scholarly journals Control of Fork-Join Processing Networks with Multiple Job Types and Parallel Shared Resources

2021 ◽  
Author(s):  
Erhun Özkan
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Optimal Scheduling ◽  
Shared Resources ◽  
Asymptotically Optimal ◽  
Scheduling Policy ◽  
Synchronization Constraints ◽  
Processing Network ◽  
Diffusion Scale ◽  
Processing Networks

A fork-join processing network is a queueing network in which tasks associated with a job can be processed simultaneously. Fork-join processing networks are prevalent in computer systems, healthcare, manufacturing, project management, justice systems, and so on. Unlike the conventional queueing networks, fork-join processing networks have synchronization constraints that arise because of the parallel processing of tasks and can cause significant job delays. We study scheduling in fork-join processing networks with multiple job types and parallel shared resources. Jobs arriving in the system fork into arbitrary number of tasks, then those tasks are processed in parallel, and then they join and leave the network. There are shared resources processing multiple job types. We study the scheduling problem for those shared resources (i.e., which type of job to prioritize at any given time) and propose an asymptotically optimal scheduling policy in diffusion scale.

Alternative routeing in fully connected queueing networks

2000 ◽  
Vol 32 (4) ◽  
pp. 962-982 ◽  
Author(s):  
C. N. Laws ◽  
Y. C. Teh
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Asymptotically Optimal ◽  
Alternative Routes ◽  
Fully Connected

We consider a fully connected queueing network in which customers have one direct and many alternative routes through the network, and where customer routeing is dynamic. We obtain an asymptotically optimal routeing policy, taking the limit as the number of queues of the network increases. We observe that good policies route customers directly, unless there is a danger of servers becoming idle, in which case customers should be routed alternatively so as to avoid such idleness, and this leads to policies that perform well in moderate-sized networks.

scholarly journals On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking

2021 ◽  
Author(s):  
Erhun Özkan
Keyword(s):  
Parallel Processing ◽  
Heavy Traffic ◽  
Resource Scheduling ◽  
System Capacity ◽  
Parallel Networks ◽  
Holding Cost ◽  
Resource Collaboration ◽  
Synchronization Constraints ◽  
Diffusion Scale ◽  
Processing Networks

We study scheduling control of parallel processing networks in which some resources need to simultaneously collaborate to perform some activities and some resources multitask. Resource collaboration and multitasking give rise to synchronization constraints in resource scheduling when the resources are not divisible, that is, when the resources cannot be split. The synchronization constraints affect the system performance significantly. For example, because of those constraints, the system capacity can be strictly less than the capacity of the bottleneck resource. Furthermore, the resource scheduling decisions are not trivial under those constraints. For example, not all static prioritization policies retain the maximum system capacity, and the ones that retain the maximum system capacity do not necessarily minimize the delay (or, in general, the holding cost). We study optimal scheduling control of a class of parallel networks and propose a dynamic prioritization policy that retains the maximum system capacity and is asymptotically optimal in diffusion scale and a conventional heavy-traffic regime with respect to the expected discounted total holding cost objective.

Optimal scheduling in queueing networks

1984 ◽  
Vol 16 (1) ◽  
pp. 13-13
Author(s):  
F. J. Massey ◽  
D. F. Miller
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Performance Measure ◽  
Optimal Scheduling ◽  
Closed Queueing Network ◽  
Service Stations ◽  
A Performance

This paper derives an algorithm for finding a scheduling discipline for scheduling N customers at M service stations in a closed queueing network so as to optimize a performance measure which depends on the configuration of customers at the service stations.

scholarly journals Optimal Schedules for Parallelizing Anytime Algorithms: The Case of Shared Resources

