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Multi-Source M/G/1/1 Queues with Probabilistic Preemption

Mohammad Moltafet, Hamid R. Sadjadpour, Zouheir Rezki, Marian Codreanu, Roy D. Yates

TL;DR

This work studies a multi-source status-update system with a single server and no buffer (M/G/1/1) under a probabilistic preemption policy. The authors derive the moment generating functions for the age of information and peak age of information for each source, expressing them through the MGFs of the system time and interdeparture time, with closed forms for these components. A semi-Markov/graph-based approach is used to compute the interdeparture time MGFs, enabling a complete MGF characterization of AoI and PAoI under the proposed policy. Numerical results on a two-source system demonstrate that properly tuned preemption (parameterized by $ heta$) can significantly reduce sum AoI compared to non-preemptive, self-preemptive, and globally preemptive policies, while highlighting the need to learn when to apply preemption. The framework generalizes several known results and provides actionable insights for managing information freshness in multi-source networks with general service times.

Abstract

We consider a multi-source status update system consisting of multiple independent sources, a single server, and a single sink. Each source generates packets according to a Poisson process, and packets are served according to a general service time distribution. The system has a capacity of one packet, i.e., no waiting buffer, and is modeled as a multi-source M/G/1/1 queueing system. We introduce a probabilistically preemptive packet management policy, under which an existing packet from the same source in the system is replaced by an arriving packet with a fixed probability. We derive the moment generating functions (MGFs) of the age of information (AoI) and peak AoI (PAoI) for each source under this policy. Numerical results demonstrate the effectiveness of the proposed packet management policy.

Multi-Source M/G/1/1 Queues with Probabilistic Preemption

TL;DR

This work studies a multi-source status-update system with a single server and no buffer (M/G/1/1) under a probabilistic preemption policy. The authors derive the moment generating functions for the age of information and peak age of information for each source, expressing them through the MGFs of the system time and interdeparture time, with closed forms for these components. A semi-Markov/graph-based approach is used to compute the interdeparture time MGFs, enabling a complete MGF characterization of AoI and PAoI under the proposed policy. Numerical results on a two-source system demonstrate that properly tuned preemption (parameterized by ) can significantly reduce sum AoI compared to non-preemptive, self-preemptive, and globally preemptive policies, while highlighting the need to learn when to apply preemption. The framework generalizes several known results and provides actionable insights for managing information freshness in multi-source networks with general service times.

Abstract

We consider a multi-source status update system consisting of multiple independent sources, a single server, and a single sink. Each source generates packets according to a Poisson process, and packets are served according to a general service time distribution. The system has a capacity of one packet, i.e., no waiting buffer, and is modeled as a multi-source M/G/1/1 queueing system. We introduce a probabilistically preemptive packet management policy, under which an existing packet from the same source in the system is replaced by an arriving packet with a fixed probability. We derive the moment generating functions (MGFs) of the age of information (AoI) and peak AoI (PAoI) for each source under this policy. Numerical results demonstrate the effectiveness of the proposed packet management policy.

Paper Structure

This paper contains 13 sections, 9 theorems, 31 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Organization
  4. System Model and Main Results
  5. AoI Definition
  6. Derivation of the MGF of the (Peak) AoI
  7. Numerical Results
  8. Conclusions
  9. Appendix
  10. Proof of Corollary \ref{['Cro_01']}
  11. Proof of Proposition \ref{['Pro1']}
  12. Proof of Lemma \ref{['prob01']}
  13. Proof of Lemma \ref{['lemmfaap']}

Key Result

Theorem 1

The MGFs of the AoI and PAoI for source $c$ under the probabilistically preemptive packet management policy, denoted by $M_{\delta_c}(s)$ and $M_{A_c}(s)$, respectively, are given by where $M_{T_c}(s)$ is the MGF of the system time $T_c$ of source $c$, which is given by $M_{Y_c}(s)$ is the MGF of the interdeparture time $Y_c$ of source $c$, which is given by where $a_c=\dfrac{\lambda_cM_U(s-\th

Figures (5)

  • Figure 1: The considered status update system.
  • Figure 2: The semi-Markov chain corresponding to the interdeparture time of two consecutive packets of source $c$.
  • Figure 3: The directed graph to calculate the MGF of the interdeparture time under the self-preemptive policy.
  • Figure 4: The sum average AoI of different policies as a function of the probability of preemption $\theta$.
  • Figure 5: The sum average AoI difference ratio (percent) for different policies as a function of the arrival rate of source one $\lambda_1$.

Theorems & Definitions (18)

  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Remark 1
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Proposition 2
  • ...and 8 more