Scheduling with Rate Adaptation under Incomplete Knowledge of Channel/Estimator Statistics

In time-varying wireless networks, the states of the communication channels are subject to random variations, and hence need to be estimated for efficient rate adaptation and scheduling. The estimation mechanism possesses inaccuracies that need to be tackled in a probabilistic framework. In this work, we study scheduling with rate adaptation in single-hop queueing networks under two levels of channel uncertainty: when the channel estimates are inaccurate but complete knowledge of the channel/estimator joint statistics is available at the scheduler; and when the knowledge of the joint statistics is incomplete. In the former case, we characterize the network stability region and show that a maximum-weight type scheduling policy is throughput-optimal. In the latter case, we propose a joint channel statistics learning - scheduling policy. With an associated trade-off in average packet delay and convergence time, the proposed policy has a stability region arbitrarily close to the stability region of the network under full knowledge of channel/estimator joint statistics.Comment: 48th Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 201

Performance bounds of opportunistic scheduling in wireless networks

In this paper, we study the performance of opportunistic scheduling in wireless networks from the perspective of information and entropy. In opportunistic scheduling, we allocate a limited number of channels to a certain number of nodes so as to maximize the network performance. Due to the inherent uncertainty of the system input represented by random variables with certain probability distributions, even under the optimal scheduling strategy, we may not achieve the best network performance. In our proposed model, we mathematically formulate the relationship between system uncertainty characterized by entropy and network performance, i.e., we give the lower and upper bounds of network performance with given entropy of the uncertain input. Based on this result, we can determine quantitatively the impact of system uncertainty on the performance of of opportunistic scheduling in wireless networks. ©2010 IEEE.published_or_final_versionThe IEEE Conference and Exhibition on Global Telecommunications Conference (GLOBECOM 2010), Miami, FL., 6-10 December 2010. In Proceedings of GLOBECOM 2010, 2010, p. 1-

A decomposition approach for commodity pickup and delivery with time-windows under uncertainty

We consider a special class of large-scale, network-based, resource allocation problems under uncertainty, namely that of multi-commodity flows with time-windows under uncertainty. In this class, we focus on problems involving commodity pickup and delivery with time-windows. Our work examines methods of proactive planning, that is, robust plan generation to protect against future uncertainty. By a priori modeling uncertainties in data corresponding to service times, resource availability, supplies and demands, we generate solutions that are more robust operationally, that is, more likely to be executed or easier to repair when disrupted. We propose a novel modeling and solution framework involving a decomposition scheme that separates problems into a routing master problem and Scheduling Sub-Problems; and iterates to find the optimal solution. Uncertainty is captured in part by the master problem and in part by the Scheduling Sub-Problem. We present proof-of-concept for our approach using real data involving routing and scheduling for a large shipment carrier’s ground network, and demonstrate the improved robustness of solutions from our approach

An optimal-control based integrated model of supply chain

Problems of supply chain scheduling are challenged by high complexity, combination of continuous and discrete processes, integrated production and transportation operations as well as dynamics and resulting requirements for adaptability and stability analysis. A possibility to address the above-named issues opens modern control theory and optimal program control in particular. Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of complexity, dynamics, uncertainty, and adaptivity. Supply chain schedule generation is represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. The calculation procedure is based on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. With the developed model, important categories of supply chain analysis such as stability and adaptability can be taken into consideration. Besides, the dimensionality of operations research-based problems can be relieved with the help of distributing model elements between an operations research (static aspects) and a control (dynamic aspects) model. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes.supply chain, model of supply chain scheduling, optimal program control theory, Pontryagin’s maximum principle, operations research model,

