Dispatching in perfectly-periodic schedules

Abstract

In a perfectly-periodic schedule, time is divided into time-slots, and each client gets a time slot precisely every predefined number of time slots, called the period of that client. Periodic schedules are useful in mobile communication where they can help save power in the mobile device, and they also enjoy the best possible smoothness. In this paper we study the question of dispatching in a perfectly periodic schedule, namely how to find the next item to schedule, assuming that the schedule is already given somehow. Simple dispatching algorithms suffer from either linear time complexity per slot or from exponential space requirement. We show that if the schedule is given in a natural tree representation, then there exists a way to get the best possible running time per slot for a given space parameter, or the best possible space (up to a polynomial) for a given time parameter. We show that in many practical cases, the running time is constant and the space complexity is polynomial.

Windows scheduling of arbitrary-length jobs on multiple machines

“…This problem differs from windows scheduling since jobs may get larger windows than they request. The unit-length case was considered in and the general case of jobs with arbitrary lengths was considered in Brakerski et al (2003).…”

Balancing perfectly periodic service schedules: An application from recycling and waste management

“…The Chinese remainder theorem was used to partition the problem into smaller independent problems. Based on this partition, the possible period lengths in our study can be partitioned into only two sets: {1} and {2, 3,4,6,8,12,16,24, 48}. The services in the first set (i.e., p = 1) need to be scheduled every week.…”

“…Bar-Noy et al [1] and Brakerski et al [4] proposed the notion of periodicity in mobile and asymmetric communication, such as bluetooth networks. A perfectly periodic schedule in Brakerski et al [4] is defined as follows.…”

Perfect periodic scheduling for three basic cycles

“…Bar-Noy et al (2002b) develop tree-based approximation algorithms for perfect periodic scheduling with the objective of minimising weighted average ratios between the allocated periodicity and requested periodicity. Brakerski et al (2003) study the question of dispatching in a perfect periodic schedule, namely how to find the next item to schedule, assuming that the schedule is already given somehow.…”

“…For example, tree scheduling algorithms (Bar-Noy et al 2002b;Brakerski et al 2003) restrict their solution space to a set of periodicities with a non-trivial greatest common divisor. Moreover, , Patil and Garg (2006), and Chen and Huang (2008) constrain solutions to those for which the ratio between any pair of two allocated periodicities is a power of 2.…”