Energy aware proactive optimized link state routing in mobile ad-hoc networks

In this paper we develop a novel energy aware routing approach for mobile ad hoc network (MANET) problems. The approach is based on using Optimized Link State Routing Protocol. Our Energy Aware OLSR labeled as OLSR_EA measures and predicts per-interval energy consumptions using the well-known Auto-Regressive Integrated Moving Average time series method. We develop a composite energy cost, by considering transmission power consumption and residual energy of each node, and use this composite energy index as the routing metric. Our extensive ns2 simulation experiments show that OLSR_EA substantially prolongs the network lifetime and saves total energy used in MANET. In our experiments we considered different scenarios considering a variety of traffic loads, node mobilities, homogeneous power consumption, and heterogeneous power consumption. Simulation results also confirm that OLSR_EA improves the traffic balance between nodes, and packet delivery ratio in higher node speed. We further develop characteristics of OLSR_EA in power-wise heterogeneous MANET to achieve efficient energy preserving performance.     

Optimal placement,scheduling, and routing to maximize lifetime in sensor networks

A wireless sensor network is a network consisting of distributed autonomouselectronic devices called sensors. Sensors have limited energy and capabilityfor sensing, data processing, and communicating, but they can collectivelybehave to provide an effective network that monitors an area and transmitinformation to gateway nodes or sinks, either directly or through other sensornodes. In most applications the network must operate for long periods of time,so the available energy resources of the sensors must be managed efficiently. Inthis paper, we first develop a mixed integer linear programming model tomaximize network lifetime by optimally determining locations of sensors andsinks, activity schedules of deployed sensors, and data flow routes from sensorsto sinks over a finite planning horizon subject to coverage, flow conservation,energy consumption, and budget constraints. Unfortunately, it is difficult tosolve this model exactly even for small instances. Therefore, we propose twoapproximate solution methods: a Lagrangean heuristic and a two-stage heuristicin which sensors are deployed and an activity schedule is found in the firststage, whereas sinks are located and sensor-to-sink data flow routes aredetermined in the second stage. Computational experiments performed on varioustest instances indicate that the Lagrangean heuristic is both efficient andaccurate and also outperforms the two-stage heuristic.     

Optimal routing in non-geostationary satellite ATM networks with intersatellite link capacity constraints

The trend toward broadband communications in space is foreseeable, and its features predestine ATM as the basic mode of operation. Some of the low and medium earth orbit satellite concepts make use of intersatellite links (ISLs) to provide global connectivity with minimal usage of terrestrial fixed network resources. Interconnecting neighbouring satellites with ISLs results in a partially meshed switching subnetwork in space. The ISLs have a time-varying distance or may even lose sight of each other. This feature of the ISL topology dynamics significantly increases the complexity of connection-oriented network operation and routing. We deal with the routing problem to minimize the virtual path connection handover rate and path delay in the time-varying ISL subnetwork topology with ISL capacity constraints. A heuristic algorithm is proposed to deal with this problem, which is based on Lagrangean relaxation and dynamic programming. When there is sufficient capacity at every ISL, the algorithm produces an optimal solution easily using only dynamic programming. For evaluation of our algorithm, some computational results have been presented. These results show that our optimization algorithm can produce a solution close to an optimal solution when there exist ISL capacity constraints.     

Variational approximations in energy space for the regulator problem with time delay

We consider a variational procedure for approximating the solution of the state regulator problem with time delay. Motivated by a dual formulation of the problem, we introduce a positive-definite functionalF over a certain energy space of Mikhlin and obtain approximating solutions by the Ritz-Trefftz idea of minimizing it over finite-dimensional subspaces. The resulting approximating solutions, in turn, furnish suboptimal solutions which converge to the optimal solution of the regulator problem with time delay. A priori error bounds in terms of splines are given. A posteriori error bounds are also obtained.     

