The problem of multi-area interchange scheduling under system uncertainty is considered. A new scheduling technique is proposed for a multi-proxy bus system based on stochastic optimization that captures uncertainty in renewable generation and stochastic load. In particular, the proposed algorithm iteratively optimizes the interface flows using a multidimensional demand and supply functions. Optimality and convergence are guaranteed for both synchronous and asynchronous scheduling under nominal assumptions.
A shortcoming of existing techniques based on proxy bus approximations is the difficulty of generalizing it for multi-area interconnected systems where multiple scheduling interfaces have to be optimized simultaneously. The challenge arises from the fact that the interfaces cannot be succinctly characterized by a pair of expected demand and supply functions --- an essential property underlying the approach in @cite_2 for the single interface scheduling. When multiple interfaces are involved, the simple idea of equating expected demand and supply functions is not applicable and there is no simple notion that the intersection of demand and supply curves gives the social welfare optimizing interchange.
@cite_2
2962920885 2170178059 2154125468 1997323680
The problem of inter-regional interchange scheduling in the presence of stochastic generation and load is considered. An interchange scheduling technique based on a two-stage stochastic minimization of expected operating cost is proposed. Because directly solving the stochastic optimization is intractable, an equivalent problem that maximizes the expected social welfare is formulated. The proposed technique leverages the operator's capability of forecasting locational marginal prices and obtains the optimal interchange schedule without iterations among operators. Several extensions of the proposed technique are also discussed. This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models. In the interference scheduling problem, one is given a set of n communication requests described by source-destination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color class can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We introduce an instance-based measure of interference, denoted by I, that enables us to improve on previous results for the interference scheduling problem. We prove the upper and lower bounds in terms of I on the number of steps needed for scheduling a set of requests. For general power assignments, we prove a lower bound of @W(I ([email protected])) steps, where @D denotes the aspect ratio of the metric. When restricting to the two-dimensional Euclidean space (as in the previous work) the bound improves to @W(I [email protected]). Alternatively, when restricting to linear power assignments, the lower bound improves even to @W(I). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only O(Ilogn) steps. A more sophisticated algorithm computes a schedule using even only O(I+log^2n) steps. For dense instances in the two-dimensional Euclidean space, this gives a constant factor approximation for scheduling under linear power assignments, which shows that the price for using linear (and, hence, energy-efficient) power assignments is bounded by a factor of O([email protected]). In addition, we extend these results for single-hop scheduling to multi-hop scheduling and combined scheduling and routing problems, where our analysis generalizes the previous results towards general metrics and improves on the previous approximation factors. We consider the problem of downlink scheduling for multiuser orthogonal frequency-division multiplexing (OFDM) systems. Opportunistic scheduling exploits the time-varying, location-dependent channel conditions to achieve multiuser diversity. Previous work in this area has focused on single-channel systems. Multiuser OFDM allows multiple users to transmit simultaneously over multiple channels. In this paper, we develop a rigorous framework to study opportunistic scheduling in multiuser OFDM systems. We derive optimal opportunistic scheduling policies under three QoS fairness constraints formultiuserOFDM systems--temporal fairness, utilitarian fairness, and minimum-performance guarantees. Our scheduler decides not only which time slot, but also which subcarrier to allocate to each user. Implementing these optimal policies involves solving a maximal bipartite matching problem at each scheduling time. To solve this problem efficiently, we apply a modified Hungarian algorithm and a simple suboptimal algorithm. Numerical results demonstrate that our schemes achieve significant improvement in system performance compared with nonopportunistic schemes.