized Kirchhoff problem in an Orlicz–Sobolev space

We show the existence of a nodal solution with two nodal domains for a generalized Kirchhoff equation of the type where Ω is a bounded domain in is a general C ¹ class function, f is a superlinear C ¹ class function with subcritical growth, Φ is defined for by setting is the operator . The proof is based on a minimization argument and a quantitative deformation lemma.     

Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities

We consider a new combinatorial optimization problem that combines network design and facility location aspects. Given a graph with two types of customers and two technologies that can be installed on the edges, the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree. In addition, besides fixed link installation costs, facility opening costs, associated to each node where primary and secondary subtree connect, have to be paid. The problem is called the Two Level Network Design Problem with Transition Facilities (TLNDF).