Modeling and optimization of energy efficient routing in wireless sensor networks

Wireless sensor networks (WSNs) have important applications in remote environmental monitoring and target tracking. The development of WSNs in recent years has been facilitated by the availability of sensors that are smaller, less expensive, and more intelligent. The design of a WSN depends significantly on its desired applications and must take into account factors such as the environment, the design objectives of the application, the associated costs, the necessary hardware, and any applicable system constraints. In this study, we propose mathematical models for a routing protocol (network design) under particular resource restrictions within a wireless sensor network. We consider two types of constraints: the distance between the linking sensors and the energy used by the sensors. The proposed models aim to identify energy-efficient paths that minimize the energy consumption of the network from the source sensor to the base station. The computational results show that the presented models can be used efficiently and applied to other network design contexts with resource restrictions (e.g., to multi-level supply chain networks).     

On collocation methods for delay differential and Volterra integral equations with proportional delay

To compute long term integrations for the pantograph differential equation with proportional delay qt, 0 < q ⩽ 1: y′(t) = ay(t) + by(qt) + f(t), y(0) = y ₀, we offer two kinds of numerical methods using special mesh distributions, that is, a rational approximant with ‘quasi-uniform meshes’ (see E. Ishiwata and Y. Muroya [Appl. Math. Comput., 2007, 187: 741-747]) and a Gauss collocation method with ‘quasi-constrained meshes’. If we apply these meshes to rational approximant and Gauss collocation method, respectively, then we obtain useful numerical methods of order p ^* = 2m for computing long term integrations. Numerical investigations for these methods are also presented.      

A real-time methodology for minimizing mean flowtime in FMSs with routing flexibility: Threshold-based alternate routing

This paper presents an efficient continuous real-time routing strategy, namely threshold-based alternate routing (TAR), to minimize mean flowtime of parts in a FMS with routing flexibility. TAR routes parts to alternate machines instead of their primary machines when the benefit in terms of waiting time obtained from routing to an alternate machine exceeds a pre-determined threshold value. This study proposes that the threshold value for each manufacturing system is unique and presents a methodology for determining its unique value. The threshold concept and the performance of TAR in minimizing mean flowtime are tested with extensive experimentation, involving intricate experimental design. TAR provides very significant improvements in system performance measures compared to other real-time rerouting methods and shows that the threshold value is unique and dependent on system parameters for each manufacturing system. The relationship between the threshold value and system parameters has also been determined.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

A semigroup method for delay equations with relatively bounded operators in the delay term

We consider well-posedness and stability of abstract partial differential equations with unbounded operators in their delay terms. We show that the problem is equivalent to an abstract Cauchy problem in a product Banach space, give sufficient conditions on the well-posedness, make a complete spectral analysis and give robust stability criteria. The results are applied to the problem of small delays and to damped plate equations.     

Cooperative differential game model based on trade-off between energy and delay for wireless sensor networks

A wireless sensor network (WSN) consists of a large number of unattended sensors with limited storage, battery power, computation, and communication capabilities, where battery power (or energy) is the most crucial resource for sensor nodes. The information sensed by sensors needs to be transmitted to sink quickly especially for the applications with delay restriction. However, it is difficult to achieve optimal energy efficiency and source-to-sink delay simultaneously. So it is very necessary to find a power control solution based tradeoff between energy and delay. In this paper, a cooperative differential game model is proposed, and a power solution is obtained which determines a fair distribution of the total cooperative cost among sources.     

An integrated approach for earthwork allocation,sequencing and routing

Planning techniques for large scale earthworks have been considered in this article. To improve these activities a “block theoretic” approach was developed that provides an integrated solution consisting of an allocation of cuts to fills and a sequence of cuts and fills over time. It considers the constantly changing terrain by computing haulage routes dynamically. Consequently more realistic haulage costs are used in the decision making process. A digraph is utilised to describe the terrain surface which has been partitioned into uniform grids. It reflects the true state of the terrain, and is altered after each cut and fill. A shortest path algorithm is successively applied to calculate the cost of each haul, and these costs are summed over the entire sequence, to provide a total cost of haulage. To solve this integrated optimisation problem a variety of solution techniques were applied, including constructive algorithms, meta-heuristics and parallel programming. The extensive numerical investigations have successfully shown the applicability of our approach to real sized earthwork problems.     

