Minimum-Length Scheduling with Finite Queues: Solution Characterization and Algorithmic Framework

TL;DR

This paper analyzes the complexity of minimum-length scheduling for multiple links sharing a channel, characterizes optimal strategies, and develops a unified algorithmic framework for exact and approximate solutions.

Contribution

It provides fundamental insights, optimality conditions, and a tractable special case for scheduling, along with a unified framework for designing algorithms.

Findings

Scheduling remains complex for any rate function.

Optimality conditions for 'one-at-a-time' and 'all-at-once' strategies.

A unified framework for exact and sub-optimal algorithms.

Abstract

We consider a set of transmitter-receiver pairs, or links, that share a common channel and address the problem of emptying backlogged queues at the transmitters in minimum time. The problem amounts to determining activation subsets of links and their time durations to form a minimum-length schedule. The problem of scheduling has been studied under various formulations before. In this paper, we present fundamental insights and solution characterizations that include: (i) showing that the complexity of the problem remains high for any continuous and increasing rate function, (ii) formulating and proving sufficient and necessary optimality conditions of two base scheduling strategies that correspond to emptying the queues using "one-at-a-time" or "all-at-once" strategies, (iii) presenting and proving the tractability of the special case in which the transmission rates are functions only of the cardinality of the link activation sets. These results are independent of physical-layer system specifications and are valid for any form of rate function. We then develop an algorithmic framework. The framework encompasses exact as well as sub-optimal, but fast, scheduling algorithms, all under a unified principle design. Through computational experiments we finally investigate the performance of several specific algorithms.