I.Ch. Paschalidis

Pricing in multiservice loss networks: static pricing, asymptotic optimality and demand substitution effects

We consider a communication network with fixed routing that can accommodate multiple service classes, differing in bandwidth requirements, demand pattern, call duration, and routing. The network charges a fee per call which can depend on the current congestion level, and which affects users demand. Building on the single-node results of Paschalidis and Tsitsiklis, 2000, we consider both problems of revenue and of welfare maximization, and show that static pricing is asymptotically optimal in a regime of many, relatively small, users. In particular, the performance of an optimal (dynamic) pricing strategy is closely matched by a suitably chosen class-dependent static price, which does not depend on instantaneous congestion. This result holds even when we incorporate demand substitution effects into the demand model. More specifically, we model the situation where price increases for a class of service might lead users to use another class as an imperfect substitute. For both revenue and welfare maximization objectives we characterize the structure of the asymptotically optimal static prices, expressing them as a function of a parsimonious number of parameters. We employ a simulation-based approach to tune those parameters and to efficiently compute an effective policy away from the limiting regime. Our approach can handle large, realistic, instances of the problem.

Asymptotically optimal transmission policies for large-scale low-power wireless sensor networks

We consider wireless sensor networks with multiple gateways and multiple classes of traffic carrying data generated by different sensory inputs. The objective is to devise joint routing, power control and transmission scheduling policies in order to gather data in the most efficient manner while respecting the needs of different sensing tasks (fairness). We formulate the problem as maximizing the utility of transmissions subject to explicit fairness constraints and propose an efficient decomposition algorithm drawing upon large-scale decomposition ideas in mathematical programming. We show that our algorithm terminates in a finite number of iterations and produces a policy that is asymptotically optimal at low transmission power levels. Furthermore, we establish that the utility maximization problem we consider can, in principle, be solved in polynomial time. Numerical results show that our policy is near-optimal, even at high power levels, and far superior to the best known heuristics at low power levels. We also demonstrate how to adapt our algorithm to accommodate energy constraints and node failures. The approach we introduce can efficiently determine near-optimal transmission policies for dramatically larger problem instances than an alternative enumeration approach.

Deployment optimization of sensornet-based stochastic location-detection systems

We propose a systematic framework for designing a stochastic indoor location detection system with associated performance guarantees using a hierarchical wireless sensor network. To detect the location of a mobile sensor, we rely on RF-characteristics of the signal transmitted by the mobile sensor, as it is received by the clusterheads. The problem of location detection is posed as a hypothesis testing problem over a discretized space. We leverage large deviations and decision theory results to characterize the probability of error and use this characterization to optimally place clusterheads. The placement problem is NP-hard and we formulate it as a linear integer programming problem. We leverage special-purpose algorithms from the theory of discrete facility location to solve large problem instances efficiently. For the resultant placement we provide asymptotic guarantees on the probability of error in location detection under quite general conditions. Numerical and simulation results show that our proposed framework is computationally feasible and the resultant clusterhead placement performs near-optimum even with a small number of observation samples.

Robust Linear Optimization: On the benefits of distributional information and applications in inventory control

Linear programming formulations cannot handle the presence of uncertainty in the problem data and even small variations in the data can render an optimal solution infeasible. A number of robust linear optimization techniques produce formulations (not necessarily linear) that guarantee the feasibility of the optimal solutions for all realizations of the uncertain data. A recent robust approach in [1] maintains the linearity of the formulation and is able to strike a balance between the conservatism and quality of a solution by allowing less robust solutions. In this work we demonstrate how to use distributional information on problem data in robust linear optimization. We adopt the robust model of [1] and present an approach that exploits distributional information on problem data to decide the level of robustness of the formulation, thus, leading to much more cost-effective solutions (by 50% or more in some instances).We apply our methodology to a stochastic inventory control problem with quality of service constraints.

Asymptotically optimal transmission policies for low-power wireless sensor networks

We consider wireless sensor networks with multiple gateways and multiple classes of traffic carrying data generated by different sensory inputs. The objective is to devise joint routing, power control and transmission scheduling policies in order to gather data in the most efficient manner while respecting the needs of different sensing tasks (fairness). We formulate the problem as maximizing the utility of transmissions subject to explicit fairness constraints. We propose an efficient decomposition algorithm drawing upon large-scale decomposition ideas in mathematical programming. We show that our algorithm terminates in a finite number of iterations and produces a policy that is asymptotically optimal at low transmission power levels. Moreover, numerical results establish that this policy is near-optimal even at high power levels. We also demonstrate how to adapt our algorithm to accommodate energy constraints and node failures. The approach we introduce can efficiently determine near-optimal transmission policies for dramatically larger problem instances than an alternative enumeration approach.

