Offline first fit scheduling in smart grids

Ranjan, Anshu; Khargonekar, Pramod P.; Sahni, Sartaj

doi:10.1109/iscc.2015.7405605

Cited by 11 publications

(8 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, for other applications, the geometric constraint in GSP does not seem to be necessary, and hence it makes sense to drop it (i.e., to rather consider DSP): this might lead to better solutions, possibly via simpler and/or more efficient algorithms. Consider for example the minimization of the peak energy consumption in smart-grids [31,44,39].…”

Section: H(i)mentioning

confidence: 99%

“…There is a very rich line of research on generalizations and variants of DSP such as online versions [34,35], tasks with availability constraints or time windows [45,44,31], a mixture of preemptable and non-preemptable tasks [39] or generalized cost functions based on the demand at each edge [10,35]. The variant of DSP with the extra feature of interrupting the tasks is known as Strip Packing with Slicing, for which there exists an FPTAS [3]; on the other hand, the case of DSP is still hard to approximate by a factor better than 3/2 as noted by Tang et al [43].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Approximation Algorithms for Demand Strip Packing

Gálvez¹,

Grandoni²,

Ameli³

et al. 2021

Preprint

View full text Add to dashboard Cite

In the Demand Strip Packing problem (DSP), we are given a time interval and a collection of tasks, each characterized by a processing time and a demand for a given resource (such as electricity, computational power, etc.). A feasible solution consists of a schedule of the tasks within the mentioned time interval. Our goal is to minimize the peak resource consumption, i.e. the maximum total demand of tasks executed at any point in time.It is known that DSP is NP-hard to approximate below a factor 3/2, and standard techniques for related problems imply a (polynomial-time) 2-approximation. Our main result is a (5/3 + ε)approximation algorithm for any constant ε > 0. We also achieve best-possible approximation factors for some relevant special cases.

show abstract

Section: H(i)mentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Approximation Algorithms for Demand Strip Packing

Gálvez¹,

Grandoni²,

Ameli³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The remaining jobs fit into a thin container of height 1. The previous best for NPDM was 2.7 approximation based on FFDH [40]. One of our key ideas is providing several new lower bounds on the optimal solution of a geometric packing, which could be useful in other related problems.…”

mentioning

confidence: 99%

Peak Demand Minimization via Sliced Strip Packing

Deppert¹,

Jansen²,

Khan³

et al. 2021

Preprint

View full text Add to dashboard Cite

We study Nonpreemptive Peak Demand Minimization (NPDM) problem, where we are given a set of jobs, specified by their processing times and energy requirements. The goal is to schedule all jobs within a fixed time period such that the peak load (the maximum total energy requirement at any time) is minimized. This problem has recently received significant attention due to its relevance in smart-grids. Theoretically, the problem is related to the classical strip packing problem (SP). In SP, a given set of axis-aligned rectangles must be packed into a fixed-width strip, such that the height of the strip is minimized. NPDM can be modeled as strip packing with slicing and stacking constraint: each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. The stacking constraint forbids solutions where two slices of the same rectangle are intersected by the same vertical line. Nonpreemption enforces the slices to be placed in contiguous horizontal locations (but may be placed at different vertical locations).We obtain a (5/3 + ε)-approximation algorithm for the problem. We also provide an asymptotic efficient polynomial-time approximation scheme (AEPTAS) which generates a schedule for almost all jobs with energy consumption (1 + ε)OPT. The remaining jobs fit into a thin container of height 1. The previous best for NPDM was 2.7 approximation based on FFDH [40]. One of our key ideas is providing several new lower bounds on the optimal solution of a geometric packing, which could be useful in other related problems. These lower bounds help us to obtain approximative solutions based on Steinberg's algorithm in many cases. In addition, we show how to split schedules generated by the AEPTAS into few segments and to rearrange the corresponding jobs to insert the thin container mentioned above.

show abstract

“…Our study is the first one taking into account malleability in the scheduling problem of rectangular-shape electrical demands (Chapter 2). In other studies, considering Strip Packing Problem of rectangular-shape electrical demands, such as [68][69][70][71] the following generated data sets are being used: Mumford-Valenzuela [85], Hopper and Turton [58], Burke [86] and especially Pedro and Guillermo Sanchez [87] Benchmarks. Unfortunately, demand malleability has not been addressed in these existing data sets.…”

Section: Computational Results For Covering Policymentioning

confidence: 99%

“…Then after showing that in general finding the optimal solution is NP hard, they tried to find some approximations for optimal policy in the presence of different levels of knowledge about the demands such as durations and power intensities. Eventually in [68][69][70][71], a set of rectangular-shape electrical demands are considered, where for each demand the power intensity and service duration is known in advance. In addition, by having the flexibility of delaying the starting time of the service, it is assumed that all demands have the same earliest start time and deadline for receiving their energy requirement.…”

Section: )mentioning

confidence: 99%

Optimal Scheduling of Random Flexible Demands in Smart Grid

Karbasioun¹

View full text Add to dashboard Cite

On the consumer side of the electrical grid, there are some demands with some kind of "flexibility" in nature. Wisely exploiting these flexibilities could result in better utilization of the available resources.Inspired by the existence of electric appliances with flexibility on their charging rate, we study the problem of optimally serving a set of "Malleable Rectangular-Shape" energy requirements in a finite time interval. That is each demand must be supplied continuously with a constant intensity and duration bounded by left-and right-malleability constraints. At each moment of time, the total power consumption of the grid is the sum of all the consumption rates of the demands being supplied at that moment. First, we assume that the malleability constraints are the same for all demands. Then, we identify the lower bound on the optimal value of the power peak. We extend our study by considering stochastic malleability constraints, where each demand has its own constraint pair. In this case, we also include a convex cost of power consumption in our treatment. In each case, we propose an on-line scheduling algorithm, which is asymptotically optimal with respect to the given cost criteria.As another type of flexible demands, we address the problem of controlling a charging station of Plug-in Hybrid Electric Vehicles (PHEVs), assuming they can tolerate rejection of their energy request. We introduce a model for a charging station, in which PHEVs are charged either directly from the electrical grid or from a local storage unit deployed for each class of customers. The control actions to be determined by the charging station operator are as follows: the probability of blocking new arrivals, the rate of charging each local storage unit, the proportion of cars being served by each local storage unit and eventually the proportion of the available power from the grid to be assigned to each class of customers. We will show how to find a control policy minimizing the utilization cost of the charging station.

show abstract

Offline first fit scheduling in smart grids

Cited by 11 publications

References 17 publications

Approximation Algorithms for Demand Strip Packing

Approximation Algorithms for Demand Strip Packing

Peak Demand Minimization via Sliced Strip Packing

Optimal Scheduling of Random Flexible Demands in Smart Grid

Contact Info

Product

Resources

About