论文标题
在交互式随机环境中指数单服务器队列
Exponential single server queues in an interactive random environment
论文作者
论文摘要
我们考虑指数级的单个服务器队列，其依赖状态的到达和服务速率在外部环境的影响下演变。队列的过渡受环境状态的影响，环境的运动取决于队列的状态（双向相互作用）。该环境的构建方式是涵盖最近运营研究文献中各种模型的方式，在该文献中，队列与库存或可靠性问题相结合。通过马尔可夫联合队列 - 环境过程，我们证明了大量此类交互式系统的可分离性，即稳态分布是产品形式并明确给出的。队列和环境在渐近和稳定状态下处理。对于不可分割的系统，我们通过Lyapunov函数开发出奇异性和指数性的性格标准。通过示例，我们通过相关可分开的系统（如上限和下限）的吞吐量来解释非分离系统服务客户（吞吐量）的界限原理。
We consider exponential single server queues with state-dependent arrival and service rates which evolve under influences of external environments. The transitions of the queues are influenced by the environment's state and the movements of the environment depend on the status of the queues (bi-directional interaction). The environment is constructed in a way to encompass various models from the recent Operations Research literature, where a queue is coupled with an inventory or with reliability issues. With a Markovian joint queueing-environment process we prove separability for a large class of such interactive systems, i.e. the steady state distribution is of product form and explicitly given. The queue and the environment processes decouple asymptotically and in steady state. For non-separable systems we develop ergodicity and exponential ergodicity criteria via Lyapunov functions. By examples we explain principles for bounding departure rates of served customers (throughputs) of non-separable systems by throughputs of related separable systems as upper and lower bound.
