Online energy efficient packet scheduling for a common deadline with and without energy harvesting

The problem of online packet scheduling to minimize the required conventional grid energy for transmitting a fixed number of packets given a common deadline is considered. The total number of packets arriving within the deadline is known, but the packet arrival times are unknown, and can be arbitrary. The proposed algorithm tries to finish the transmission of each packet assuming all future packets are going to arrive at equal time intervals within the left-over time. The proposed online algorithm is shown to have competitive ratio that is logarithmic in the number of packet arrivals. The hybrid energy paradigm is also considered, where in addition to grid energy, energy is also available via extraction from renewable sources. The objective here is to minimize the grid energy use. A suitably modified version of the previous algorithm is also shown to have competitive ratio that is logarithmic in the number of packet arrivals

Resource Allocation in Green Dense Cellular Networks: Complexity and Algorithms

This paper studies the problem of user association, scheduling and channel allocation in dense cellular networks with energy harvesting base stations (EBSs). In this problem, the EBSs are powered solely by renewable energy and each user has a request for downloading data of certain size with a deadline constraint. The objective is to maximize the number of associated and scheduled users while allocating the available channels to the users and respecting the energy and deadline constraints. First, the computational complexity of this problem is characterized by studying its NP-hardness in different cases. Next, efficient algorithms are proposed in each case. The case of a single channel and a single EBS is solved using two polynomial-time optimal algorithms---one for arbitrary deadlines and a less-complex one for common deadlines. The case of a single channel and multiple EBSs is solved by proposing an efficient constant-factor approximation algorithm. The case of multiple channels is efficiently solved using a heuristic algorithm. Finally, our theoretical analysis is supplemented by simulation results to illustrate the performance of the proposed algorithms.Comment: Submitted to TV

Online Energy Harvesting Problem Over An Arbitrary Directed Acyclic Graph Network

A communication network modelled by a directed acyclic graph (DAG) is considered, over which a source wishes to send a specified number of bits to a destination node. Each node of the DAG is powered by a separate renewable energy source, and the harvested energy is used to facilitate the source destination data flow. The challenge here is to find the optimal rate and power allocations across time for each node on its outgoing edges so as to minimize the time by which the destination receives a specified number of bits. An online setting is considered where an algorithm only has causal information about the energy arrivals. Using the competitive ratio as the performance metric, i.e. the ratio of the cost of the online algorithm and the optimal offline algorithm, maximized over all inputs, a {\it lazy} online algorithm with a competitive ratio of $2+\delta$ for any $\delta>0$ is proposed. Incidentally, $2$ is also a lower bound to the competitive ratio of any online algorithm for this problem. Our lazy online algorithm is described and analyzed via defining a novel max-flow problem over a DAG, where the rate on the subset of outgoing edges of any node are related/constrained. An optimal algorithm to find max-flow with these constraints is also provided, which may be of independent interest.Comment: Sub-result: An optimal algorithm to find the max flow in a DAG with non-polymatroidal rate constraints on subsets of edge

Online Energy Minimization Under A Peak Age of Information Constraint

We consider a node where packets of fixed size are generated at arbitrary intervals. The node is required to maintain the peak age of information (AoI) at the monitor below a threshold by transmitting potentially a subset of the generated packets. At any time, depending on packet availability and current AoI, the node can choose the packet to transmit, and its transmission speed. We consider a power function (rate of energy consumption) that is increasing and convex in transmission speed, and the objective is to minimize the energy consumption under the peak AoI constraint at all times. For this problem, we propose a (customized) greedy policy, and analyze its competitive ratio (CR) by comparing it against an optimal offline policy by deriving some structural results. We show that for polynomial power functions, the CR upper bound for the greedy policy is independent of the system parameters, such as the peak AoI, packet size, time horizon, or the number of packets generated. Also, we derive a lower bound on the competitive ratio of any causal policy, and show that for exponential power functions (e.g., Shannon rate function), the competitive ratio of any causal policy grows exponentially with increase in the ratio of packet size to peak AoI.Comment: 13 pages, 6 figure