17293889
Complexity of Task Graph Scheduling with Fixed Communication Capacity
Consider a scheduling problem of parallel computations in multiprocessor systems. Let a parallel program be modeled by a task graph, where vertices represent tasks and arcs the communications between tasks. An interprocessor communication time incurs when two tasks assigned to two different processors have to communicate. Such a scheduling problem has recently been studied in the literature, mostly for the case where interprocessor communication times are fully determined. In this paper, we consider the scheduling problem with communication resource constraints. More specifically, we consider the case where all interprocessor communications take place on a network of bounded capacity. We consider two variants of the problem: communications with independent-data semantics and common-data semantics. We show that even for very specific subproblems, viz. scheduling of general graphs on two processors and scheduling of binary trees on an infinite number of processors, the minimization of the makespan of parallel programs in such a multiprocessor system is strongly -hard. We first establish the results for the case of capacity 1, referred to as the single-bus system. We then extend the results to the more general case of fixed communication capacities. As a consequence, the general scheduling problem of parallel programs with communication resource constraints is strongly -hard. These results are to be contrasted with the corresponding scheduling problems without contraint on the communication capacity, where the two-processor case has unknown time complexity and the infinite-processor case is polynomial. Our results are also extended to the case of broadcasting communications, and can be applied to multiprocessor systems with shared memory.
774892
Single Machine Scheduling Subject To Precedence Delays
Abstract A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by precedence delays, i.e., a task can start its execution only after any of its predecessors has completed and the delay between the two tasks has elapsed. In the case of unit execution times and integer lengths of delays, the problem is shown to be NP-hard in the strong sense. In the case of integer execution times and unit length of delays, the problem is polynomial, and an O(n2) optimal algorithm is provided. Both preemptive and non-preemptive cases are considered.
7929531
Closed-Form Deterministic End-to-End Performance Bounds for the Generalized Processor Sharing Scheduling Discipline
The Generalized Processor Sharing (GPS) schedulingdiscipline is an important scheduling mechanism that can support both class isolation and bandwidth sharing among different service classes, thus making itan appealing choice for networks providing multiple services with Quality-of-Service guarantees. In this paper, we study a broad classof GPS networks known as Consistent Relative Session Treatment}(CRST) GPS networks and establish closed-form end-to-end performance boundsfor CRST GPS networks. This result generalizes the results of Parekhand Gallager (1994) where simple, closed-form end-to-end performancebounds are derived for a special sub-class of CRST GPS networks, theso-called Rate Proportional Processor Sharing (RPPS) GPS networks, but performance bounds for the general CRST GPS networks do not haveclosed-form. Our result is obtained through the notion of CRSTpartition, which in fact yields a broader class of CRST GPS networksthan the one originally defined in (Parekh and Gallager, 1993). Moreover,our approach is quite general. It not only applies to the deterministicanalysis of GPS networks, but can also be employed in the study of GPSnetworks in a stochastic setting.
252821
Performance Analysis of Stochastic Timed Petri Nets Using Linear Programming Approach
Stochastic timed Petri nets are a useful tool in the performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems. In general, performance measures of stochastic timed Petri nets are difficult to obtain for practical problems due to their sizes. In this paper, we provide a method to efficiently compute upper and lower bounds for the throughputs and mean token numbers for a large class of stochastic timed Petri nets. Our approach is based on uniformization technique and linear programming.
16029762
Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates
Abstract This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an earliest due date first algorithm provides an optimal nonpreemptive schedule for unit-execution-time (UET) tasks, the preemptive priority scheduling algorithm, referred to as smallest laxity first, provides an optimal preemptive schedule for real-execution-time (RET) tasks. When the objective is to minimize the makespan, we get the same kind of result between highest level first schedules solving nonpreemptive tasks with UET and the longest remaining path first schedule for the corresponding preemptive scheduling problem with RET tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained.
