First Fit Decreasing Research Articles

Optimal virtual network function placement in multi-cloud service function chaining architecture

Service Function Chaining (SFC) is the problem of deploying various network service instances over geographically distributed data centers and providing inter-connectivity among them. The goal is to enable the network traffic to flow smoothly through the underlying network, resulting in an optimal quality of experience to the end-users. Proper chaining of network functions leads to optimal utilization of distributed resources. This has been a de-facto model in the telecom industry with network functions deployed over underlying hardware. Though this model has served the telecom industry well so far, it has been adapted mostly to suit the static behavior of network services and service demands due to the deployment of the services directly over physical resources. This results in network ossification with larger delays to the end-users, especially with the data-centric model in which the computational resources are moving closer to end users. A novel networking paradigm, Network Function Virtualization (NFV), meets the user demands dynamically and reduces operational expenses (OpEx) and capital expenditures (CapEx), by implementing network functions in the software layer known as virtual network functions (VNFs). VNFs are then interconnected to form a complete end-to-end service, also known as service function chains (SFCs). In this work, we study the problem of deploying service function chains over network function virtualized architecture. Specifically, we study virtual network function placement problem for the optimal SFC formation across geographically distributed clouds. We set up the problem of minimizing inter-cloud traffic and response time in a multi-cloud scenario as an ILP optimization problem, along with important constraints such as total deployment costs and service level agreements (SLAs). We consider link delays and computational delays in our model. The link queues are modeled as M/D/1 (single server/Poisson arrival/deterministic service times) and server queues as M/M/1 (single server/Poisson arrival/exponential service times) based on the statistical analysis. In addition, we present a novel affinity-based approach (ABA) to solve the problem for larger networks. We provide a performance comparison between the proposed heuristic and simple greedy approach (SGA) used in the state-of-the-art systems. Greedy approach has already been widely studied in the literature for the VM placement problem. Especially we compare our proposed heuristic with a greedy approach using first-fit decreasing (FFD) method. By observing the results, we conclude that the affinity-based approach for placing the service functions in the network produces better results compared against the simple greedy (FFD) approach in terms of both, total delays and total resource cost. We observe that with a little compromise (gap of less than 10% of the optimal) in the solution quality (total delays and cost), affinity-based heuristic can solve the larger problem more quickly than ILP.

FFD Variants for Virtual Machine Placement in Cloud Computing Data Centers

Virtualization technology is used to efficiently utilize the resources of a Cloud datacenter by running multiple virtual machines (VMs) on a single physical machine (PM) as if each VM is a standalone PM. Efficient placement/consolidation of VMs into PMs can reduce number of active PMs which consequently reduces resource wastage and power consumption. Therefore, VM placement algorithms need to be optimized to reduce the number of PMs required for VM Placements. In this paper, two heuristic based Vector Bin Packing algorithms called FFDmean and FFDmedian are proposed for VM placement. These algorithms use First Fit Decreasing (FFD) technique. FFD preprocesses VMs by sorting all VMs in descending order of their sizes. Since a VM is multidimensional therefore, it is difficult to decide on its size. For this, FFDmean and FFDmedian use measures of central tendency, i.e. mean and median as heuristics, respectively, in order to estimate the size of a VM. The goal of these algorithms is to utilize the PM resources efficiently so that the number of required PMs for accommodation of all VMs can be reduced. CloudSim toolkit is used to carry out the cloud simulation and experiments. Algorithms are compared over three metrics, i.e. hosts used, power consumption and resource utilization efficiency. The results reveal that FFDmean and FFDmedian remarkably outperformed two existing algorithms called Dot-Product and L2 in all three metrics when PM resources were limited.

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Providing resource for virtual services in cloud computing which requires saving the resource and minimizing the amount of energy consumption is critical. In this study, we propose the resource model and linear programming formulation for multi-dimensional resource allocation problem. Based on the Particle Swarm Optimization algorithm, RA-PSO algorithm was designed to solve and evaluate through CloudSim simulation tool compared with FirstFit Decreasing (FFD) algorithm. The parameters include the number of physical machines being used and the amount of energy consumption. The experimental results show that the proposed RA-PSO algorithm yields a better performance than FFD algorithm.

