The workload of a generalized n -site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the steady-state Laplace–Stieltjes transform (LST) of the total workload in the first k sites ( $$k\le n$$ k ≤ n ) just after gate openings and at arbitrary epochs is derived. In a special case, the former (just after gate openings) turns out to be an LST of the sum of k independent random variables. The second model is a 2-site ASIP with leakage from the first queue. Gate openings occur at exponentially distributed intervals, and the external input processes to the stations are two independent subordinator Lévy processes. The steady-state joint workload distribution right after gate openings, right before gate openings and at arbitrary epochs is derived. The third model is a shot-noise counterpart of the second model where the workload at the first queue behaves like a shot-noise process. The steady-state total amount of work just before a gate opening turns out to be a sum of two independent random variables.

中文翻译：

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ASIP 排队网络中的工作负载分布

研究了广义 n 位非对称简单包含过程 (ASIP) 的工作量。分析了三个模型。第一个模型是一个串行网络，它的前 k 个站点 ( $$k\le n$$ k ≤ n ) 的总工作量的稳态拉普拉斯-斯蒂尔捷斯变换 (LST) 在门打开之后和任意时期是派生的。在特殊情况下，前者（就在门打开之后）结果是 k 个独立随机变量之和的 LST。第二种模型是 2 站点 ASIP，从第一个队列泄漏。闸门打开以指数分布的间隔发生，站的外部输入过程是两个独立的从属 Lévy 过程。推导出门开启之后、门开启之前和任意时期的稳态联合工作负载分布。第三个模型是第二个模型的散粒噪声对应物，其中第一个队列的工作负载表现为散粒噪声过程。门打开之前的稳态总工作量结果是两个独立随机变量的总和。