The future Internet promises to support time-sensitive services that require ultra low latencies and reliabilities of 99.99%. Recent advances in cellular and WiFi connections enhance the network to meet high reliability and ultra low latencies. However, the aforementioned services require that the server processing time ensures low latencies with high reliability, otherwise the end-to-end performance is not met. To that end, in this paper we use queuing theory to model the sojourn time distribution for Ultra-Reliable Low Latency Communication services of M/M/R-JSQ-PS systems: Markovian queues with R CPU servers following a join shortest queue processor-sharing discipline (for example Linux systems). We develop open-source simulation software, and develop and compare six analytical approximations for the sojourn time distribution. The proposed approximations yield Wasserstein distances below 2 time units, and upon medium loads incur into errors of less than 1.78 time units (e.g., milliseconds) for the 99.99th percentile sojourn time. Moreover, the proposed sojourn time approximations are stable regardless the number of CPUs and stay close to the simulations.

翻译：未来互联网承诺支持需要超低延迟和99.99%的超低延迟和累犯性能的具有时间敏感性的服务。蜂窝和无线网络连接的最近进展加强了网络,以满足高度可靠性和超低延迟性能。然而,上述服务要求服务器处理时间确保低延迟且高度可靠,否则终端到终端的性能达不到。为此,我们使用排队理论,模拟超可靠低拉度超可靠通信系统M/M/R/R-JSQ-PS系统的隔间时间分布:在加入最短的排队处理器共享纪律(例如Linux系统)后,有 RCPU服务器的Markovian队列。我们开发了开放源模拟软件,开发并比较了6个用于隔断时间分布的分析近似值。拟议的近似使Wasserstein距离低于2小时单位,而中等负荷时,误差少于1.78分钟的M/M/R/R-JSQ-PSQ-PS:99/mile sojourn时间。此外,拟议的软盘时间缩缩模模模模准,不论CPOI的停留和紧紧紧贴数是多少。此外的模拟。