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When to Preempt in a Status Update System?

Subhankar Banerjee, Sennur Ulukus

TL;DR

It is shown that it is optimal for the sampler-scheduler pair to sample a new packet immediately upon the reception of an update packet at the monitor, and a double-threshold sampling policy is proposed which is shown to be an optimal policy under some assumptions on the queue statistic.

Abstract

We consider a time-slotted status update system with an error-free preemptive queue. The goal of the sampler-scheduler pair is to minimize the age of information at the monitor by sampling and transmitting the freshly sampled update packets to the monitor. The sampler-scheduler pair also has a choice to preempt an old update packet from the server and transmit a new update packet to the server. We formulate this problem as a Markov decision process (MDP) and find the optimal sampling policy. We find a sufficient, and also separately a necessary, condition for the always preemption policy to be an optimal policy. We show that it is optimal for the sampler-scheduler pair to sample a new packet immediately upon the reception of an update packet at the monitor. We propose a double-threshold sampling policy which we show to be an optimal policy under some assumptions on the queue statistic.

When to Preempt in a Status Update System?

TL;DR

It is shown that it is optimal for the sampler-scheduler pair to sample a new packet immediately upon the reception of an update packet at the monitor, and a double-threshold sampling policy is proposed which is shown to be an optimal policy under some assumptions on the queue statistic.

Abstract

We consider a time-slotted status update system with an error-free preemptive queue. The goal of the sampler-scheduler pair is to minimize the age of information at the monitor by sampling and transmitting the freshly sampled update packets to the monitor. The sampler-scheduler pair also has a choice to preempt an old update packet from the server and transmit a new update packet to the server. We formulate this problem as a Markov decision process (MDP) and find the optimal sampling policy. We find a sufficient, and also separately a necessary, condition for the always preemption policy to be an optimal policy. We show that it is optimal for the sampler-scheduler pair to sample a new packet immediately upon the reception of an update packet at the monitor. We propose a double-threshold sampling policy which we show to be an optimal policy under some assumptions on the queue statistic.
Paper Structure (4 sections, 11 theorems, 21 equations, 2 figures)

This paper contains 4 sections, 11 theorems, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Optimal Scheduling Algorithm
  4. Numerical Results

Key Result

Theorem 1

It is always optimal for the scheduler-sampler pair to sample a new update packet from the source and transmit the packet to the monitor immediately after the scheduler decides to preempt a currently serving update packet.

Figures (2)

  • Figure 1: A sampler-scheduler pair decides the packet flow through the server such that the monitor receives as fresh information as possible about the source. The sampler-scheduler pair decides when to take a fresh sample, and when (if at all) to preempt a packet being served at the queue.
  • Figure 2: A pictorial representation of policy $\bar{\pi}$ with ${v}_{th,1}^{\bar{\pi}}=2$, ${v}_{th,2}^{\bar{\pi}}=3$. The green boxes represent the successful transmissions. The cyan circles represent a packet generation. Note that, if a packet is in the server and a new packet is generated by the sampler, then the old packet is preempted from the server, for example, see time slot $4$. Gray curves shows the age at the monitor.

Theorems & Definitions (11)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Corollary 1
  • Theorem 6
  • Theorem 7
  • Theorem 8
  • Theorem 9
  • ...and 1 more