Multi-Capacity Combinatorial Ordering GA in Application to Cloud resources allocation and efficient virtual machines consolidation

This paper describes a novel approach making use of genetic algorithms to find optimal solutions for multi-dimensional vector bin packing problems with the goal to improve cloud resource allocation and Virtual Machines (VMs) consolidation. Two algorithms, namely Combinatorial Ordering First-Fit Genetic Algorithm (COFFGA) and Combinatorial Ordering Next Fit Genetic Algorithm (CONFGA) have been developed for that and combined. The proposed hybrid algorithm targets to minimise the total number of running servers and resources wastage per server. The solutions obtained by the new algorithms are compared with latest solutions from literature. The results show that the proposed algorithm COFFGA outperforms other previous multi-dimension vector bin packing heuristics such as Permutation Pack (PP), First Fit (FF) and First Fit Decreasing (FFD) by 4%, 34%, and 39%, respectively. It also achieved better performance than the existing genetic algorithm for multi-capacity resources virtual machine consolidation (RGGA) in terms of performance and robustness. A thorough explanation for the improved performance of the newly proposed algorithm is given.

Best-Harmonically-Fit Periodic Task Assignment Algorithm on Multiple Periodic Resources

The periodic task set assignment problem in the context of multiple processors has been studied for decades. Different heuristic approaches have been proposed, such as the Best-Fit (BF), the First-Fit (FF), and the Worst-Fit (WF) task assignment algorithms. However, when processors are not dedicated but only periodically available to the task set, whether existing approaches still provide good performance or if there is a better task assignment approach in the new context are research problems which, to our best knowledge, have not been studied by the real-time research community. In this paper, we present the Best-Harmonically-Fit (BHF) task assignment algorithm to assign periodic tasks on multiple periodic resources. By periodic resource we mean that for every fixed time interval, i.e., the period, the resource always provides the same amount of processing capacity to a given task set. Our formal analysis indicates that if a harmonic task set is also harmonic with a resource's period, the resource capacity can be fully utilized by the task set. Based on this analysis, we present the Best-Harmonically-Fit task assignment algorithm. The experimental results show that, on average, the BHF algorithm results in $53.26$ , $42.54$ , and $27.79$ percent higher resource utilization rate than the Best-Fit Decreasing (BFD), the First-Fit Decreasing (FFD), and the Worst-Fit Decreasing (WFD) task assignment algorithms, respectively; but comparing to the optimal resource utilization rate found by exhaustive search, it is about $11.63$ percent lower.

Minimizing talent cost and operating cost in film production

Budgeting is one of the most critical issues in film production. This study addresses a cost minimization issue in scene arrangement and talent scheduling, where the latter refers to the determination of a shooting sequence so as to minimize the total holding cost of all actors and actresses. This paper generalizes the talent scheduling model by incorporating the constraints of daily operating capacity, which confines the total duration of scenes arranged within each single shooting day. The operating cost of shooting days is also introduced. The cost structure of the studied problem comprises the total retention cost of the actors and actresses, and the total operating cost of the active work days. In this paper, we use the next fit (NF) algorithm and the first fit decreasing (FFD) algorithm to allocate scenes to work days so as to provide initial solutions for further improvements. Dynamic programming, iterated local search, and tabu search are adopted to constitute the second-phase improvement procedures. We conduct a series of computational experiments to examine the performance of the proposed solution approaches.

An energy-optimization-based method of task scheduling for a cloud video surveillance center

The number of cloud video surveillance (CVS) systems has been increasing rapidly over the last decade. Since CVS systems are big energy consumers, it is urgent to take the problem of optimizing the energy consumption of CVS systems into consideration. In this study, we build a task scheduling model, and present a method of scheduling that minimizes energy consumption by reducing the number of virtual machines. The optimization problem is first formulated as a multi-dimensional bin-packing problem due to the constrains on the resources (sizes of the bandwidth, the memory, the hard disk, the CPU utilization, etc.). We convert the problem into a one-dimensional bin-packing problem by making use of the relationships between the resources, and solve it using the greedy best-fit search algorithm. This method greatly reduces the computational expense and can be used in a real-time fashion. An experimental system is designed to evaluate the method, and four experiments are carried out to demonstrate the validity of the method. Experimental results show that the method not only largely improved the resource utilization and reduces energy consumption but also the scheduling time was significantly decreased when handling the same number of video tasks. And it is obviously superior to the common approach and First Fit Decreasing (FFD) algorithm.

