Modeling Interfering Sources in Shared Queues for Timely Computations in Edge Computing Systems

TL;DR

This paper develops an analytical model for Age of Information in a two-hop edge computing system with multiple sources, accounting for interference traffic modeled as a Markov modulated Poisson process, and proposes a model reduction technique for large source numbers.

Contribution

It introduces a Markov chain-based analytical model for AoI in two-hop edge systems with interference traffic, and proposes a state reduction method for large N.

Findings

The model accurately predicts AoI distribution for various system configurations.

The approximation effectively simplifies interference traffic modeling for many sources.

Numerical results validate the model's accuracy and computational efficiency.

Abstract

Most existing stochastic models on age of information (AoI) focus on a single shared server serving status update packets from $N>1$ sources where each packet update stream is Poisson, i.e., single-hop scenario. In the current work, we study a two-hop edge computing system for which status updates from the information sources are still Poisson but they are not immediately available at the shared edge server, but instead they need to first receive service from a transmission server dedicated to each source. For exponentially distributed and heterogeneous service times for both the dedicated servers and the edge server, and bufferless preemptive resource management, we develop an analytical model using absorbing Markov chains (AMC) for obtaining the distribution of AoI for any source in the system. Moreover, for a given tagged source, the traffic arriving at the shared server from the $N-1$ un-tagged sources, namely the interference traffic, is not Poisson any more, but is instead a Markov modulated Poisson process (MMPP) whose state space grows exponentially with $N$. Therefore, we propose to employ a model reduction technique that approximates the behavior of the MMPP interference traffic with two states only, making it possible to approximately obtain the AoI statistics even for a very large number of sources. Numerical examples are presented to validate the proposed exact and approximate models.