17231470
Dynamic scheduling of parallel computations
Structures of parallel programs are usually represented by task graphs in the scheduling literature. Such graphs are sometimes obtained at compile time. In many other cases, however, they can be determined only at run time. In this paper, we consider the scheduling of parallel computations whose task graphs are generated at run time. We analyze the case where the task graph is a random out-tree. When the number of offspring of a task has a geometric distribution whose parameter is decreasing and convex in the level, then the breadth-first policy stochastically minimizes the makespan. If, however, this parameter is increasing and concave, then the depth-first policy stochastically minimizes the makespan.
28594120
Pattern recognition using Markov random field models
In this paper, we propose Markov random field models for pattern recognition, which provide a flexible and natural framework for modelling the interactions between spatially related random variables in their neighbourhood systems. The proposed approach is superior to conventional approaches in many aspects. This paper introduces the concept of states into Markov random filed models, presents a theoretic analysis of the approach, discusses issues of designing neighbourhood system and cliques, and analyses properties of the models. We have applied our method to the recognition of unconstrained handwritten numerals. The experimental results show that the proposed approach can achieve high performance.
14189544
Verification, refinement and scheduling of real-time programs
Abstract A real-time program can be developed by refining a specification into program code. Verification of the timing properties of the program is then usually done at two levels: verification of the ordering of timed actions in the program and proof that execution of the program on a specific system will meet its timing requirements. Refinement is done within a formal model but the second step requires a different framework in which scheduling theory analysis is used and actual program execution times can be taken into account. The implementation of a program on a system is said to be feasible or schedulable if it will meet all the timing deadlines. This paper shows how the feasibility of scheduling a real-time program can also be proved as a step in the refinement of the program from its specification. Verification of this step of refinement makes use of methods from scheduling theory within a formal system development framework.
31153136
An Adaptive Scheduling Algorithm for Molecule Docking Design on Grid
Grid provides a promising platform for the efficient execution of drug molecular docking design. Scheduling such applications is challenging for the heterogeneity, autonomy, and dynamic adaptability of grid resources. Assuming resource owners have a preemptive priority, we propose an adaptive algorithm of jobs scheduling based on time balancing strategy, which solves parallel molecular docking task by using the idle resources in the Grid. A mathematical model is developed to predict performance, which also considers systems with heterogeneous machine utilization and heterogeneous service distribution. According to the time balancing policy, ligands are partitioned into several subtasks and scheduled. The expected value of molecular docking completion time is predicted with performance model. To get better parallel computing performance, an optimal subset of heterogeneous resources with the shortest parallel executing time of tasks can be selected with the algorithm.
13004956
Consistency checking of UML requirements
This paper discusses how to check consistency of UML requirements model which consists of a use case model and a conceptual class model with system constraints. Based on a given semantics, the requirements consistency can be defined and checked formally. The consistency among use cases and constraints are classified into five types. A system operation of interaction between actor and system is formally defined as a pair of pre and post conditions. An atomic use case is described as one system operation, and a composed use case may be defined as several system operations described by an activity diagram. Thus, each use case can also be modelled as a pair of pre and post conditions by composing the pre and post conditions of system operations by introducing a sequence composition operation. Requirement consistency can be logically checked based on the semantics. A simple library system is used as a case study to illustrate the feasibility of the method.
15321284
From Durational Specifications to TLA Designs of Timed Automata
Different temporal logics tend to emphasise different aspects of a hybrid system. In this paper, we study the predicative interpretation of Duration Calculus (DC) and Temporal Logic of Actions (TLA) and the link between them. A notation called generic composition is used to simplify the manipulation of predicates. The modalities of possibility and necessity become generic composition and its inverse of converse respectively. The transformation between different temporal logics is also characterised as such modalities. The formalism provides a framework in which human experience about hybrid system development can be formalised as refinement laws. A high-level durational specification can be decomposed to two durational specifications driven by an automaton. In such a stepwise design process, durational features are reduced while automaton features increase gradually. The application of the technique is demonstrated in the case study of the gas burner problem.