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

TL;DR

The paper tackles AoI analysis in a two-hop edge computing system with $N>1$ sources where interference at the shared edge server arises from preemptive, bufferless queues, breaking the Poisson arrival assumption. It develops an absorbing Markov chain (AMC) framework to obtain AoI distributions, modeling the interfering traffic as a Markov Modulated Poisson Process (MMPP) and introducing a two-state MMPP approximation that matches the first three moments and the DC spectrum $\tau_c$. The exact approach uses a superposition MMPP with $2^{N-1}$ states, while the two-state approximation dramatically reduces state-space, enabling accurate AoI statistics for large $N$. Numerical results show the Poisson approximation is inadequate and the two-state MMPP approach closely tracks the exact model, validating a scalable method for timeliness analysis in multi-source edge networks with realistic interference.

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.

Figures (4)

• Figure 1: Sample path of the AoI process for tagged source-$1$.
• Figure 2: From the perspective of source-1, status update system with $N$ sources with Poisson packet arrivals $\lambda_n$ from source-$n$, $N$ dedicated preemptive transmission servers with service rate $\mu_n$ for source-$n$, and one shared server with service rate $\sigma$.
• Figure 3: $\mathbb{E}[\Delta_1]$ depicted as a function of $N$ for interference MMPP modeling methods 1-3 when $\delta=0.2$.
• Figure 4: $\mathbb{E}[\Delta_1]$ depicted as a function of $N$ for interference MMPP modeling methods 1-3 when $\delta=1$.