A splitter location–allocation problem in designing fiber optic access networks

This paper deals with a physical access network design problem of fiber-to-the-home passive optical network (FTTH-PON). The design of FTTH-PON access network seeks the cost effective location of optical splitters that provide optical connectivity from central office to subscribers in a given service area. We formulate the problem as a multi-level capacitated facility location problem on a tree topology with nonlinear link cost. Dealing with the nonlinear link cost, we propose an objective function relaxation approach to obtain tight upper and lower bounds. We develop valid inequalities that enhance the lower bound and propose a local search heuristic procedure that improves the upper bound. Valid inequalities force integrality condition on the number of splitters placed at nodes. Local search heuristic improves the initial greedy solution by placing splitters on the sub-root nodes of a given tree network. Computational results demonstrate the effectiveness of the proposed solution procedures.     

Hierarchical location–allocation models for congested systems

In this paper we address the issue of locating hierarchical facilities in the presence of congestion. Two hierarchical models are presented, where lower level servers attend requests first, and then, some of the served customers are referred to higher level servers. In the first model, the objective is to find the minimum number of servers and their locations that will cover a given region with a distance or time standard. The second model is cast as a maximal covering location (MCL) formulation. A heuristic procedure is then presented together with computational experience. Finally, some extensions of these models that address other types of spatial configurations are offered.     

Multi-source facility location–allocation and inventory problem

We consider a joint facility location–allocation and inventory problem that incorporates multiple sources of warehouses. The problem is motivated by a real situation faced by a multinational applied chemistry company. In this problem, multiple products are produced in several plants. Warehouse can be replenished by several plants together because of capabilities and capacities of plants. Each customer in this problem has stochastic demand and certain amount of safety stock must be maintained in warehouses so as to achieve certain customer service level. The problem is to determine number and locations of warehouses, allocation of customers demand and inventory levels of warehouses. The objective is to minimize the expected total cost with the satisfaction of desired demand weighted average customer lead time and desired cycle service level. The problem is formulated as a mixed integer nonlinear programming model. Utilizing approximation and transformation techniques, we develop an iterative heuristic method for the problem. An experiment study shows that the proposed procedure performs well in comparison with a lower bound.     

A location–allocation problem for a web services provider in a competitive market

Web Services have become a viable component technology in distributed e-commerce platforms. Due to the move to high-speed Internet communication and tremendous increases in computing power, network latency has begun to play a more important role in determining service response time. Hence, the locations of a Web Services provider’s facilities, customer allocation, and the number of servers at each facility have a significant impact on its performance and customer satisfaction. In this paper we introduce a location–allocation model for a Web Services provider in a duopoly competitive market. Demands for services of these servers are available at each node of a network, and a subset of nodes is to be chosen to locate one or more servers in each. The objective is to maximize the provider’s profit. The problem is formulated and analyzed. An exact solution approach is developed and the results of its efficiency are reported.     

Allocation search methods for a generalized class of location–allocation problems

We consider a generalized class of location–allocation problems, in which N new facilities are to be located in the plane with respect to M objects. Each object is associated with a convex cost function, specifying the expenses for serving the object from any location in the plane.     

A location–allocation heuristic for the capacitated multi-facility Weber problem with probabilistic customer locations

The capacitated multi-facility Weber problem is concerned with locating m facilities in the Euclidean plane, and allocating their capacities to n customers at minimum total cost. The deterministic version of the problem, which assumes that customer locations and demands are known with certainty, is a non-convex optimization problem and difficult to solve. In this work, we focus on a probabilistic extension and consider the situation where the customer locations are randomly distributed according to a bivariate distribution. We first present a mathematical programming formulation, which is even more difficult than its deterministic version. We then propose an alternate location–allocation local search heuristic generalizing the ideas used originally for the deterministic problem. In its original form, the applicability of the heuristic depends on the calculation of the expected distances between the facilities and customers, which can be done for only very few distance and probability density function combinations. We therefore propose approximation methods which make the method applicable for any distance function and bivariate location distribution.     

