论文标题
稳定性结果是在离散时间中同步队列的任意维度
Stability Results on Synchronized Queues in Discrete-Time for Arbitrary Dimension
论文作者
论文摘要
在一批同步的队列中，只能一次或根本不可一次或不提供服务，这意味着如果至少一个队列为空，则服务仍然空闲。我们建议，在离散时间设置中，$ n $同步的队列对于\ {2,3 \} $ in \ {2,3 \} $的$ n \且对于$ n \ geq 4 $不稳定。得出了在原始状态空间的商空间上运行的此类系统与随机行走的离散时间马尔可夫链（DTMC）之间的对应关系。使用这种关系，我们通过证明DTMC的$ n \ geq 4 $和null-recurrent（因此Quasi-strentential）通过$ n \ in \ {2,3 \} $进行评估，通过评估无限的二线系数。 忽略商空间的特殊结构，可以根据Pólya定理在随机步行中解释命题，因为该空间的尺寸为$ d-1 $。
In a batch of synchronized queues, customers can only be serviced all at once or not at all, implying that service remains idle if at least one queue is empty. We propose that a batch of $n$ synchronized queues in a discrete-time setting is quasi-stable for $n \in \{2,3\}$ and unstable for $n \geq 4$. A correspondence between such systems and a random-walk-like discrete-time Markov chain (DTMC), which operates on a quotient space of the original state-space, is derived. Using this relation, we prove the proposition by showing that the DTMC is transient for $n \geq 4$ and null-recurrent (hence quasi-stability) for $n \in \{2,3\}$ via evaluating infinite power sums over skewed binomial coefficients. Ignoring the special structure of the quotient space, the proposition can be interpreted as a result of Pólya's theorem on random walks, since the dimension of said space is $d-1$.
