Howard Jay Siegel

A Comparison of Eleven Static Heuristics for Mapping a Class of Independent Tasks onto Heterogeneous Distributed Computing Systems

Mixed-machine heterogeneous computing (HC) environments utilize a distributed suite of different high-performance machines, interconnected with high-speed links, to perform different computationally intensive applications that have diverse computational requirements. HC environments are well suited to meet the computational demands of large, diverse groups of tasks. The problem of optimally mapping (defined as matching and scheduling) these tasks onto the machines of a distributed HC environment has been shown, in general, to be NP-complete, requiring the development of heuristic techniques. Selecting the best heuristic to use in a given environment, however, remains a difficult problem, because comparisons are often clouded by different underlying assumptions in the original study of each heuristic. Therefore, a collection of 11 heuristics from the literature has been selected, adapted, implemented, and analyzed under one set of common assumptions. It is assumed that the heuristics derive a mapping statically (i.e., off-line). It is also assumed that a metatask (i.e., a set of independent, noncommunicating tasks) is being mapped and that the goal is to minimize the total execution time of the metatask. The 11 heuristics examined are Opportunistic Load Balancing, Minimum Execution Time, Minimum Completion Time, Min?min, Max?min, Duplex, Genetic Algorithm, Simulated Annealing, Genetic Simulated Annealing, Tabu, and A*. This study provides one even basis for comparison and insights into circumstances where one technique will out-perform another. The evaluation procedure is specified, the heuristics are defined, and then comparison results are discussed. It is shown that for the cases studied here, the relatively simple Min?min heuristic performs well in comparison to the other techniques.

Dynamic Mapping of a Class of Independent Tasks onto Heterogeneous Computing Systems

Dynamic mapping (matching and scheduling) heuristics for a class of independent tasks using heterogeneous distributed computing systems are studied. Two types of mapping heuristics are considered, immediate mode and batch mode heuristics. Three new heuristics, one for batch mode and two for immediate mode, are introduced as part of this research. Simulation studies are performed to compare these heuristics with some existing ones. In total five immediate mode heuristics and three batch mode heuristics are examined. The immediate mode dynamic heuristics consider, to varying degrees and in different ways, task affinity for different machines and machine ready times. The batch mode dynamic heuristics consider these factors, as well as aging of tasks waiting to execute. The simulation results reveal that the choice of which dynamic mapping heuristic to use in a given heterogeneous environment depends on parameters such as (a) the structure of the heterogeneity among tasks and machines and (b) the arrival rate of the tasks.

Task Matching and Scheduling in Heterogeneous Computing Environments Using a Genetic-Algorithm-Based Approach

To exploit a heterogeneous computing (HC) environment, an application task may be decomposed into subtasks that have data dependencies. Subtask matching and scheduling consists of assigning subtasks to machines, ordering subtask execution for each machine, and ordering intermachine data transfers. The goal is to achieve the minimal completion time for the task. A heuristic approach based on a genetic algorithm is developed to do matching and scheduling in HC environments. It is assumed that the matcher/scheduler is in control of a dedicated HC suite of machines. The characteristics of this genetic-algorithm-based approach include: separation of the matching and the scheduling representations, independence of the chromosome structure from the details of the communication subsystem, and consideration of overlap among all computations and communications that obey subtask precedence constraints. It is applicable to the static scheduling of production jobs and can be readily used to collectively schedule a set of tasks that are decomposed into subtasks. Some parameters and the selection scheme of the genetic algorithm were chosen experimentally to achieve the best performance. Extensive simulation tests were conducted. For small-sized problems (e.g., a small number of subtasks and a small number of machines), exhaustive searches were used to verify that this genetic-algorithm-based approach found the optimal solutions. Simulation results for larger-sized problems showed that this genetic-algorithm-based approach outperformed two nonevolutionary heuristics and a random search.

Scheduling resources in multi-user, heterogeneous, computing environments with SmartNet

It is increasingly common for computer users to have access to several computers on a network, and hence to be able to execute many of their tasks on any of several computers. The choice of which computers execute which tasks is commonly determined by users based on a knowledge of computer speeds for each task and the current load on each computer. A number of task scheduling systems have been developed that balance the load of the computers on the network, but such systems tend to minimize the idle time of the computers rather than minimize the idle time of the users. The paper focuses on the benefits that can be achieved when the scheduling system considers both the computer availabilities and the performance of each task on each computer. The SmartNet resource scheduling system is described and compared to two different resource allocation strategies: load balancing and user directed assignment. Results are presented where the operation of hundreds of different networks of computers running thousands of different mixes of tasks are simulated in a batch environment. These results indicate that, for the computer environments simulated, SmartNet outperforms both load balancing and user directed assignments, based on the maximum time users must wait for their tasks to finish.

