In this paper, I develop a generalized method to approximate end-to-end delay (average delay, jitter and density functions) in packet-switched networks (PSNs) of any size under 1) Kleinrock's independence assumption (KIA) and 2) when packet lengths are kept unchanged when they traverse from node to node in a network, which is an Alternative to Kleinrock's independence assumption (AKIA). I introduce a new phase-type distribution $C(\mathbf{p},\boldsymbol \theta)$; and then use results from the network flow theory and queueing theory to show that the end-to-end delay in PSNs under KIA and AKIA are two different random variables approximately described by $C(\mathbf{p},\boldsymbol \theta)$. When PSNs have AKIA, I show from simulation that the method under AKIA significantly reduces end-to-end delay approximation errors and provides close approximation compared with the method under KIA.
翻译:在本文中,我开发了一种通用方法,用以在包装开关网络从节点转向节点时,当包装长度保持不变,这是克莱洛克独立假设的一种替代办法(AKIA)。 我引入了一个新的阶段类型分配$C(mathbf{p},\boldsymbol\theta)美元;然后使用网络流理论和排队理论的结果,以表明在KIA和AKIA中,包装开关网络从节点到节点的延迟是两个不同的随机变量,大致由$C(mathbf{p},\boldsymbol\theta)描述。在“克莱洛克洛克”独立假设(AKISA)中,我通过模拟显示,“AKIA”下的方法大大减少了端到端的延迟近似误,并提供了与“KIA”下方法的近似值。