Functional Large Deviation Principles for Waiting and Departure Processes
Functional Large Deviation Principles for Waiting and Departure Processes
复制标题
候车和出发过程的功能性大偏差原则
DOI：
--
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
W. Whitt
中科院分区：
文献类型：
--
作者：
A. Puhalskii;W. Whitt
建立了具有无限等待空间和先进先出服务规则的单服务员排队系统的等待和离开过程的功能大偏差原理。我们应用扩展的收缩原理表明，这些过程服从FLDPs的函数空间D的非均匀Skorohod拓扑之一，只要到达和服务过程服从FLDPs和速率函数是有限的适当的不连续函数。我们应用我们以前的FLDPs的逆过程，以获得一个FLDP的等待时间在一个队列中的叠加到达过程。我们得到的FLDPs队列内的非循环网络表明，FLDPs继承的过程所产生的网络操作的出发，叠加，和随机分裂。为此，我们也得到了分裂点过程的FLDPs。对于确定性到达过程和确定性服务过程的特殊情况，我们得到了方便的明确表达式的离开过程的速率函数，但不是更一般。一般来说，偏离过程的速率函数显然必须进行数值计算。我们还获得了一个FLDP的出发过程中完成的工作，这有重要的应用程序的概念，有效的带宽准入控制和容量规划的分组通信网络。
We establish functional large deviation principles (FLDPs) for waiting and departure processes in single-server queues with unlimited waiting space and the first-in first-out service discipline. We apply the extended contraction principle to show that these processes obey FLDPs in the function space D with one of the nonuniform Skorohod topologies whenever the arrival and service processes obey FLDPs and the rate function is finite for appropriate discontinuous functions. We apply our previous FLDPs for inverse processes to obtain an FLDP for the waiting times in a queue with a superposition arrival process. We obtain FLDPs for queues within acyclic networks by showing that FLDPs are inherited by processes arising from the network operations of departure, superposition, and random splitting. For this purpose, we also obtain FLDPs for split point processes. For the special cases of deterministic arrival processes and deterministic service processes, we obtain convenient explicit expressions for the rate function of the departure process, but not more generally. In general, the rate function for the departure process evidently must be calculated numerically. We also obtain an FLDP for the departure process of completed work, which has important application to the concept of effective bandwidths for admission control and capacity planning in packet communication networks.