A Novel Dynamic Virtual Machine Consolidation Algorithm Based on Correlation Coefficient Analysis and Bin Packing

Virt ual Machine Consolidation (VMC) is known as a crucial method to improve system resource utilization and service level agreement in a datacenter. In this paper, we propose a novel algorithm named Segmentation Iteration Correlation Combination (SICC) expressly for the VMC. In this algorithm we integrate the methods of statistic regression modeling, Pearson correlation coefficient analysis and off-line Bin packing to establish a new process strategy to achieve excellent higher one dimensional resource utilization of a datacenter. The SICC operates based on an innovative two-stage strategy: the first stage is to divide all the Virtual Machines (VM) into several groups and reduce the peak-mean difference value of the VM resource utilization inside each VM group as much as possible by the Correlation Coefficient Serial analysis and one kind of improved VM dynamic complementary consolidation algorithm, derived from the algorithm of Iterative Correlation Match Algorithm (ICMA). When the difference of peak-mean value is small enough, we can take advantage of the Bin Packing methods in the second stage to improve resource utilization on account of the reasonable VM consolidation order. The numerical simulation indicates that the algorithm feature 3 % to 20% performance improvement in resource utilization to ICMA algorithm and approximate 50% performance improvement in resource utilization to First Fit Decreasing (FFD) with the same dynamic initial conditions.

Static Task Partitioning for Locked Caches in Multicore Real-Time Systems

Growing processing demand on multitasking real-time systems can be met by employing scalable multicore architectures. For such environments, locking cache lines for hard real-time systems ensures timing predictability of data references and may lower worst-case execution time. This work studies the benefits of cache locking on massive multicore architectures with private caches in the context of hard real-time systems. In shared cache architectures, the cache is a single resource shared among all of the tasks. However, in scalable cache architectures with private caches, conflicts exist only among the tasks scheduled on one core. This calls for a cache-aware allocation of tasks onto cores. The objective of this work is to increase the predictability of memory accesses resolved by caches while reducing the number of cores for a given task set. This allows designers to reduce the footprint of their subsystem of real-time tasks and thereby cost, either by choosing a product with fewer cores as a target or to allow more subsystems to be co-located on a given fixed number of cores. Our work proposes a novel variant of the cache-unaware First Fit Decreasing (FFD) algorithm called Naive locked First Fit Decreasing (NFFD) policy. We propose two cache-aware static scheduling schemes: (a) Greedy First Fit Decreasing (GFFD) and (b) Colored First Fit Decreasing (CoFFD) for task sets where tasks do not have intratask conflicts among locked regions (Scenario A). NFFD is capable of scheduling high utilization task sets that FFD cannot schedule. Experiments also show that CoFFD consistently outperforms GFFD, resulting in a lower number of cores and lower system utilization. CoFFD reduces the number of core requirements by 30% to 60% compared to NFFD. For a more generic case where tasks have intratask conflicts, we split the task partitioning between two phases: task selection and task allocation (Scenario B). Instead of resolving conflicts at a global level, these algorithms resolve conflicts among regions while allocating a task onto a core and unlocking at region level instead of task level. We show that a combination of dynamic ordering (task selection) with Chaitin’s Coloring (task allocation) scheme reduces the number of cores required by up to 22% over a basic scheme (in a combination of monotone ordering and regional FFD). Regional unlocking allows this scheme to outperform CoFFD for medium utilization task sets from Scenario A. However, CoFFD performs better than any other scheme for high utilization task sets from Scenario A. Overall, this work is unique in considering the challenges of future multicore architectures for real-time systems and provides key insights into task partitioning and cache-locking mechanisms for architectures with private caches.

