Distributed Scheduling in Time Dependent Environments: Algorithms and Analysis

TL;DR

This paper analyzes distributed scheduling algorithms in large, time-dependent multi-user channels, focusing on delay, QoS, and capacity scaling, with new models for large user populations and channels modeled by Gilbert-Elliott processes.

Contribution

It introduces a simplified, accurate model for large user systems and analyzes performance under time-dependent channels, extending queueing theory results.

Findings

Convergence of collision probability to its average as users grow

Capacity scaling laws for time-dependent channels

Effective models for large user populations

Abstract

Consider the problem of a multiple access channel in a time dependent environment with a large number of users. In such a system, mostly due to practical constraints (e.g., decoding complexity), not all users can be scheduled together, and usually only one user may transmit at any given time. Assuming a distributed, opportunistic scheduling algorithm, we analyse the system's properties, such as delay, QoS and capacity scaling laws. Specifically, we start with analyzing the performance while \emph{assuming the users are not necessarily fully backlogged}, focusing on the queueing problem and, especially, on the \emph{strong dependence between the queues}. We first extend a known queueing model by Ephremides and Zhu, to give new results on the convergence of the probability of collision to its average value (as the number of users grows), and hence for the ensuing system performance metrics, such as throughput and delay. This model, however, is limited in the number of users one can analyze. We thus suggest a new model, which is much simpler yet can accurately describes the system behaviour when the number of users is large. We then proceed to the analysis of this system under the assumption of time dependent channels. Specifically, we assume each user experiences a different channel state sequence, expressing different channel fluctuations (specifically, the Gilbert-Elliott model). The system performance under this setting is analysed, along with the channel capacity scaling laws.