We consider transmission of packets over queue-length sensitive unreliable links, where packets are randomly corrupted through a noisy channel whose transition probabilities are modulated by the queue-length. The goal is to characterize the capacity of this channel. We particularly consider multiple-access systems, where transmitters dispatch encoded symbols over a system that is a superposition of continuous-time $\mathsf {GI}_{k}/\mathsf {GI}/1$ queues. A server receives and processes symbols in order of arrivals with queue-length dependent noise. We first determine the capacity of single-user queue-length dependent channels. Further, we characterize the best and worst dispatch processes for $\mathsf {GI}/\mathsf {M}/1$ queues and the best and worst service processes for $\mathsf {M}/\mathsf {GI}/1$ queues. Then, the multiple-access channel capacity is obtained using point processes. When the number of transmitters is large and each arrival process is sparse, the superposition of arrivals approaches a Poisson point process. In characterizing the Poisson approximation, we show that the capacity of the multiple-access system converges to that of a single-user $\mathsf {M}/\mathsf {GI}/1$ queue-length dependent system, and an upper bound on the convergence rate is obtained. This implies that the best and worst server behaviors of single-user $\mathsf {M}/\mathsf {GI}/1$ queues are preserved in the sparse multiple-access case.

中文翻译：

---

队列长度敏感系统中的多址访问

我们考虑在队列长度敏感的不可靠链路上传输数据包，其中，数据包通过一个嘈杂的信道随机破坏，该信道的传输概率由队列长度调制。目的是表征该通道的容量。我们特别考虑多址系统，其中发射机在系统上分配编码符号，该系统是连续时间的叠加 $ \ mathsf {GI} _ {k} / \ mathsf {GI} / 1 $ 队列。服务器以到达队列的顺序接收和处理符号，并带有依赖于队列长度的噪声。我们首先确定单用户队列长度相关通道的容量。此外，我们描述了最佳和最差的调度流程 $ \ mathsf {GI} / \ mathsf {M} / 1 $ 队列以及最佳和最差服务流程 $ \ mathsf {M} / \ mathsf {GI} / 1 $ 队列。然后，使用点处理来获得多路访问信道容量。当发射器的数量很大并且每个到达过程稀疏时，到达的叠加将接近泊松点过程。在表征泊松近似时，我们表明多路访问系统的容量收敛到单用户的容量 $ \ mathsf {M} / \ mathsf {GI} / 1 $ 依赖于队列长度的系统，并获得收敛速度的上限。这意味着单用户的最佳和最差服务器行为 $ \ mathsf {M} / \ mathsf {GI} / 1 $ 在稀疏多路访问的情况下保留队列。