Peter Värbrand

Resource optimization of spatial TDMA in ad hoc radio networks: a column generation approach

Wireless communications using ad hoc networks are receiving an increasing interest. The most attractive feature of ad hoc networks is the flexibility. The network is set up by a number of units in an ad hoc manner, without the need of any fixed infrastructure. Communication links are established between two units if the signal strength is sufficiently high. As not all pairs of nodes can establish direct links, the traffic between two units may have to be relayed through other units. This is known as the multihop functionality. Design of ad hoc networks is a challenging task. In this paper we study the problem of resource allocation with spatial TDMA (STDMA) as the access control scheme. Previous work for this problem has mainly focused on heuristics, whose performance is difficult to analyze when optimal solutions are not known. We develop, for both node-oriented and link-oriented allocation strategies, mathematical programming formulations for resource optimization. We further present a column generation approach, which, in our numerical experiments, constantly yields optimal or near-optimal solutions. Our results provide important benchmarks when evaluating heuristic on-line algorithms for resource optimization using STDMA.

Decision support tools for ambulance dispatch and relocation

In this paper, the development of decision support tools for dynamic ambulance relocation and automatic ambulance dispatching is described. The ambulance dispatch problem is to choose which ambulance to send to a patient. The dynamic ambulance relocation problem occurs in the operational control of ambulances. The objective is to find new locations for some of the ambulances, to increase the preparedness in the area of responsibility. Preparedness is a way of evaluating the ability to serve potential patients with ambulances now and in the future. Computational tests using a simulation model show that the tools are beneficial in reducing the waiting periods for the patients.

Automated optimization of service coverage and base station antenna configuration in UMTS networks

Deployment and maintenance of UMTS networks involve optimizing a number of network configuration parameters in order to meet various service and performance requirements. In this article we address automated optimization of service coverage and radio base station antenna configuration. We consider three key configuration parameters: transmit power of the common pilot channel (CPICH), antenna tilt, and antenna azimuth. CPICH power greatly influences coverage. From a resource management point of view, satisfying the coverage requirement using minimum CPICH power offers several performance advantages. In particular, less CPICH power leads to less interference and higher system capacity. Optimal CPICH power, in its turn, is highly dependent on how the other two parameters, tilt and azimuth, are configured at radio base station antennas. Optimizing antenna tilt and azimuth network-wise, with the objective of minimizing the CPICH power consumption, is a challenging task. The solution approach in this article adopts automated optimization. Our optimization engine is a simulated annealing algorithm. Staring from an initial configuration, the algorithm searches effectively in the solution space of possible configurations in order to find improvements. The algorithm is computationally efficient; thus, we can optimize large networks without using excessive computing resources. We present a case study for a UMTS planning scenario in Lisbon. For this network, automated optimization saves up to 70 percent of the CPICH power used in the reference network configuration. In addition, the optimized network configuration offers significant performance improvement in terms of fewer overloaded cells and lower downlink load factor

A column generation method for spatial TDMA scheduling in ad hoc networks

An ad hoc network can be set up by a number of units without the need of any permanent infrastructure. Two units establish a communication link if the channel quality is sufficiently high. As not a ...

A Global Optimization Approach for the Linear Two-Level Program

Linear two-level programming deals with optimization problems in which the constraint region is implicity determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the linear two-level programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques. A small example is solved in order to illustrate the approach.

On the nucleolus of the basic vehicle routing game

In the vehicle routing cost allocation problem the aim is to find a good cost allocation method, i.e., a method that according to specified criteria allocates the cost of an optimal route configuration among the customers. We formulate this problem as a co-operative game in characteristic function form and give conditions for when the core of the vehicle routing game is nonempty.One specific solution concept to the cost allocation problem is the nucleolus, which minimizes maximum discontent among the players in a co-operative game. The class of games we study is such that the values of the characteristic function are obtained from the solution of a set of mathematical programming problems. We do not require an explicit description of the characteristic function for all coalitions. Instead, by applying a constraint generation approach, we evaluate information about the function only when it is needed for the computation of the nucleolus.

The Heterogeneous Vehicle-Routing Game

In this paper, we study a cost-allocation problem that arises in a distribution-planning situation at the Logistics Department at Norsk Hydro Olje AB, Stockholm, Sweden. We consider the routes from one depot during one day. The total distribution cost for these routes is to be divided among the customers that are visited. This cost-allocation problem is formulated as a vehicle-routing game (VRG), allowing the use of vehicles with different capacities. Cost-allocation methods based on different concepts from cooperative game theory, such as the core and the nucleolus, are discussed. A procedure that can be used to investigate whether the core is empty or not is presented, as well as a procedure to compute the nucleolus. Computational results for the Norsk Hydro case are presented and discussed.

A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of nonlinear variables

We show that the production-transportation problem involving an arbitrary fixed number of factories with concave production cost is solvable in strongly polynomial time. The algorithm is based on a parametric approach which takes full advantage of the specific structure of the problem: monotonicity of the objective function along certain directions, small proportion of nonlinear variables and combinatorial properties implied by transportation constraints.

The flight perturbation problem

Airlines spend considerable time, effort and financial resources on planning. It is essential to create a competitive timetable and construct a fleet and a crew schedule that utilizes these resources to the maximum. Unfortunately, it is all too common that an airline is faced with the necessity of reconstructing their schedules due to some unforeseen event, for example an aircraft breakdown or a crew member that is indisposed. In this paper, an application that can help airlines solve the complex problem of reconstructing aircraft schedules is presented. A mixed integer multicommodity flow model with side constraints is developed and further reformulated into a set packing model using the Dantzig—Wolfe decomposition. Cancellations, delays and aircraft swaps are used to resolve the perturbation, and the model ensures that the schedule returns to normal within a certain time. Two column generation schemes for heuristically solving the model are tested on real problem data obtained from a Swedish domestic airline. The computational tests show that the application is capable of presenting high quality solutions in a few seconds and therefore can be used as a dynamic decision support tool by the airlines.

The traveling salesman game: An application ofcost allocation in a gas and oil company

In this article, a cost allocation problem that arises in a distribution planning situation atthe Logistics Department at Norsk Hydro Olje AB is studied. A specific tour is considered,for which the total distribution cost is to be divided among the customers that are visited.This problem is formulated as a traveling salesman game, and cost allocation methods basedon different concepts from cooperative game theory, such as the nucleolus, the Shapleyvalue and the t-value, are discussed. Additionally, a new concept is introduced: the demandnucleolus. Computational results for the Norsk Hydro case are presented and discussed.