9,667 research outputs found
An Integer Network Flow Problem with Bridge Capacities
In this paper a modified version of dynamic network
ows is discussed. Whereas dynamic network flows are widely analyzed already, we consider a dynamic flow problem with aggregate arc capacities called Bridge
Problem which was introduced by Melkonian [Mel07]. We extend his research to integer flows and show that this problem is strongly NP-hard. For practical relevance we also introduce and analyze the hybrid bridge problem, i.e. with underlying networks whose arc capacity can limit aggregate flow (bridge problem) or the flow entering an arc at each time (general dynamic flow). For this kind of problem we present efficient procedures for
special cases that run in polynomial time. Moreover, we present a heuristic for general hybrid graphs with restriction on the number of bridge arcs.
Computational experiments show that the heuristic works well, both on random graphs and on graphs modeling also on realistic scenarios
Scheduling unit processing time arc shutdown jobs to maximize network flow over time: complexity results
We study the problem of scheduling maintenance on arcs of a capacitated
network so as to maximize the total flow from a source node to a sink node over
a set of time periods. Maintenance on an arc shuts down the arc for the
duration of the period in which its maintenance is scheduled, making its
capacity zero for that period. A set of arcs is designated to have maintenance
during the planning period, which will require each to be shut down for exactly
one time period. In general this problem is known to be NP-hard. Here we
identify a number of characteristics that are relevant for the complexity of
instance classes. In particular, we discuss instances with restrictions on the
set of arcs that have maintenance to be scheduled; series parallel networks;
capacities that are balanced, in the sense that the total capacity of arcs
entering a (non-terminal) node equals the total capacity of arcs leaving the
node; and identical capacities on all arcs
Mathematical Models and Algorithms for Network Flow Problems Arising in Wireless Sensor Network Applications
We examine multiple variations on two classical network flow problems, the maximum flow and minimum-cost flow problems. These two problems are well-studied within the optimization community, and many models and algorithms have been presented for their solution. Due to the unique characteristics of the problems we consider, existing approaches cannot be directly applied. The problem variations we examine commonly arise in wireless sensor network (WSN) applications. A WSN consists of a set of sensors and collection sinks that gather and analyze environmental conditions. In addition to providing a taxonomy of relevant literature, we present mathematical programming models and algorithms for solving such problems. First, we consider a variation of the maximum flow problem having node-capacity restrictions. As an alternative to solving a single linear programming (LP) model, we present two alternative solution techniques. The first iteratively solves two smaller auxiliary LP models, and the second is a heuristic approach that avoids solving any LP. We also examine a variation of the maximum flow problem having semicontinuous restrictions that requires the flow, if positive, on any path to be greater than or equal to a minimum threshold. To avoid solving a mixed-integer programming (MIP) model, we present a branch-and-price algorithm that significantly improves the computational time required to solve the problem. Finally, we study two dynamic network flow problems that arise in wireless sensor networks under non-simultaneous flow assumptions. We first consider a dynamic maximum flow problem that requires an arc to transmit a minimum amount of flow each time it begins transmission. We present an MIP for solving this problem along with a heuristic algorithm for its solution. Additionally, we study a dynamic minimum-cost flow problem, in which an additional cost is incurred each time an arc begins transmission. In addition to an MIP, we present an exact algorithm that iteratively solves a relaxed version of the MIP until an optimal solution is found
One More Weight is Enough: Toward the Optimal Traffic Engineering with OSPF
Traffic Engineering (TE) leverages information of network traffic to generate
a routing scheme optimizing the traffic distribution so as to advance network
performance. However, optimize the link weights for OSPF to the offered traffic
is an known NP-hard problem. In this paper, motivated by the fairness concept
of congestion control, we firstly propose a new generic objective function,
where various interests of providers can be extracted with different parameter
settings. And then, we model the optimal TE as the utility maximization of
multi-commodity flows with the generic objective function and theoretically
show that any given set of optimal routes corresponding to a particular
objective function can be converted to shortest paths with respect to a set of
positive link weights. This can be directly configured on OSPF-based protocols.