Linear,non-approximated models for optimal routing in hazardous environments

A linear optimisation model is presented for the routing of vehicles through hazardous environments or for routing vehicles carrying hazardous materials. The model seeks to find the route with the minimum cost and the minimum probability of accident. As opposed to previously published models, the formulation is linear and no approximations are needed, even in the case of high risk. Several forms of considering risk are presented, as well as a simple method of solution in polynomial time. An example is shown and solved.     

Pricing,routing, and incentive compatibility in multiserver queues

This paper studies pricing and incentive issues in the assignment of customers to servers in a system that suffers congestion effects. When customers have private information about their waiting costs, a system administrator who wishes to maximize steady-sate net benefits per unit of time (i.e. total benefits from service minus total waiting costs) may do so using a pricing and routing scheme that is incentive compatible; that is, no customer has any incentive to reveal his private information untruthfully. When the system administrator wants to maximize toll revenue, the optimal scheme involves higher tolls, and hence lower congestion, than is socially optimal.     

Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay

In this paper, we discuss local and global existence and uniqueness results for first order impulsive functional differential equations with multiple delay. We shall rely on a nonlinear alternative of Leray–Schauder. For the global existence and uniqueness we apply a recent nonlinear alternative of Leray–Schauder type in Fréchet spaces, due to M. Frigon and A. Granas [Résultats de type Leray–Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161–168]. The goal of this paper is to extend the problems considered by A. Ouahab [Local and global existence and uniqueness results for impulsive differential equations with multiple delay, J. Math. Anal. Appl. 323 (2006) 456–472].     

Some new results for a logistic almost periodic system with infinite delay and discrete delay

A nonautonomous logistic almost periodic system with infinite delay and discrete delay is considered. Our result shows that the system is globally asymptotically stable under the condition for the boundedness of the system. By using almost periodic functional Hull theory and new computational techniques, we show that the almost periodic system has a unique globally asymptotically stable strictly positive almost periodic solution under the condition for the boundedness of the system. Some recent results are improved, and an open question is answered.     

Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls

Recently, an increasing number of papers on vehicle routing problems with backhauling has been published. Different types of backhauling problems are discussed. Two of them—the vehicle routing problem with backhauls and so-called ‘mixed loads’ (VRPBM) and the vehicle routing problem with simultaneous delivery and pick-up (VRPSDP)—are closely related. In this paper, we discuss that relationship. Our findings are that previously published results for VRPSDP instances obtained by using a heuristic suggested for the VRPBM do not take into account specific properties of the VRPSDP. As a result of the analysis of the relation between both problem types the possibility of solving the VRPBM by applying an insertion heuristic based on the concept of ‘residual capacities’ originally designed for the VRPSDP is investigated. Numerical results indicate that, for certain instances, this approach is more favourable than the application of a heuristic suggested for the VRPBM in the literature.     

A numerical study of energy consumption and time efficiency of sensor networks with different structural topologies and routing methods

This paper reports a numerical study of energy consumption and time efficiency of sensor networks with five different structural topologies and four different routing methods, regarding their performances and costs, which might provide some references and guidelines for designing sensor networks under various conditions for possible applications.     

Pullback attractors of 2D Navier–Stokes equations with weak damping,distributed delay,and continuous delay

In this present paper, the existence of pullback attractors for the 2D Navier–Stokes equation with weak damping, distributed delay, and continuous delay has been considered, by virtue of classical Galerkin's method, we derived the existence and uniqueness of global weak and strong solutions. Using the Aubin–Lions lemma and some energy estimate in the Banach space with delay, we obtained the uniform bounded and existence of uniform pullback absorbing ball for the solution semi‐processes; we concluded the pullback attractors via verifying the pullback asymptotical compactness by the generalized Arzelà–Ascoli theorem. Copyright © 2016 John Wiley & Sons, Ltd.