Correction to “Queue-proportional rate allocation with per-link information in multihop wireless networks”

There is a gap in the proofs of both Propositions 3 and 4 in the correspondence “Queue-Proportional Rate Allocation with Per-Link Information in Multihop Wireless Networks,” previously published in the Queueing Systems (see Li and Srikant 2016). We filled this gap in the proofs for the multihop networks (see Li and Srikant in Queueing Syst 84:203–210, 2016), where each route at most has two links. In this note, we completely fill the gap in the proofs in our original paper (see Li and Srikant in Queueing Syst 83:329–359, 2016).     

On the convergence of the Weiszfeld algorithm for continuous single facility location–allocation problems

A general family of single facility continuous location–allocation problems is introduced, which includes the decreasingly weighted ordered median problem, the single facility Weber problem with supply surplus, and Weber problems with alternative fast transportation network. We show in this paper that the extension of the well known Weiszfeld iterative decrease method for solving the corresponding location problems with fixed allocation yields an always convergent scheme for the location allocation problems. In a generic way, from each starting point, the limit point will be a locally minimal solution, whereas for each possible exceptional situation, a possible solution is indicated. Some computational results are presented, comparing this method with an alternating location–allocation approach. The research of the second author was partially supported by the grant of the Algerian Ministry of High Education 001BIS/PNE/ENSEIGNANTS/BELGIQUE.     

Modeling max–min fair bandwidth allocation in BitTorrent communities

This paper gives an exact mathematical programming model and algorithm of the max–min fairness bandwidth allocation problem in multi-swarm peer-to-peer content sharing community. The proposed iterative method involves solution of LP and MILP problems of large scale. Based on real-world data traces, numerical experiments demonstrate that the new algorithm is computationally faster than an earlier developed one for larger problem sizes, and it provides better numerical stability. Moreover, even if its execution is stopped after some initial steps it still grants feasible solution with good approximation to max–min fairness.     

Exact solutions for logistic reaction–diffusion equations in biology

Reaction–diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.     

Sequential location—allocation of public facilities in one- and two-dimensional space: Comparison of several policies

The present paper examines the sequential location—allocation problems of public facilities in one- and two-dimensional space under several policies. It is shown that the efficiency loss due to the adoption of a myopic policy is not so large, contrary to common belief, provided that the efficiency can be measured by the total transportation cost of users and by the total capacity of facilities. If the total serving area is sufficiently narrow, then the spatial allocations of optimal solutions in two-dimensional problems can be closely approximated by those in one-dimensional problems.     

A multirate W-method for electrical networks in state–space formulation

Subunits of coupled technical systems typically behave on differing time scales, which are often separated by several orders of magnitude. An ordinary integration scheme is limited by the fastest changing component, whereas so-called multirate methods employ an inherent step size for each subsystem to exploit these settings. However, the realization of the coupling terms is crucial for any convergence. Thus the approach to return to one-step methods within the multirate concept is promising. This paper introduces the multirate W-method for ordinary differential equations and gives a theoretical discussion in the context of partitioned Rosenbrock–Wanner methods. Finally, the MATLAB implementation of an embedded scheme of order (3)2 is tested for a multirate version of Prothero–Robinson's equation and the inverter-chain-benchmark.     

Modeling and measuring double-frequency jitter in one-way master–slave networks

The double-frequency jitter is one of the main problems in clock distribution networks. In previous works, some analytical and numerical aspects of this phenomenon were studied and results were obtained for one-way master-slave (OWMS) architectures. Here, an experimental apparatus is implemented, allowing to measure the power of the double-frequency signal and to confirm the theoretical conjectures.     

Large time behavior in a fractional chemotaxis–Navier–Stokes system with logistic source

This paper deals with a coupled chemotaxis–Navier–Stokes system with logistic source and a fractional diffusion of order on three dimensional periodic torus . Since there is no classical solution in the three-dimensional full Navier–Stokes equations, our main purpose of this paper is to investigate the global existence of weak solutions to the above system in the case of a weaker diffusion, and after some waiting time, the weak solutions in fact become smooth and converge to the semi-trivial steady state