In this paper, we consider a problem of assigning n independent tasks onto m identical processors in such a way that the overall execution time of the tasks will be minimized. Unlike conventional task assignment problem, we assume that the execution time of each task is not fixed in advance, and merely upper and lower bounds of the execution time are given at the compile time. In the following, we first provide a theoretical analysis of several conventional scheduling policies in terms of the worst case slowdown compared with the outcome of an optimal off-line scheduling policy. It is shown that the best known algorithm in the literature achieves a worst case performance ratio of 1 + 1/f(n) where f(n) = O(n2/3) for any fixed m, which approaches to one by increasing n to the infinity. We then propose a new scheme that achieves better worst case ratio of 1 + 1/g(n) where g(n) = Θ (n/log n) for any fixed m, which approaches to one more quickly than previous schemes.

This paper investigates the usefulness of a new priority list for two-processor scheduling problem of program nets. Firstly, we discuss the weakness of a previously proposed priority list and then introduce a new priority list. Through simulation experiment we show that the new priority list is better than the previous one and can generate the same length of schedules as GA scheduling, which implies the new priority list can generate approximately optimal schedules.

This paper provides a list-scheduling method for program nets executed with two processors. The program nets dealt with in this paper are acyclic and SWITCH-less, and the priority list proposed in this paper consists of both dynamic and static lists. First, we point out the weakness of a previously proposed priority list and propose a new priority list. Then we give properties of the new priority list and further prove this new priority list can generate optimal schedules for the program nets whose AND-nodes possess at most single input edge. Finally, we compare the new priority list with the previous one to show the new priority list can generate shorter schedules than the previous for the nets whose AND-nodes may have two input edges.

Software Radio has been proposed in the 1990s as the solution to flexible transceiver design for future wireless systems. Potential advantages and drawbacks of this approach have been described and analysed in verbose format in many articles. However, a mathematical perspective of the software radio design problem is to be found in the literature only once. Despite this attempt to develop a sound formal description the conclusions do not reach beyond algorithm design. Open issues in system design are often mentioned, but remain unresolved hitherto. We develop a novel mathematical perspective of software radio, and we formulate the design problem accordingly, by means of an integer linear programming (ILP) representation. This type of problem is well-known in computer science and operations research, but it has never been linked to software radio design before. In a first approach to solve the ILP problem we reduce it to a scheduling problem with processor constraints. In the remainder of the theoretical section we introduce the notions of granularity G and speedup s to assess the quality of modular implementations. A random runtime argument leads the way to a system-theoretic approach to modular design issues such as maximizing speedup over a great number of different implementations. For the special case G = 1 we deduce the speedup potential of a primitive graph in analytical form. In the experimental section we compare simulation results to our theory, and we extend the experiments to a more complicated graph which stems from a real software radio design project. The paper concludes with a discussion and a brief outlook to future research issues.

The paper develops the transformation rules in order to use the Stochastic Petri Net model to evaluate the performance of various task scheduling algorithms. The transformation rules are applied to DFRN scheduling algorithm to investigate its effectiveness. The performance comparison reveals that the proposed approach provides very accurate evaluation for the scheduling algorithm when the Communication to Computation Ratio value is small.

This paper deals with two-processor nonpreemptive scheduling problem for acyclic SWITCH-less program nets including two types of nodes: AND-node and OR-node. Compared with task graphs that are a special case of acyclic SWITCH-less program nets and include only AND-nodes, the multiprocessor scheduling problem of general acyclic SWITCH-less program nets is more complicated. Since multiprocessor scheduling problem for general task graphs is NP-hard, so is for acyclic SWITCH-less program nets generally. In this paper, we suppose the acyclic SWITCH-less program nets satisfy: (i) each AND-node and OR-node have 1 and 0 node firing time, respectively; (ii) each AND-node possesses single input edge. For such a class of acyclic SWITCH-less program nets, we first propose a hybrid priority list L that consists of both dynamic and static sub-lists. Then we prove that, for a given acyclic SWITCH-less program net to be executed by two identical processors, the schedule generated by L is optimal.

A parallel program with a fixed degree of parallelism cannot be executed efficiently, or at all, by a parallel computer with a different degree of parallelism. This will cause a problem in the distribution of software applications in the near future when parallel computers with various degrees of parallelism will be widely used. In this paper we propose a way to make the machine code of the programs parallelism-independent, i.e. executable in minimum time on parallel computers with any degree of parallelism. We propose and evaluate three parallelism-independent scheduling algorithms for direct acyclic graphs (DAGs) of tasks with non-uniform execution times. To prove their efficiency, we performed simulations both with random DAGs and DAGs extracted from real applications. We evaluate them in terms of schedule length, computation time and size of the scheduled program. Their results are compared to those of the traditional CP/MISF algorithm which is used separately for each number of processors.

