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Optimizing queues with deadlines under infrequent monitoring

Faraz Farahvash, Ao Tang

TL;DR

This paper looks into policies that only monitor the system (and subsequently take actions) after a packet arrival, and introduces a heuristic algorithm called “AB-n” for general deadlines.

Abstract

In this paper, we aim to improve the percentage of packets meeting their deadline in discrete-time M/M/1 queues with infrequent monitoring. More specifically, we look into policies that only monitor the system (and subsequently take actions) after a packet arrival. We model the system as an MDP and provide the optimal policy for some special cases. Furthermore, we introduce a heuristic algorithm called "AB-n" for general deadlines. Finally, we provide numerical results demonstrating the desirable performance of "AB-n" policies.

Optimizing queues with deadlines under infrequent monitoring

TL;DR

This paper looks into policies that only monitor the system (and subsequently take actions) after a packet arrival, and introduces a heuristic algorithm called “AB-n” for general deadlines.

Abstract

In this paper, we aim to improve the percentage of packets meeting their deadline in discrete-time M/M/1 queues with infrequent monitoring. More specifically, we look into policies that only monitor the system (and subsequently take actions) after a packet arrival. We model the system as an MDP and provide the optimal policy for some special cases. Furthermore, we introduce a heuristic algorithm called "AB-n" for general deadlines. Finally, we provide numerical results demonstrating the desirable performance of "AB-n" policies.
Paper Structure (28 sections, 2 theorems, 21 equations, 5 figures, 1 table)

This paper contains 28 sections, 2 theorems, 21 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Previous Results
  4. Earliest Deadline First (EDF)
  5. An intuitive Example
  6. Drop Positive Gain Policy (DPGP)
  7. Queue as an MDP
  8. General definition
  9. MDP Design
  10. S
  11. $\mathcal{A}$
  12. P
  13. r
  14. On the equivalence of the MDP and original problem
  15. MDP optimization
  16. ...and 13 more sections

Key Result

Lemma 1

If the queue is not empty, the interval between two consecutive state transitions comes from a geometric distribution with parameter $\lambda+\mu$ and the probability of an arrival triggering the state transition is $\frac{\lambda}{\lambda+\mu}$.

Figures (5)

  • Figure 2: Optimal policy for D=2
  • Figure 3: optimal policy boundary for D=3
  • Figure 4: Optimal policy boundary for D=4
  • Figure 5: $AB-n$ Performance
  • Figure 6: $AB-n$ performance compared with previous algorithms

Theorems & Definitions (14)

  • Definition
  • Remark
  • Remark
  • Definition
  • Remark
  • Lemma 1
  • proof
  • Remark
  • Remark
  • Theorem 1
  • ...and 4 more