Suppose a single server has $K$ channels, each of which performs a different task. Customers arrive to the server via a nonhomogenous Poisson process with intensity $lambda(t)$ and select $0$ to $K$ tasks for the server to perform. Each channel services the tasks in its queue independently, and the customer's job is complete when the last task selected is complete. The stress to the server is a constant multiple $eta$ of the number of tasks selected by each customer, and thus the stress added to the server by each customer is random. Under this model, we provide the survival function for such a server in both the case of independently selected channels and correlated channels. A numerical comparison of expected lifetimes for various arrival rates is given, and the relationship between the dependency of channel selection and expected server lifetime is presented.
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机译：假设单个服务器具有$ k $通道，每个服务器每次执行不同的任务。 客户通过强度$ lambda（t）$的非源性泊松过程到达服务器，并为服务器选择$ 0 $ k $任务。 对服务器的压力是每个客户选择的任务数量的常量多个$ eta $，因此每个客户添加到服务器的压力是随机的。 在此模型下，我们在独立所选择的信道和相关信道的情况下提供这种服务器的生存函数。 给出了对各种到达率的预期寿命的数值比较，并且呈现了频道选择和预期服务器生命周期之间的关系。
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