2003 ◽  
Vol 19 ◽  
pp. 73-138 ◽  
Author(s):  
L. Finkelstein ◽  
S. Markovitch ◽  
E. Rivlin
Keyword(s):  
Scheduling Algorithm ◽  
Latin Square ◽  
Optimal Scheduling ◽  
Statistical Characteristics ◽  
Shared Resources ◽  
Anytime Algorithms ◽  
Initial State ◽  
Scheduling Policy ◽  
Deterministic Algorithms ◽  
Single Processor

The performance of anytime algorithms can be improved by simultaneously solving several instances of algorithm-problem pairs. These pairs may include different instances of a problem (such as starting from a different initial state), different algorithms (if several alternatives exist), or several runs of the same algorithm (for non-deterministic algorithms). In this paper we present a methodology for designing an optimal scheduling policy based on the statistical characteristics of the algorithms involved. We formally analyze the case where the processes share resources (a single-processor model), and provide an algorithm for optimal scheduling. We analyze, theoretically and empirically, the behavior of our scheduling algorithm for various distribution types. Finally, we present empirical results of applying our scheduling algorithm to the Latin Square problem.

scholarly journals Finite Queueing Modeling and Optimization: A Selected Review

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
F. R. B. Cruz ◽  
T. van Woensel
Keyword(s):  
Performance Evaluation ◽  
Queueing Networks ◽  
Queueing Network ◽  
Expansion Method ◽  
Network Analyzer ◽  
Modeling And Optimization ◽  
Product Engineering ◽  
Service Rates

This review provides an overview of the queueing modeling issues and the related performance evaluation and optimization approaches framed in a joined manufacturing and product engineering. Such networks are represented as queueing networks. The performance of the queueing networks is evaluated using an advanced queueing network analyzer: the generalized expansion method. Secondly, different model approaches are described and optimized with regard to the key parameters in the network (e.g., buffer and server sizes, service rates, and so on).

scholarly journals Robust scheduling for flexible processing networks

2017 ◽  
Vol 49 (2) ◽  
pp. 603-628 ◽  
Author(s):  
Ramtin Pedarsani ◽  
Jean Walrand ◽  
Yuan Zhong
Keyword(s):  
Queueing Networks ◽  
Complex Structure ◽  
Job Flows ◽  
Heterogeneous Servers ◽  
Robust Scheduling ◽  
System Parameters ◽  
Balanced Allocation ◽  
Service Rates ◽  
Length Changes ◽  
Processing Networks

Abstract Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these networks is the lack of reliable estimates of system parameters, and an attractive approach for addressing this challenge is to design robust policies, i.e. policies that do not use system parameters such as arrival and/or service rates for making scheduling decisions. In this paper we propose a general framework for the design of robust policies. The main technical novelty is the use of a stochastic gradient projection method that reacts to queue-length changes in order to find a balanced allocation of service resources to incoming tasks. We illustrate our approach on two broad classes of processing systems, namely the flexible fork-join networks and the flexible queueing networks, and prove the rate stability of our proposed policies for these networks under nonrestrictive assumptions.

scholarly journals Optimal control of queueing networks: an approach via fluid models

2002 ◽  
Vol 34 (02) ◽  
pp. 313-328
Author(s):  
Nicole Bäuerle
Keyword(s):  
Optimal Control ◽  
Decision Rule ◽  
Average Cost ◽  
Queueing Networks ◽  
Optimal Decision ◽  
Stochastic Network ◽  
Asymptotically Optimal ◽  
Multiclass Queueing Networks ◽  
Optimal Decision Rule ◽  
Multiclass Queueing

We consider a general control problem for networks with linear dynamics which includes the special cases of scheduling in multiclass queueing networks and routeing problems. The fluid approximation of the network is used to derive new results about the optimal control for the stochastic network. The main emphasis lies on the average-cost criterion; however, the β-discounted as well as the finite-cost problems are also investigated. One of our main results states that the fluid problem provides a lower bound to the stochastic network problem. For scheduling problems in multiclass queueing networks we show the existence of an average-cost optimal decision rule, if the usual traffic conditions are satisfied. Moreover, we give under the same conditions a simple stabilizing scheduling policy. Another important issue that we address is the construction of simple asymptotically optimal decision rules. Asymptotic optimality is here seen with respect to fluid scaling. We show that every minimizer of the optimality equation is asymptotically optimal and, what is more important for practical purposes, we outline a general way to identify fluid optimal feedback rules as asymptotically optimal. Last, but not least, for routeing problems an asymptotically optimal decision rule is given explicitly, namely a so-called least-loaded-routeing rule.