Optimal state estimation and control of space systems under severe uncertainty

This thesis presents novel methods and algorithms for state estimation and optimal control under generalised models of uncertainty. Tracking, scheduling, conjunction assessment, as well as trajectory design and analysis, are typically carried out either considering the nominal scenario only or under assumptions and approximations of the underlying uncertainty to keep the computation tractable. However, neglecting uncertainty or not quantifying it properly may result in lengthy design iterations, mission failures, inaccurate estimation of the satellite state, and poorly assessed risk metrics. To overcome these challenges, this thesis proposes approaches to incorporate proper uncertainty treatment in state estimation, navigation and tracking, and trajectory design. First, epistemic uncertainty is introduced as a generalised model to describe partial probabilistic models, ignorance, scarce or conflicting information, and, overall, a larger umbrella of uncertainty structures. Then, new formulations for state estimation, optimal control, and scheduling under mixed aleatory and epistemic uncertainties are proposed to generalise and robustify their current deterministic or purely aleatory counterparts. Practical solution approaches are developed to numerically solve such problems efficiently. Specifically, a polynomial reinitialisation approach for efficient uncertainty propagation is developed to mitigate the stochastic dimensionality in multi-segment problems. For state estimation and navigation, two robust filtering approaches are presented: a generalisation of the particle filtering to epistemic uncertainty exploiting samples’ precomputations; a sequential filtering approach employing a combination of variational inference and importance sampling. For optimal control under uncertainty, direct shooting-like transcriptions with a tunable high-fidelity polynomial representation of the dynamical flow are developed. Uncertainty quantification, orbit determination, and navigation analysis are incorporated in the main optimisation loop to design trajectories that are simultaneously optimal and robust. The methods developed in this thesis are finally applied to a variety of novel test cases, ranging from LEO to deep-space missions, from trajectory design to space traffic management. The epistemic state estimation is employed in the robust estimation of debris’ conjunction analyses and incorporated in a robust Bayesian framework capable of autonomous decision-making. An optimisation-based scheduling method is presented to efficiently allocate resources to heterogeneous ground stations and fusing information coming from different sensors, and it is applied to the optimal tracking of a satellite in highly perturbed very-low Earth orbit, and a low-resource deep-space spacecraft. The optimal control methods are applied to the robust optimisation of an interplanetary low-thrust trajectory to Apophis, and to the robust redesign of a leg of the Europa Clipper tour with an initial infeasibility on the probability of impact with Jupiter’s moon.This thesis presents novel methods and algorithms for state estimation and optimal control under generalised models of uncertainty. Tracking, scheduling, conjunction assessment, as well as trajectory design and analysis, are typically carried out either considering the nominal scenario only or under assumptions and approximations of the underlying uncertainty to keep the computation tractable. However, neglecting uncertainty or not quantifying it properly may result in lengthy design iterations, mission failures, inaccurate estimation of the satellite state, and poorly assessed risk metrics. To overcome these challenges, this thesis proposes approaches to incorporate proper uncertainty treatment in state estimation, navigation and tracking, and trajectory design. First, epistemic uncertainty is introduced as a generalised model to describe partial probabilistic models, ignorance, scarce or conflicting information, and, overall, a larger umbrella of uncertainty structures. Then, new formulations for state estimation, optimal control, and scheduling under mixed aleatory and epistemic uncertainties are proposed to generalise and robustify their current deterministic or purely aleatory counterparts. Practical solution approaches are developed to numerically solve such problems efficiently. Specifically, a polynomial reinitialisation approach for efficient uncertainty propagation is developed to mitigate the stochastic dimensionality in multi-segment problems. For state estimation and navigation, two robust filtering approaches are presented: a generalisation of the particle filtering to epistemic uncertainty exploiting samples’ precomputations; a sequential filtering approach employing a combination of variational inference and importance sampling. For optimal control under uncertainty, direct shooting-like transcriptions with a tunable high-fidelity polynomial representation of the dynamical flow are developed. Uncertainty quantification, orbit determination, and navigation analysis are incorporated in the main optimisation loop to design trajectories that are simultaneously optimal and robust. The methods developed in this thesis are finally applied to a variety of novel test cases, ranging from LEO to deep-space missions, from trajectory design to space traffic management. The epistemic state estimation is employed in the robust estimation of debris’ conjunction analyses and incorporated in a robust Bayesian framework capable of autonomous decision-making. An optimisation-based scheduling method is presented to efficiently allocate resources to heterogeneous ground stations and fusing information coming from different sensors, and it is applied to the optimal tracking of a satellite in highly perturbed very-low Earth orbit, and a low-resource deep-space spacecraft. The optimal control methods are applied to the robust optimisation of an interplanetary low-thrust trajectory to Apophis, and to the robust redesign of a leg of the Europa Clipper tour with an initial infeasibility on the probability of impact with Jupiter’s moon

Charging Scheduling of Electric Vehicles with Local Renewable Energy under Uncertain Electric Vehicle Arrival and Grid Power Price

In the paper, we consider delay-optimal charging scheduling of the electric vehicles (EVs) at a charging station with multiple charge points. The charging station is equipped with renewable energy generation devices and can also buy energy from power grid. The uncertainty of the EV arrival, the intermittence of the renewable energy, and the variation of the grid power price are taken into account and described as independent Markov processes. Meanwhile, the charging energy for each EV is random. The goal is to minimize the mean waiting time of EVs under the long term constraint on the cost. We propose queue mapping to convert the EV queue to the charge demand queue and prove the equivalence between the minimization of the two queues' average length. Then we focus on the minimization for the average length of the charge demand queue under long term cost constraint. We propose a framework of Markov decision process (MDP) to investigate this scheduling problem. The system state includes the charge demand queue length, the charge demand arrival, the energy level in the storage battery of the renewable energy, the renewable energy arrival, and the grid power price. Additionally the number of charging demands and the allocated energy from the storage battery compose the two-dimensional policy. We derive two necessary conditions of the optimal policy. Moreover, we discuss the reduction of the two-dimensional policy to be the number of charging demands only. We give the sets of system states for which charging no demand and charging as many demands as possible are optimal, respectively. Finally we investigate the proposed radical policy and conservative policy numerically

A New Robust Optimization Approach for Scheduling Under Uncertainty:

Abstract The problem of scheduling under bounded uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to mixed-integer linear programming (MILP) problems produces "robust" solutions which are in a sense immune against bounded uncertainty. Both the coefficients in the objective function, the left-hand-side parameters and the right-hand-side parameters of the inequalities are considered. Robust optimization techniques are developed for two types of uncertain data: bounded uncertainty and bounded and symmetric uncertainty. By introducing a small number of auxiliary variables and constraints, a deterministic robust counterpart problem is formulated to determine the optimal solution given the (relative) magnitude of uncertain data, feasibility tolerance, and "reliability level" when a probabilistic measurement is applied. The robust optimization approach is then applied to the scheduling under uncertainty problem. Based on a novel and effective continuous-time short-term scheduling model proposed by Floudas and coworkers [Ind. Eng. Chem. Res. 37 (1998a