Advance reservation is important to guarantee the quality of services of jobs by allowing exclusive access to resources over a defined time interval on resources. It is a challenge for the scheduler to organize available resources efficiently and to allocate them for parallel AR jobs with deadline constraint appropriately. This paper provides a slot-based data structure to organize available resources of multiprocessor systems in a way that enables efficient search and update operations, and formulates a suite of scheduling policies to allocate resources for dynamically arriving AR requests. The performance of the scheduling algorithms were investigated by simulations with different job sizes and durations, system loads and scheduling flexibilities. Simulation results show that job sizes and durations, system load and the flexibility of scheduling will impact the performance metrics of all the scheduling algorithms, and the PE-Worst-Fit algorithm becomes the best algorithm for the scheduler with the highest acceptance rate of AR requests, and the jobs with the First-Fit algorithm experience the lowest average slowdown. The data structure and scheduling policies can be used to organize and allocate resources for parallel AR jobs with deadline constraint in large-scale computing systems.
Many data structures and scheduling algorithms have been proposed for advance reservations. Most of them are suitable for AR requests with immediate deadlines, and only few of them were specifically designed for AR requests with general deadlines. For AR request with immediate deadlines, such data structure as array @cite_6 , linked-list @cite_22 , trees @cite_1 @cite_6 @cite_20 and queues @cite_30 @cite_14 have already been widely studied. These data structures are primarily used for admission control and focused on finding out whether it's feasible for the scheduler to accept an AR request to start at a definite time and keep on running for a given period. In @cite_14 the author presents a good summary and comparison of them when they are used for single- or multi-processor AR jobs with immediate deadline constraint. However, they are not specifically designed for AR requests with general deadline constraint. Based on existing scheduling theory and algorithms for jobs with or without deadlines, some variants of scheduling algorithms for jobs with advance reservations have been studied in Grid-like systems @cite_25 @cite_23 @cite_2 @cite_20 and their impact on the users and the systems were investigated in terms of turnaround time, slowdown, or utilization.
@cite_30 @cite_14 @cite_22 @cite_1 @cite_6 @cite_23 @cite_2 @cite_25 @cite_20
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We study the problem of non-preemptive scheduling to minimize energy consumption for devices that allow dynamic voltage scaling. Specifically, consider a device that can process jobs in a non-preemptive manner. The input consists of (i) the set R of available speeds of the device, (ii) a set J of jobs, and (iii) a precedence constraint Π among J. Each job j in J, defined by its arrival time aj, deadline dj, and amount of computation cj, is supposed to be processed by the device at a speed in R. Under the assumption that a higher speed means higher energy consumption, the power-saving scheduling problem is to compute a feasible schedule with speed assignment for the jobs in J such that the required energy consumption is minimized. This paper focuses on the setting of weakly dynamic voltage scaling, i.e., speed change is not allowed in the middle of processing a job. To demonstrate that this restriction on many portable power-aware devices introduces hardness to the power-saving scheduling problem, we prove that the problem is NP-hard even if aj = aj ′ and dj = dj ′ hold for all j,j ′∈ Jand |R|=2. If |R|<∞, we also give fully polynomial-time approximation schemes for two cases of the general NP-hard problem: (a) all jobs share a common arrival time, and (b) Π = ∅ and for any j,j ′ ∈ J, aj ≤ aj ′ implies dj ≤ dj ′. To the best of our knowledge, there is no previously known approximation algorithm for any special case of the NP-hard problem. The main aim of this note is to show that a polynomial-time algorithm for the scheduling problem 1|r j ; p j = p| ∑ Uj given by Carlier in (1981) is incorrect. In this problem we are given n jobs with release times and deadlines. All jobs have the same processing time p. The objective is to find a non-preemptive schedule that maximizes the number of jobs completed by their deadlines. The feasibility version of this problem, where we ask whether all jobs can meet their deadlines, has been studied thoroughly. Polynomial-time algorithms for this version were first found, independently, by Simons (1978) and Carlier (1981). A faster algorithm, with running time O(n log n), was subsequently given by (1981). The elegant feasibility algorithm of Carlier (1981) is based on dynamic programming and it processes jobs from left to right on the time-axis. For each time t, it constructs a partial schedule with jobs that complete at or before time t. Carlier also attempted to apply the same technique to design a polynomial-time algorithm for the maximization version, 1|r j ; p j = p| ∑ Uj , and claimed an O(n3 log n)-time algorithm. His result is now widely cited in the literature. We show, however, that this algorithm is not correct, by giving an instance on which it produces a sub-optimal schedule. Our counter-example can be, in fact, extended to support a broader claim, namely that even the general approach from Carlier (1981) cannot yield a polynomial-time algorithm. By this general approach we mean a class of algorithms that processes the input from left to right and make decisions based on the deadline ordering, and not their exact values. The question remains as to how efficiently can we solve the scheduling problem 1|r j ; p j = p| ∑ Uj . Baptiste (1999) gave an O(n7)-time algorithm for the more general version of this problem where jobs have weights. We show how to modify his algorithm to obtain a faster, O(n5)-time algorithm for the non-weighted case. These last two results are discussed only briefly in this note. The complete proofs can be found in the full version of this paper, see (2004). Advance reservations are a useful method to allocate resources of various kinds in many different environments. Among others, a major advantage of this kind of reservation is the improved admission probability for requests that are made sufficiently early. In order to implement reliable admission control for these requests, it is important to store information in data structures about future allocations and to provide fast access to the available information. In this paper, two data structures are examined: a tree specially designed to support advance reservations is compared to arrays. Both structures are examined analytically and by measurements in a realistic network management system capable of advance reservations. It turns out that arrays are far better suited to support the required operations, in particular when large time intervals need to be scanned. We present polylogarithmic approximations for the R|prec|Cmax and R|prec|∑jwjCj problems, when the precedence constraints are “treelike” – i.e., when the undirected graph underlying