Memory-Aware Scheduling Parallel Real-Time Tasks for Multicore Systems

2021 ◽  
Vol 31 (04) ◽  
pp. 613-634
Author(s):  
Zhenyang Lei ◽  
Xiangdong Lei ◽  
Jun Long
Keyword(s):  
Real Time ◽  
Data Access ◽  
Main Memory ◽  
Second Phase ◽  
Shared Resources ◽  
Access Memory ◽  
Worst Case ◽  
Scheduling Policy ◽  
The Core ◽  
Level Scheduling

Shared resources on the multicore chip, such as main memory, are increasingly becoming a point of contention. Traditional real-time task scheduling policies focus on solely on the CPU, and do not take in account memory access and cache effects. In this paper, we propose parallel real-time tasks scheduling (PRTTS) policy on multicore platforms. Each set of tasks is represented as a directed acyclic graph (DAG). The priorities of tasks are assigned according to task periods Rate Monotonic (RM). Each task is composed of three phases. The first phase is read memory stage, the second phase is execution phase and the third phase is write memory phase. The tasks use locks and critical sections to protect data access. The global scheduler maintains the task pool in which tasks are ready to be executed which can run on any core. PRTTS scheduling policy consists of two levels: the first level scheduling schedules ready real-time tasks in the task pool to cores, and the second level scheduling schedules real-time tasks on cores. Tasks can preempt the core on running tasks of low priority. The priorities of tasks which want to access memory are dynamically increased above all tasks that do not access memory. When the data accessed by a task is in the cache, the priority of the task is raised to the highest priority, and the task is scheduled immediately to preempt the core on running the task not accessing memory. After accessing memory, the priority of these tasks is restored to the original priority and these tasks are pended, the preempted task continues to run on the core. This paper analyzes the schedulability of PRTTS scheduling policy. We derive an upper-bound on the worst-case response-time for parallel real-time tasks. A series of extensive simulation experiments have been performed to evaluate the performance of proposed PRTTS scheduling policy. The results of simulation experiment show that PRTTS scheduling policy offers better performance in terms of core utilization and schedulability rate of tasks.

Software for Queueing Analysis

2018 ◽  
pp. 255-291
Keyword(s):  
Queueing Networks ◽  
Discrete Event ◽  
Queueing Network ◽  
Queueing Analysis ◽  
Discrete Events ◽  
Technical Literature ◽  
Event Simulation ◽  
Statistical Program ◽  
Service Times ◽  
Waiting Lines

Chapter 8 gives a brief discussion of computer simulation for discrete events. The chapter lists software programs in the technical literature that outline programs for the simulation of discrete events, both of commercial origin and free programs. In addition to the lists submitted, the authors present specialized packages for analysis and simulation of waiting lines in the R language. Statistical considerations are presented, which must be taken into account when obtaining data from simulations in situations of waiting lines. Chapter 8 presents three packages of the statistical program R: the “queueing” analysis package provides versatile tools for analysis of birth- and death-based Markovian queueing models and single and multiclass product-form queueing networks; “simmer” package is a process-oriented and trajectory-based discrete-event simulation (DES) package for R; and, the purpose of the “queuecomputer” package is to calculate, deterministically, the outputs of a queueing network, given the arrival and service times of all the customers. It also uses simulation for the implementation of a method for the calculation of queues with arbitrary arrival and service times. For each theme, the authors show the use of the packages in R.

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