This paper aims at improving effectiveness of previously proposed hybrid priority lists, {L*i=LdLsi}, that are applied in nonpreemptive 2-processor scheduling of general acyclic SWITCH-less program nets, where Ld and Lsi are dynamic and static priority lists respectively. Firstly, we investigate the effectiveness of Ld through experiments. According to the experimental results, we reconstruct Ld to propose its improved list L1d. Then analyzing the construction methodology of the static priority lists {Lsi}, we propose a substituted list L2d by taking into account of the factor: remaining firing numbers of nodes. Finally, we combine a part of L1d and L2d to propose a new priority list L**. Through scheduling simulation on 400 program nets, we find the new priority list L** can generate shorter schedules, close to ones of GA (Genetic Algorithm) scheduling that has been shown exceedingly effective but costing much computation time.

In static multiprocessor scheduling, heuristic algorithms have been widely used. Instead of gaining execution speed, most of them show non promising solutions since they search only a part of solution spaces. In this paper, we propose a scheduling algorithm using the genetic algorithm (GA) which is a well-known stochastic search algorithm. The proposed algorithm, named ordered-deme GA (OGA), is based on the multiple subpopulation GA, where a global population is divided into several subpopulations (demes) and each demes evolves independently. To find better schedules, the OGA orders demes from the highest to the lowest deme and migrates both the best and the worst individuals at the same time. In addition, the OGA adaptively assigns different mutation probabilities to each deme to improve search capability. We compare the OGA with well-known heuristic algorithms and other GAs for random task graphs and the task graphs from real numerical problems. The results indicate that the OGA finds mostly better schedules than others although being slower in terms of execution time.

PARAdeg has been defined to try to measure parallelism inherent in a program net. Studies on computation of PARAdeg have been done, but the quantitative evaluation, on how much PARAdeg fits parallelism of program nets, has not been studied. In this paper, we do the evaluation by applying genetic algorithm to measure firing completion times when PARAdeg processors, and less and more processors are provided for 400 program nets. Our experimental results show that the firing completion times decrease rapidly with increase of processors till PARAdeg and slowly when processors are increased to more than PARAdeg, which implies PARAdeg is a reasonable standard to measure parallelism of program nets.

All the existing scheduling algorithms order the instructions of the program in such a way that it can be executed in minimal time only for one fixed number of processors. In this paper we propose a new scheduling method, called Parallelism-Independent Scheduling Method, which enables the execution of the scheduled program on parallel computers with any degree of parallelism in near-optimal time. We propose three Parallelism-Independent algorithms, which have the following phases: obtaining a parallel schedule by using a list scheduling heuristics, optimization of the parallel schedule by rearranging the tasks in each level, so that they can be executed efficiently with different degrees of parallelism, serialization of the parallel schedule, and insertion of markers for the parallel execution limits. The three algorithms differ in their optimization phase. To prove the efficiency of our algorithms, we have made simulations with random directed acyclic graphs with different size and degree of parallelism. We compared the results in terms of schedule length to those obtained using the Critical Path Algorithm separately for each degree of parallelism.

In this paper, we consider the static multiprocessor scheduling problem for a class of multiprocessor systems consisting of m ( 1) identical processors connected by a complete network. The objective of this survey is to give a panoramic view of theoretical and/or practical approaches for solving the problem, that have been extensively conducted during the past three decades.

This paper deals with two-processor scheduling for general acyclic SWITCH-less program nets with random node firing times. First, we introduce a hybrid priority list L* that has been shown to generate optimal schedules for the acyclic SWITCH-less program nets with unity node firing times, of which AND-nodes possess at most single input edge. Then considering the factors of existence of the AND-nodes with two input edges as well as random node firing times, we extend L* to design a new dynamic priority list Ld and four static priority lists {Lsii=1,2,3,4}; and then combining Ld and Lsi (i=1,2,3,4) we propose four hybrid priority lists {L*ii=1,2,3,4}. Finally, we apply genetic algorithm to evaluate the schedules generated by the four lists through simulations on 400 program nets. Our simulation results show two of the four lists can generate reasonably good schedules.

This paper deals with two-processor scheduling for a class of program nets, that are acyclic and SWITCH-less, and of which each node has unity node firing time. Firstly, we introduce a hybrid priority list L* that generates optimal schedules for the nets whose AND-nodes possess at most single input edge. Then we extend L* to suit for general program nets to give a new priority list L**. Finally, we use genetic algorithm to do the performance evaluation for the schedules generated by L** and show these schedules are quite close to optimal ones.

We discuss a processor scheduling problem for parallel logic simulation of combinational circuits. In the processor scheduling problem, to be discussed in this paper, for logic simulation using time–first method, the time needed for each gate evaluation is not given beforehand, and is not constant. This feature distinguishes the processor scheduling problem from typical task scheduling problems. First, we devise newly Algorithm MET to solve the processor scheduling problem. The key idea of Algorithm MET is to determine processor scheduling incrementally and dynamically. Then, experimental evaluations using well–known twelve benchmark combinational circuits show the usefulness of Algorithm, MET, compared with conventional static algorithms. We believe that this is a first step to implement parallel logic simulation of combinational circuits.