Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Improving Makespan in Dynamic Task Scheduling for Cloud Robotic Systems with Time Window Constraints

Saeid Alirezazadeh, Luís A. Alexandre

TL;DR

This work proposes the grid of all tasks balancing algorithm (GTBA) for distributing and scheduling tasks with minimum makespan, a combinatorial method that describes a way to distribute tasks among processing units and schedule them when a set of tasks arrives in such a way that the makespan is minimized.

Abstract

A scheduling method in a robotic network cloud system with minimal makespan is beneficial as the system can complete all the tasks assigned to it in the fastest way. Robotic network cloud systems can be translated into graphs where nodes represent hardware with independent computing power and edges represent data transmissions between nodes. Time window constraints on tasks are a natural way to order tasks. The makespan is the maximum amount of time between when the first node to receive a task starts executing its first scheduled task and when all nodes have completed their last scheduled task. Load balancing allocation and scheduling ensures that the time between when the first node completes its scheduled tasks and when all other nodes complete their scheduled tasks is as short as possible. We propose a grid of all tasks to ensure that the time window constraints for tasks are met. We propose grid of all tasks balancing algorithm for distributing and scheduling tasks with minimum makespan. We theoretically prove the correctness of the proposed algorithm and present simulations illustrating the obtained results.

Improving Makespan in Dynamic Task Scheduling for Cloud Robotic Systems with Time Window Constraints

TL;DR

This work proposes the grid of all tasks balancing algorithm (GTBA) for distributing and scheduling tasks with minimum makespan, a combinatorial method that describes a way to distribute tasks among processing units and schedule them when a set of tasks arrives in such a way that the makespan is minimized.

Abstract

A scheduling method in a robotic network cloud system with minimal makespan is beneficial as the system can complete all the tasks assigned to it in the fastest way. Robotic network cloud systems can be translated into graphs where nodes represent hardware with independent computing power and edges represent data transmissions between nodes. Time window constraints on tasks are a natural way to order tasks. The makespan is the maximum amount of time between when the first node to receive a task starts executing its first scheduled task and when all nodes have completed their last scheduled task. Load balancing allocation and scheduling ensures that the time between when the first node completes its scheduled tasks and when all other nodes complete their scheduled tasks is as short as possible. We propose a grid of all tasks to ensure that the time window constraints for tasks are met. We propose grid of all tasks balancing algorithm for distributing and scheduling tasks with minimum makespan. We theoretically prove the correctness of the proposed algorithm and present simulations illustrating the obtained results.

Paper Structure

This paper contains 11 sections, 2 theorems, 16 equations, 13 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method Overview
  4. Preliminaries
  5. Key Method (Allocation of Sorted Tasks to Processing Units)
  6. Task Ordering Procedure
  7. Proof of optimality
  8. Experiments
  9. Complexity
  10. Scalability
  11. Conclusion

Key Result

Proposition 1

(ASTPU method) Let $A=\{a_1, \ldots, a_n\}$ be a list of positive real numbers and $m\geq 1$ be an integer. Assume that we are randomly removing one of $a_i$'s and putting it in exactly one of the $m$ places and do the same process untill the set $A$ is empty. Let $X_j$, for $j=1,\ldots,m$, be rando

Figures (13)

  • Figure 1: The intuition of the proposed method to minimize the makespan and balance the loads.
  • Figure 2: Creating columns with blocks on top of each other such that the total square differences between the length of columns and the $\mu$ line is minimum.
  • Figure 3: Average makespan (in milliseconds) in a single time step.
  • Figure 4: $TCD$ (in milliseconds) as a function of number of arrival tasks in a single time step. It is possible to see that the ILBA, BLBA, and BGA have always larger $TCD$ compared with GTBA method.
  • Figure 5: Average makespan (in milliseconds) for each of the 200 time steps for $50$ experiments, where the number of arriving tasks follows a Poisson distribution with parameter $7$. The straight lines are the average makespans of all experiments for each method.
  • ...and 8 more figures

Theorems & Definitions (7)

  • Remark 1
  • Definition 4.1
  • Remark 2
  • Proposition 1
  • proof
  • Corollary 1
  • proof