Covert queueing problem with a Markovian statistic

TL;DR

This paper studies a covert queueing scenario where a server admits non-Willie jobs secretly, using Markovian statistics to detect such covert behavior and establish conditions for maintaining covertness.

Contribution

It introduces a Markovian statistical framework for covert queueing and characterizes the detection limits for Willie to identify non-Willie jobs.

Findings

Derived hypothesis testing methods for detecting non-Willie jobs.

Established upper bounds on non-Willie job arrival rates for covertness.

Analyzed the impact of Markovian statistics on covert queueing detection.

Abstract

Based on the covert communication framework, we consider a covert queueing problem that has a Markovian statistic. Willie jobs arrive according to a Poisson process and require service from server Bob. Bob does not have a queue for jobs to wait and hence when the server is busy, arriving Willie jobs are lost. Willie and Bob enter a contract under which Bob should only serve Willie jobs. As part of the usage statistic, for a sequence of N consecutive jobs that arrived, Bob informs Willie whether each job was served or lost (this is the Markovian statistic). Bob is assumed to be violating the contract and admitting non-Willie (Nillie) jobs according to a Poisson process. For such a setting, we identify the hypothesis testing to be performed (given the Markovian data) by Willie to detect the presence or absence of Nillie jobs. We also characterize the upper bound on arrival rate of Nillie jobs such that the error in the hypothesis testing of Willie is arbitrarily large, ensuring covertness in admitting Nillie jobs.