信息年龄在Erlang损失系统中的分布
Distribution of Age of Information in the Erlang Loss System
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中文总结 AI 辅助
本文通过吸收马尔可夫链方法，推导了Erlang损失系统中三种更新管理策略下信息年龄与峰值信息年龄的精确矩阵指数分布，并扩展到多源场景，为年龄约束下的服务器配置提供依据。
中文摘要 AI 辅助
本文研究了在无缓冲设置中信息年龄（AoI）和峰值信息年龄（PAoI）的精确分布。在该设置中，由一个或多个信息源根据各自的泊松过程生成的时间戳更新（或已处理任务）被提交到共享的c个同质服务器池，这些服务器的服务时间服从指数分布，即所谓的M/M/c/c或Erlang损失系统。我们考虑了当新更新到达时发现所有服务器均繁忙时所采用的三种更新管理策略：到达的更新被阻塞（非抢占，NP），如同Erlang损失系统中的情况；或者它抢占其自身源中一个随机选择的正在服务的更新（随机抢占，PR）；或者抢占最陈旧的此类更新（抢占最陈旧，PS）。所有三种策略都保持了与底层Erlang损失系统相关的服务器占用过程的相同生灭结构。然而，它们的AoI和PAoI分布可能非常不同。我们采用的方法是吸收马尔可夫链（AMC）方法，其中单个AoI周期（而非系统的整个样本路径）由吸收马尔可夫链建模。通过AMC方法，我们以矩阵指数形式推导出AoI和PAoI的精确分布。该方法扩展到多个源共享同一服务器池的情况，其中给定源的AoI仅通过其余源的聚合更新率受到它们的影响。数值示例说明了我们研究结果的含义，包括在年龄违规约束下基于分布的服务器配置。
英文摘要
In this paper, we study the exact distributions of the age of information (AoI) and peak AoI (PAoI) in a bufferless setting in which time-stamped updates, or processed tasks, generated by one or several information sources according to a Poisson process for each source, are submitted to a shared pool of $c$ homogeneous servers with exponentially distributed service times, i.e., the so-called M/M/c/c or the Erlang loss system. We consider three update management policies which come into play when a new update arrives to find all the servers busy: the arriving update is blocked (non-preemptive, NP) as in the Erlang loss system, or it preempts a randomly chosen update of its own source in service (preempt at random, PR), or the stalest such update (preempt the stalest, PS). All three policies preserve the same birth-death structure of the server occupancy process associated with the underlying Erlang loss system. However, their AoI and PAoI distributions can be very different. The approach we take is the absorbing Markov chain (AMC) method, in which a single AoI cycle, rather than the entire sample path of the system, is modeled by an absorbing Markov chain. Via the AMC method, we derive the exact distributions of AoI and PAoI in matrix-exponential form. The method extends to multiple sources sharing the same pool of servers, with the AoI of a given source being affected by the remaining sources only through their aggregate update rate. Numerical examples illustrate the implications of our findings, including distribution-based server provisioning under age violation constraints.
发表机构
- Bilkent University（比尔肯特大学）
- University of Maryland（马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。