Enhancing Survivability in Virtualized Data Centers: A Service-Aware Approach

In this paper, we propose a service-aware approach to enhance survivability in virtualized data centers. The idea is to create and maintain a Survivable Virtual Infrastructure (SVI) for each service or tenant, which includes Virtual Machines (VMs) hosting the corresponding application and their backup VMs. A fundamental problem is to determine how to map each SVI to a data center network with minimum operational costs while satisfying each VM's resource requirements and bandwidth demands between VMs before and after failures. This problem can be naturally divided into two subproblems: VM Placement (VMP) and Virtual Link Mapping (VLM). We first present a general optimization framework. Then we propose an efficient algorithm for VMP, and a polynomial-time optimal algorithm for VLM, which can be used as subroutines in the framework. We also present an effective heuristic algorithm that jointly solves two subproblems. It has been shown by extensive simulation results based on the real VM workload traces collected from Syracuse University's green data center that compared to the First Fit Decreasing (FFD) and shortest path routing based baseline algorithm, the proposed algorithms significantly reduce the reserved bandwidth, and yield comparable results in terms of the number of active servers. \begin{keywords}Cloud Computing, Data Center, Service-aware, Survivability, Virtual Machine Management. \end{keywords}

An experimental comparison of some heuristics for cardinality constrained bin packing problem

An experimental comparison of some heuristics for cardinality constrained bin packing problem Background: Bin packing is an NPhard optimization problem of packing items of given sizes into minimum number of capacitylimited bins. Besides the basic problem, numerous other variants of bin packing exist. The cardinality constrained bin packing adds an additional constraint that the number of items in a bin must not exceed a given limit Nmax. Objectives: Goal of the paper is to present a preliminary experimental study which demostrates adaptations of the new algorithms to the general cardinality constrained bin packing problem. Methods/Approach: Straightforward modifications of First Fit Decreasing (FFD), Refined First Fit (RFF) and the algorithm by Zhang et al. for the bin packing problem are compared to four cardinality constrained bin packing problem specific algorithms on random lists of items with 0%, 10%, 30% and 50% of large items. The behaviour of all algorithms when cardinality constraint Nmax increases is also studied. Results: Results show that all specific algorithms outperform the general algorithms on lists with low percentage of big items. Conclusions: One of the specific algorithms performs better or equally well even on lists with high percentage of big items and is therefore of significant interest. The behaviour when Nmax increases shows that specific algorithms can be used for solving the general bin packing problem as well.

A Rank-based VM Consolidation Method for Power Saving in Datacenters

In this paper, we propose a simple but flexible virtual machine consolidation method for power saving. This method is specifically designed for datacenters where heterogeneous high-density blade servers host dozens or even hundreds of virtual machines. This method utilizes an extended First-Fit Decreasing (FFD) algorithm. It selects a migration destination server on the basis of server rank. The rank represents server selection priority and is uniquely assigned to each physical server. Our simulation results show that this method reduces power consumption by 34.5% under a typical workload and 33.8% under a random workload.

Bin‐packing problem with concave costs of bin utilization

AbstractWe consider a generalized one‐dimensional bin‐packing model where the cost of a bin is a nondecreasing concave function of the utilization of the bin. Four popular heuristics from the literature of the classical bin‐packing problem are studied: First Fit (FF), Best Fit (BF), First Fit Decreasing (FFD), and Best Fit Decreasing (BFD). We analyze their worst‐case performances when they are applied to our model. The absolute worst‐case performance ratio of FF and BF is shown to be exactly 2, and that of FFD and BFD is shown to be exactly 1.5. Computational experiments are also conducted to test the performance of these heuristics. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Minimum and maximum utilization bounds for multiprocessor rate monotonic scheduling

The utilization bound for real-time rate monotonic (RM) scheduling on uniprocessors is extended to multiprocessors with partitioning-based scheduling. This allows fast schedulability tests to be performed on multiprocessors and quantifies the influence of key parameters, such as the number of processors and task sizes on the schedulability of the system. The multiprocessor utilization bound is a function of the allocation algorithm, so among all the allocation algorithms there exists at least one allocation algorithm providing the minimum multiprocessor utilization bound, and one allocation algorithm providing the maximum multiprocessor utilization bound. We prove that the multiprocessor utilization bound associated with the allocation heuristic worst fit (WF) coincides with that minimum if we use Liu and Layland's bound (LLB) as the uniprocessor schedulability condition. In addition, we present a class of allocation algorithms sharing the same multiprocessor utilization bound which coincides with the aforementioned maximum using LLB. The heuristics first fit decreasing (FFD) and best fit decreasing (BFD) belong to this class. Thus, not even an optimal allocation algorithm can guarantee a higher multiprocessor utilization bound than that of FFD and BFD using LLB. Finally, the pessimism of the multiprocessor utilization bounds is estimated through extensive simulations.