A dynamic matching and scheduling algorithm for heterogeneous computing systems

A heterogeneous computing system provides a variety of different machines, orchestrated to perform an application whose subtasks have diverse execution requirements. The subtasks must be assigned to machines (matching) and ordered for execution (scheduling) such that the overall application execution time is minimized. A new dynamic mapping (matching and scheduling) heuristic called the hybrid remapper is presented here. The hybrid remapper is based on a centralized policy and improves a statically, obtained initial matching and scheduling by remapping to reduce the overall execution time. The remapping is non-preemptive and the execution of the hybrid remapper can be overlapped with the execution of the subtasks. During application execution, the hybrid remapper uses run-time values for the subtask completion times and machine availability times whenever possible. Therefore, the hybrid remapper bases its decisions on a mixture of run-time and expected values. The potential of the hybrid remapper to improve the performance of initial static mappings is demonstrated using simulation studies.

Efficient multicast stream authentication using erasure codes

We describe a novel method for authenticating multicast packets that is robust against packet loss. Our focus is to minimize the size of the communication overhead required to authenticate the packets. Our approach is to encode the hash values and the signatures with Rabins Information Dispersal Algorithm (IDA) to construct an authentication scheme that amortizes a single signature operation over multiple packets. This strategy is especially efficient in terms of space overhead, because just the essential elements needed for authentication (i.e., one hash per packet and one signature per group of packets) are used in conjunction with an erasure code that is space optimal. Using asymptotic techniques, we derive the authentication probability of our scheme using two different bursty loss models. A lower bound of the authentication probability is also derived for one of the loss models. To evaluate the performance of our scheme, we compare our technique with four other previously proposed schemes using empirical results.

Efficient multicast packet authentication using signature amortization

We describe a novel method for authenticating multicast packets that is robust against packet loss. Our main focus is to minimize the size of the communication overhead required to authenticate the packets. Our approach is to encode the hash values and the signatures with Rabins Information Dispersal Algorithm (IDA) to construct an authentication scheme that amortizes a single signature operation over multiple packets. This strategy is especially efficient in terms of space overhead, because just the essential elements needed for authentication (i.e., one hash per packet and one signature per group of packets) are used in conjunction with an erasure code that is space optimal. To evaluate the performance of our scheme, we compare our technique with four other previously proposed schemes using analytical and empirical results. Two different bursty loss models are considered in the analyses.

The Multistage Cube: A Versatile Interconnection Network

The cube network can support both MIMD and SIMD processing in distributed systems. It allows flexible communications in systems like PASM, PUMPS, and the BMD test bed.

Study of multistage SIMD interconnection networks

Four SIMD multistage networks - Fengs data manipulator, STARAN flip network, omega network, and indirect binary n-cube—are analyzed. Three parameters - topology, interchange box, and control structure—are defined. It is shown that the latter three networks use equivalent topologies and differences in their capabilities result from the other parameters. An augmented data manipulator network using a modified control structure to perform more single pass interconnections than the other networks is presented. Some problems may be solved more efficiently if the 2n processing elements of an SIMD machine can be partitioned into submachines of size 2r. Single and multiple control partitioning are defined. The capabilities of these multistage networks to perform in these partioned environments are discussed.

Time and cost trade-off management for scheduling parallel applications on Utility Grids

With the growth of Utility Grids and various Grid market infrastructures, the need for efficient and cost effective scheduling algorithms is also increasing rapidly, particularly in the area of meta-scheduling. In these environments, users not only may have conflicting requirements with other users, but also they have to manage the trade-off between time and cost such that their applications can be executed most economically in the minimum time. Thus, selection of the best Grid resources becomes a challenge in such a competitive environment. This paper presents three novel heuristics for scheduling parallel applications on Utility Grids that manage and optimize the trade-off between time and cost constraints. The performance of the heuristics is evaluated through extensive simulations of a real-world environment with real parallel workload models to demonstrate the practicality of our algorithms. We compare our scheduling algorithms against existing common meta-schedulers experimentally. The results show that our algorithms outperform existing algorithms by minimizing the time and cost of application execution on Utility Grids.