the precedences is a forest. We also obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment – this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion+dilation”, as in other job shop scheduling approaches. The first step in our algorithm for the R|prec|Cmax problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random delays technique of Leighton, Maggs and Rao to the case of trees. For the weighted completion time, we show a certain type of reduction to the makespan problem, which dovetails well with the lower bound we employ for the makespan problem. For the special case of chains, we show a dependent rounding technique which leads to improved bounds on the weighted completion time and new bicriteria bounds for the flow time. This paper studies a flexible scheduling data structure that is used to manage out-of-order service requests in real-time service-oriented architecture (RT-SOA) applications. We propose a hierarchical TBTree (hTBTree) to record server availability across a hierarchy of time intervals with different degrees of time granularity. Real-time services need to find enough time interval in hTBTree for their requested executions. The structure of hTBTree is designed to record only the availability of a resource during a time interval rather than the specific reserved time-slots for each request. It thus will automatically adjust existing reservations within their service intervals to make room for new reservation requests. Simulations have been conducted to study the acceptance ratio and performance of different tree-based data structures. Results show that by allowing flexibility in reservations, hTBTree can accept more real-time service requests compared with other fixed time-slot reservation scheme such as segment tree and the original TBTree. In this way, it also increases the overall system utilization. We give a new and efficient approximation algorithm for scheduling precedence-constrained jobs on machines with different speeds. The problem is as follows. We are given n jobs to be scheduled on a set of m machines. Jobs have processing times and machines have speeds. It takes pj si units of time for machine i with speed si to process job j with processing requirement pj. Precedence constraints between jobs are given in the form of a partial order. If j?k, processing of job k cannot start until job j's execution is completed. The objective is to find a non-preemptive schedule to minimize the makespan of the schedule. Chudak and Shmoys (1997, “Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA),” pp. 581?590) gave an algorithm with an approximation ratio of O(log m), significantly improving the earlier ratio of O(m) due to Jaffe (1980, Theoret. Comput. Sci.26, 1?17). Their algorithm is based on solving a linear programming relaxation. Building on some of their ideas, we present a combinatorial algorithm that achieves a similar approximation ratio but runs in O(n3) time. Our algorithm is based on a new and simple lower bound which we believe is of independent interest. We present new approximation algorithms for the problem of scheduling precedence-constrained jobs on parallel machines that are uniformly related. That is, there arenjobs andmmachines; each jobjrequirespjunits of processing, and is to be processed on one machine without interruption; if it is assigned to machinei, which runs at a given speedsi, it takespj sitime units. There also is a partial order ? on the jobs, wherej?kimplies that jobkmay not start processing until jobjhas been completed. We consider two objective functions:Cmax=maxjCj, whereCjdenotes the completion time of jobj, and ?jwjCj, wherewjis a weight that is given for each jobj. For the first objective, the best previously known result is anOm-approximation algorithm, which was shown by Jaffe more than 15 years ago. We give anO(logm)-approximation algorithm. We also show how to extend this result to obtain anO(logm)-approximation algorithm for the second objective, albeit with a somewhat larger constant. These results also extend to settings in which each jobjhas a release daterjbefore which the job may not begin processing. In addition, we obtain stronger performance guarantees if there are a limited number of distinct speeds. Our results are based on a new linear programming-based technique for estimating the speed at which each job should be run, and a variant of the list scheduling algorithm of Graham that can exploit this additional information. In 1966, Graham showed that a simple procedure called list scheduling yields a 2-approximation algorithm for the central problem of scheduling precedence constrained jobs on identical machines to minimize makespan. To date this has remained the best algorithm, and whether it can or cannot be improved has become a major open problem in scheduling theory. We address this problem by establishing a quite surprising relation between the approximability of the considered problem and that of scheduling precedence constrained jobs on a single machine to minimize weighted completion time. More specifically, we prove that if the single machine problem is hard to approximate within a factor of @math , then the considered parallel machine problem, even in the case of unit processing times, is hard to approximate within a factor of @math , where @math tends to 0 as @math tends to 0. Combining this with Bansal and Khot's recent hardness result for the single machine problem gives that it is NP-hard to improve upon the approximation ratio obtained by Graham, assuming a new variant of the unique games conjecture. In general, two types of resource reservations in computer networks can be distinguished: immediate reservations which are made in a just-in-time manner and advance reservations which allow to reserve resources a long time before they are actually used. Advance reservations are especially useful for grid computing but also for a variety of other applications that require network quality-of-service, such as content distribution networks or even mobile clients, which need advance reservation to support handovers for streaming video. With the emerged MPLS standard, explicit routing can be implemented also in IP networks, thus overcoming the unpredictable routing behavior which so far prevented the implementation of advance reservation services. The impact of such advance reservation mechanisms on the performance of the network with respect to the amount of admitted requests and the allocated bandwidth has so far not been examined in detail. We show that advance reservations can lead to a reduced performance of the network with respect to both metrics. The analysis of the reasons shows a fragmentation of the network resources. In advance reservation environments, additional new services can be defined such as malleable reservations and can lead to an increased performance of the network. Four strategies for scheduling malleable reservations are presented and compared. The results of the comparisons show that some strategies increase the resource fragmentation and are therefore unsuitable in the considered environment while others lead to a significantly better performance of the network. Besides discussing the performance issue, the software architecture of a management system for advance reservations is presented.