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.

中文翻译：

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带有马尔可夫统计量的隐蔽排队问题

基于隐性通信框架，我们考虑具有马尔可夫统计量的隐性排队问题。Willie 作业根据泊松过程到达并需要服务器 Bob 提供服务。Bob 没有等待作业的队列，因此当服务器繁忙时，到达的 Willie 作业将丢失。威利和鲍勃签订了一份合同，根据该合同，鲍勃只能为威利工作。作为使用统计的一部分，对于到达的 N 个连续作业的序列，Bob 通知 Willie 每个作业是服务还是丢失（这是马尔可夫统计）。假设 Bob 违反了合同并根据泊松过程接受了非 Willie (Nillie) 的工作。对于这样的设置，我们确定 Willie 要执行的假设检验（给定马尔可夫数据）以检测 Nillie 作业的存在与否。