Energy-Efficient Transmission Schedule for Delay-Limited Bursty Data Arrivals under Non-Ideal Circuit Power Consumption

This paper develops a novel approach to obtaining energy-efficient transmission schedules for delay-limited bursty data arrivals under non-ideal circuit power consumption. Assuming a-prior knowledge of packet arrivals, deadlines and channel realizations, we show that the problem can be formulated as a convex program. For both time-invariant and time-varying fading channels, it is revealed that the optimal transmission between any two consecutive channel or data state changing instants, termed epoch, can only take one of the three strategies: (i) no transmission, (ii) transmission with an energy-efficiency (EE) maximizing rate over part of the epoch, or (iii) transmission with a rate greater than the EE-maximizing rate over the whole epoch. Based on this specific structure, efficient algorithms are then developed to find the optimal policies that minimize the total energy consumption with a low computational complexity. The proposed approach can provide the optimal benchmarks for practical schemes designed for transmissions of delay-limited data arrivals, and can be employed to develop efficient online scheduling schemes which require only causal knowledge of data arrivals and deadline requirements.Comment: 30 pages, 7 figure

Energy of taut strings accompanying Wiener process

Let $W$ be a Wiener process. The function $h(\cdot)$ minmizing energy $\int_0^T h'(t)^2\, dt$ among all functions satisfying $W(t)-r \le h(t) \le W(t)+ r$ on an interval $[0,T]$ is called taut string. This is a classical object well known in Variational Calculus, Mathematical Statistics, etc. We show that the energy of this taut string on large intervals is equivalent to $C^2 T\, /\, r^2$ where $C$ is some finite positive constant. While the precise value of $C$ remains unknown, we give various theoretical bounds for it as well as rather precise results of computer simulation. While the taut string clearly depends on entire trajectory of $W$, we also consider an adaptive version of the problem by giving a construction (Markovian pursuit) of a random function based only on the past values of $W$ and having minimal asymptotic energy. The solution, an optimal pursuit strategy, quite surprisingly turns out to be related with a classical minimization problem for Fisher information on the bounded interval

Computational Dynamics of a 3D Elastic String Pendulum Attached to a Rigid Body and an Inertially Fixed Reel Mechanism

A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be dynamically varied. The string is assumed to have distributed mass and elasticity that permits axial deformations. The rigid body is attached to the string at an arbitrary point, and the resulting string pendulum system exhibits nontrivial coupling between the elastic wave propagation in the string and the rigid body dynamics. Variational methods are used to develop coupled ordinary and partial differential equations of motion. Computational methods, referred to as Lie group variational integrators, are then developed, based on a finite element approximation and the use of variational methods in a discrete-time setting to obtain discrete-time equations of motion. This approach preserves the geometry of the configurations, and leads to accurate and efficient algorithms that have guaranteed accuracy properties that make them suitable for many dynamic simulations, especially over long simulation times. Numerical results are presented for typical examples involving a constant length string, string deployment, and string retrieval. These demonstrate the complicated dynamics that arise in a string pendulum from the interaction of the rigid body motion, elastic wave dynamics in the string, and the disturbances introduced by the reeling mechanism. Such interactions are dynamically important in many engineering problems, but tend be obscured in lower fidelity models.Comment: 17 pages, 14 figure

Finite Horizon Online Lazy Scheduling with Energy Harvesting Transmitters over Fading Channels

Lazy scheduling, i.e. setting transmit power and rate in response to data traffic as low as possible so as to satisfy delay constraints, is a known method for energy efficient transmission.This paper addresses an online lazy scheduling problem over finite time-slotted transmission window and introduces low-complexity heuristics which attain near-optimal performance.Particularly, this paper generalizes lazy scheduling problem for energy harvesting systems to deal with packet arrival, energy harvesting and time-varying channel processes simultaneously. The time-slotted formulation of the problem and depiction of its offline optimal solution provide explicit expressions allowing to derive good online policies and algorithms