Multiple Resource Requirements Research Articles

Liveness Analysis and Deadlock Control for Automated Manufacturing Systems With Multiple Resource Requirements

This paper focuses on the liveness analysis and deadlock control for automated manufacturing systems (AMSs) with multiple resource requirements. Such an AMS is modeled by a class of generalized Petri nets called systems of simple sequential processes with multiple resources (S3PMR). It is shown that a deadlock of the considered AMSs can be characterized by the saturation of a structural object in S3PMR, called perfect resource transition-circuit (PRT-circuit). As a consequence, an S3PMR is live if and only if no PRT-circuit is saturated at any reachable marking. To ensure the system liveness, one has to prevent all PRT-circuits from being saturated at all reachable markings. To develop a structurally simple Petri net deadlock controller, we present the concept of an effective transition cover, which is a special subset of PRT-circuits that may be saturated. Then by designing a control place with a proper control variable for each PRT-circuit in an effective transition cover, we obtain a deadlock controller for the system. The needed control variables are determined by an integer linear program. Since the number of PRT-circuits in an effective transition cover is much less than that of all PRT-circuits that need to control, our controller is of small structural size. For an AMS with saturable PRT-circuits, there exists at least a transition cover. An algorithm is presented for checking the effectiveness of transition covers, and transforming noneffective transition covers into effective ones. Finally, some examples are used to illustrate the proposed method.

Randomized Algorithms for Scheduling Multi-Resource Jobs in the Cloud

We consider the problem of scheduling jobs with multiple-resource requirements (CPU, memory, and disk) in a distributed server platform, motivated by data-parallel and cloud computing applications. Jobs arrive dynamically over time and require certain amount of multiple resources for the duration of their service. When a job arrives, it is queued and later served by one of the servers that has sufficient remaining resources to serve it. The scheduling of jobs is subject to two constraints: 1) packing constraints : multiple jobs can be served simultaneously by a single server if their cumulative resource requirement does not exceed the capacity of the server, and 2) non-preemption : to avoid costly preemptions, once a job is scheduled in a server, its service cannot be interrupted or migrated to another server. Prior scheduling algorithms rely on either bin packing heuristics which have low complexity but can have a poor throughput, or MaxWeight solutions that can achieve maximum throughput but repeatedly require to solve or approximate instances of a hard combinatorial problem (Knapsack) over time. In this paper, we propose a randomized scheduling algorithm for placing jobs in servers that can achieve maximum throughput with low complexity. The algorithm is naturally distributed and each queue and each server needs to perform only a constant number of operations per time unit. Extensive simulation results, using both synthetic and real traffic traces, are presented to evaluate the throughput and delay performance compared to prior algorithms.

Using genetic algorithms (GA) and a coloured timed Petri net (CTPN) for modelling the optimization-based schedule generator of a generic production scheduling system

The semiconductor manufacturing industry is one of the most complicated manufacturing systems in the world. Considering its complex problem nature, such as the unrelated parallel machine environment, dynamic job arrival, non-pre-emption, inseparable sequence-dependent set-up time, multiple-resource requirements, general precedence constraint, and job recirculation, this study proposed the optimization-based schedule generator (OptSG) for solving the generalized scheduling problems arising from the semiconductor manufacturing environment. The separation of the problem structure and problem configuration in OptSG contributes to the structural independence, making OptSG robust and convenient in analysis and problem-solving in real settings with changing properties. Meanwhile, an MILP model was proposed as a benchmark to estimate the validity of OptSG. Inseparable sequence-dependent set-up time and multiple-resource requirements that have not been addressed simultaneously in the literature were considered in this model. By using different evaluation criteria, including makespan, total completion time and maximum tardiness, experiments were conducted to compare the solutions of the MILP model, OptSG and dispatching rule-based heuristics (DRBH). The results validated the solution quality of OptSG.

A multi-dimensional scheduling scheme in a Grid computing environment

In this paper, we propose a novel distributed resource-scheduling algorithm capable of handling multiple resource requirements for jobs that arrive in a Grid computing environment. In our proposed algorithm, referred to as multiple resource scheduling (MRS) algorithm, we take into account both the site capabilities and the resource requirements of jobs. The main objective of the algorithm is to obtain a minimal execution schedule through efficient management of available Grid resources. We first propose a model in which the job and site resource characteristics can be captured together and used in the scheduling algorithm. To do so, we introduce the concept of a n-dimensional virtual map and resource potential. Based on the proposed model, we conduct rigorous simulation experiments with real-life workload traces reported in the literature to quantify the performance. We compare our strategy with most of the commonly used algorithms in place on performance metrics such as job wait times, queue completion times, and average resource utilization. Our combined consideration of job and resource characteristics is shown to render high-performance with respect to above-mentioned metrics in the environment. Our study also reveals the fact that MRS scheme has a capability to adapt to both serial and parallel job requirements, especially when job fragmentation occurs. Our experimental results clearly show that MRS outperforms other strategies and we highlight the impact and importance of our strategy.

On Multidimensional Packing Problems

We study the approximability of multidimensional generalizations of three classical packing problems: multiprocessor scheduling, bin packing, and the knapsack problem. Specifically, we study the vector scheduling problem, its dual problem, namely, the vector bin packing problem, and a class of packing integer programs. The vector scheduling problem is to schedule n d-dimensional tasks on m machines such that the maximum load over all dimensions and all machines is minimized. The vector bin packing problem, on the other hand, seeks to minimize the number of bins needed to schedule all n tasks such that the maximum load on any dimension across all bins is bounded by a fixed quantity, say, 1. Such problems naturally arise when scheduling tasks that have multiple resource requirements. Finally, packing integer programs capture a core problem that directly relates to both vector scheduling and vector bin packing, namely, the problem of packing a maximum number of vectors in a single bin of unit height. We obtain a variety of new algorithmic as well as inapproximability results for these three problems.

An Algorithm for Optimal Project Scheduling under Multiple Resource Constraints

An algorithm is described which permits the computation of optimal (minimum-duration) solutions for the resource-constrained project network scheduling problem under conditions of multiple resource requirements per job (activity). The approach is a form of bounded enumeration and employs techniques originally developed for the solution of the assembly line balancing problem. Initial computational results are given, along with an example of the type problems solved. Among the advantages of the procedure are that resource requirements can vary over job duration, and various assumptions concerning job continuity are allowable, with no extra computational effort.