Application of genetic algorithm for bin packing

In this paper we have analysed the bin packing problem by applying Genetic Algorithm (GA). In this analysis we have represented the problem as an optimization problem and considered the objective function as fitness function for GA. The numerical results obtained from the GA indicate that the GA is robust and it yields better results when compared with the results obtained from other heuristics such as First Fit Decreasing (FFD) and Best Fit Decreasing (BFD)

Analysis of a Compound Bin Packing Algorithm

Consider the classic bin packing problem, in which we seek to pack a list of items into the minimum number of unit-capacity bins. The worst-case performance of a compound bin packing algorithm that selects the better packing produced by two previously analyzed heuristics, namely, FFD (first fit decreasing) and B2F (best two fit) is investigated. FFD and B2F can asymptotically require as many as $\frac{11}{9}$ and $\frac{5}{4}$ times the optimal number of bins, respectively. A new technique, weighting function averaging, is introduced to prove that our compound algorithm is superior to the individual heuristics on which it is based, never using more than $\frac{6}{5}$ times the optimal number of bins.

A one-dimensional cutting stock problem in the aluminium industry and its solution

When producing window frames made out of aluminium one faces the decision problem to determine how many aluminium profiles of a given standard length have to be bought to fulfill production requirements. As results of the currently implemented First Fit Decreasing (FFD) heuristic were regarded unsatisfactorily, a new code—based on the column generation procedure of Gilmore and Gomory—has been developed and supplemented by a one-pass branching up procedure to achieve integrality. Algorithmic details about the integrality achievement phase as well as results obtained when solving real world cutting stock problems on a personal computer are provided.

Analysis of a Hybrid Algorithm for Packing Unequal Bins

We consider a bin-packing problem where the sizes of the bins are allowed to vary and where the goal is to maximize the number of pieces packed. This problem is NP-hard. We examine a new efficient approximation algorithm which is a hybrid of two algorithms reported earlier, First-Fit Decreasing (FFD) and Best-Two Fit (B2F). The hybrid is iterative: it attempts to pack smaller and smaller suffixes of its list of pieces until it succeeds in packing an entire suffix. During each attempt, the hybrid operates by partitioning the current list of pieces and packing one part by B2F and afterward packing the other part of its list by FFD. We prove that no instance of the problem exists where an optimal algorithm can pack more than $\tfrac{4}{3}$ the number of pieces the hybrid can pack. We also give a sequence of examples for which the ratio of the number of pieces packed optimally and by our algorithm increases asymptotically to $\frac{4}{3}$.

A [formula omitted] theorem for bin packing

The FIRST FIT DECREASING algorithm for bin packing has long been famous for its guarantee that no packing it generates will use more than 11 9 = 1.222… times the optimal number of bins. We present a simple modified version that has essentially the same running time, should perform at least as well on average, and yet provides a guarantee of 71 60 = 1.18333… .

A new proof for the first-fit decreasing bin-packing algorithm

This paper provides a new proof of a classical result of bin-packing, namely the 11 9 performance bound for the first-fit decreasing algorithm. In bin-packing, a list of real numbers in (0,1] is to be packed into a minimal number of bins, each of which holds a total of at most 1. The first-fit decreasing (FFD) algorithm packs each number in order of nonincreasing size into the first bin in which it fits. In his doctoral dissertation, D. S. Johnson (“Near-Optimal Bin Packing Algorithms,” Doctoral thesis, MIT, Cambridge, Mass., 1973) proved that for every list L, FFD(L) ⩽ 11 9 OPT(L) + 4 , where FFD( L) and OPT( L) denote the number of bins used by FFD and an optimal packing, respectively. Unfortunately, his proof required more than 100 pages! This paper contains a much shorter and simpler proof that FFD(L) ⩽ 11 9 OPT(L) + 3 .