A Semi-Definite programming-based Underestimation method for global optimization in molecular docking

The paper introduces a new global optimization method that is targeted to solve molecular docking problems, an important class of problems in computational biology. The search method is based on finding general convex quadratic underestimators to the binding energy function that is funnel-like. Finding the optimum underestimator requires solving a semi-definite programming problem, hence the name Semi-Definite programming based Underestimation (SDU). The optimal underestimator is used to bias sampling in the search region. A detailed comparison of SDU with a related method of Convex Global Underestimator (CGU), a discussion of the convergence properties of SDU, and computational results of the application of SDU to a number of rigid protein-protein docking problems are provided.

Target-pursuing scheduling and routing policies for multiclass queueing networks

We propose a parametric class of myopic scheduling and routing policies for open and closed multiclass queueing networks. In open networks, they steer the state of the system toward a predetermined and fixed target, while, in closed networks they steer instantaneous throughputs toward a fixed target. In both cases, the proposed policies measure distance from the target using a weighted norm. In open networks, we establish that for an L2 norm the corresponding policies are stable. In closed networks, we establish that with proper target selection the corresponding policy is efficient, that is, attains bottleneck throughput in the infinite population limit. In both open and closed networks, the proposed policies are amenable to distributed implementation using local state information. We exploit the work in a previous paper to select appropriate parameter values and outline how optimal parameter values can be computed. We report numerical results indicating that we obtain near-optimal policies (when the optimal can be computed) and significantly outperform heuristic alternatives. This work has applications in a number of areas including optimizing the processing of information in sensor networks.

On maximizing the utility of uplink transmissions in sensor networks under explicit fairness constraints

We consider wireless sensor networks with multiple gateways, multiple classes of traffic, and no restrictions on routing and transmission scheduling other than those imposed by the wireless medium. The objective is to schedule uplink transmissions in order to maximize the overall system utility under explicit fairness constraints. We propose a decomposition algorithm drawing upon large-scale decomposition ideas in mathematical programming. We show that in the region of small powers, in which most sensor networks operate, this algorithm terminates with an optimal solution in a finite number of iterations. Moreover, we show that an associated subproblem can be transformed to a maximum weighted matching problem and is therefore solvable in polynomial time. We also consider how to optimize sensor power levels in order to save energy while achieving a certain utility goal. Our approach can efficiently determine the optimal transmission policy for dramatically larger problem instances than an alternative enumeration approach.

Large deviations-based asymptotics for inventory control in supply chains

We consider a model of a capacitated single-class supply chain consisting of a tandem of production facilities and propose production policies in two cases: (a) when each facility has access to its local inventory only, and (b) when it has knowledge of the total downstream inventory. In case (a) the proposed policy guarantees stockout probabilities at each stage to stay bounded below given constants (service level constraints). In case (b) we minimize total expected inventory cost subject to service level constraints. In both cases we rely upon large deviations asymptotics to analytically obtain the policy parameters; this leads to huge computational savings compared to simulation. Our model can accommodate autocorrelated demand and service processes, both critical features of modern failure-prone manufacturing systems. We demonstrate that detailed distributional information on demand and service processes, which is incorporated into large deviations asymptotics, is critical in inventory control decisions. Some extensions to a multiclass setting are discussed.

Optimizing location detection services in wireless sensor networks

We propose a systematic framework for placing a given number of clusterheads in a hierarchical wireless sensor network to facilitate location detection service. The problem of location detection is posed as a hypothesis testing problem over a discretized space. Then, the clusterheads are placed in locations that maximize the worst case Chernoff distance between the conditional densities over all location pairs. Linear integer programming is used to determine the optimal placement. The resultant placement provides an asymptotic guarantee on the probability of error in location detection under quite general conditions. We obtain numerical results on the scalability of our proposed mathematical programming, and quantify the performance of the location detection system with the resultant clusterhead placement by simulation. Numerical and simulation results show that our proposed framework is computationally feasible and the resultant clusterhead placement performs near-optimum even with a small number of observation samples.