On these bases, we employ the Network Entropy Maximization(NEM) framework and
develop a new OSPF-based routing protocol, SPEF, to realize a flexible way to
split traffic over shortest paths in a distributed fashion. Actually, comparing
to OSPF, SPEF only needs one more weight for each link and provably achieves
optimal TE. Numerical experiments have been done to compare SPEF with the
current version of OSPF, showing the effectiveness of SPEF in terms of link
utilization and network load distribution
User equilibrium traffic network assignment with stochastic travel times and late arrival penalty
The classical Wardrop user equilibrium (UE) assignment model assumes traveller choices are based on fixed, known travel times, yet these times are known to be rather variable between trips, both within and between days; typically, then, only mean travel times are represented. Classical stochastic user equilibrium (SUE) methods allow the mean travel times to be differentially perceived across the population, yet in a conventional application neither the UE or SUE approach recognises the travel times to be inherently variable. That is to say, there is no recognition that drivers risk arriving late at their destinations, and that this risk may vary across different paths of the network and according to the arrival time flexibility of the traveller. Recent work on incorporating risky elements into the choice process is seen either to neglect the link to the arrival constraints of the traveller, or to apply only to restricted problems with parallel alternatives and inflexible travel time distributions. In the paper, an alternative approach is described based on the ‘schedule delay’ paradigm, penalising late arrival under fixed departure times. The approach allows flexible travel time densities, which can be fitted to actual surveillance data, to be incorporated. A generalised formulation of UE is proposed, termed a Late Arrival Penalised UE (LAPUE). Conditions for the existence and uniqueness of LAPUE solutions are considered, as well as methods for their computation. Two specific travel time models are then considered, one based on multivariate Normal arc travel times, and an extended model to represent arc incidents, based on mixture distributions of multivariate Normals. Several illustrative examples are used to examine the sensitivity of LAPUE solutions to various input parameters, and in particular its comparison with UE predictions. Finally, paths for further research are discussed, including the extension of the model to include elements such as distributed arrival time constraints and penalties
A bi-level model of dynamic traffic signal control with continuum approximation
This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure
A Complementarity Model for the European Natural Gas Market
In this paper, we present a detailed and comprehensive complementarity model for computing market equilibrium values in the European natural gas system. Market players include producers and their marketing arms which we call "transmitters", pipeline and storage operators, marketers, LNG liquefiers, regasifiers, tankers, and three end-use consumption sectors. The economic behavior of producers, transmitters, pipeline and storage operators, liquefiers and regasifiers is modeled via optimization problems whose Karush-Kuhn-Tucker (KKT) optimality conditions in combination with market-clearing conditions form the complementarity system. The LNG tankers, marketers and consumption sectors are modeled implicitly via appropriate cost functions, aggregate demand curves, and ex-post calculations, respectively. The model is run on several case studies that highlight its capabilities, including a simulation of a disruption of Russian supplies via Ukraine.European natural gas market, global LNG market, mixed complementarity problem
Polynomial Time Algorithms For Some Multi-Level Lot-Sizing Problems With Production Capacities
We consider a model for a serial supply chain in which production, inventory, and
transportation decisions are integrated, in the presence of production capacities and for
different transportation cost functions. The model we study is a generalization of the
traditional single-item economic lot-sizing model, adding stationary production capacities
at the manufacturer, as well as multiple intermediate storage levels (including the retailer
level), and transportation between these levels. Allowing for general concave production
costs and linear holding costs, we provide polynomialtime algorithms for the cases where the
transportation costs are either linear, or are concave with a fixed-charge structure. In the
latter case, we make the additional common and reasonable assumption that the variable
transportation and inventory costs are such that holding inventories at higher levels in the
supply chain is more attractive from a variable cost perspective. The running times of the
algorithms are remarkably insensitive to the number of levels in the supply chain
Dynamic traffic equilibria with route and departure time choice
This thesis studies the dynamic equilibrium behavior in traffic networks and it is motivated by rush-hour congestion. It is well understood that one of the key causes of traffic congestion relies on the behavior of road users. These do not coordinate their actions in order to avoid the creation of traffic jams, but rather make choices that favor only themselves and not the community. An equilibrium occurs when everyone is satisfied with his own choices and would not benefit from changing them. We focus on dynamic mathematical models where the congestion delay of a road varies over time, depending on the amount of traffic that has crossed it up to that specific moment and independently on the pattern of traffic that will cross it at a later time. We mainly consider settings with arbitrary network topologies where users choose both the route and departure time and we tackle questions such as the followings: - Does an equilibrium always exist? - Can there be different equilibria? - How can an equilibrium behavior be computed? - How can one set tolls on roads so that, in an equilibrium, there is no congestion and social welfare is maximized
Optimal Orchestration of Virtual Network Functions
-The emergence of Network Functions Virtualization (NFV) is bringing a set of
novel algorithmic challenges in the operation of communication networks. NFV
introduces volatility in the management of network functions, which can be
dynamically orchestrated, i.e., placed, resized, etc. Virtual Network Functions
(VNFs) can belong to VNF chains, where nodes in a chain can serve multiple
demands coming from the network edges. In this paper, we formally define the
VNF placement and routing (VNF-PR) problem, proposing a versatile linear
programming formulation that is able to accommodate specific features and
constraints of NFV infrastructures, and that is substantially different from
existing virtual network embedding formulations in the state of the art. We
also design a math-heuristic able to scale with multiple objectives and large
instances. By extensive simulations, we draw conclusions on the trade-off
achievable between classical traffic engineering (TE) and NFV infrastructure
efficiency goals, evaluating both Internet access and Virtual Private Network
(VPN) demands. We do also quantitatively compare the performance of our VNF-PR
heuristic with the classical Virtual Network Embedding (VNE) approach proposed
for NFV orchestration, showing the computational differences, and how our
approach can provide a more stable and closer-to-optimum solution
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