Trunking Efficiency
引言
学习无线互联网时，老师的课件中提到了Trunking Efficiency的概念，当时不太清楚，在网上查找资料时找到了一个课件，解答了自己的疑惑，故记录。
Trunking
The fact that users access the system in a random and independent fashion is used carefully by the engineers so that a small number of channels can support a potentially large number of users — the concept of trunking. Simply put, trunking system utilizes the statistical behavior of users to dynamically assign channels to users on demand so that the total number of users accommodated in a system can be substantially larger than the number of channels.
上面这段文字的表述指明了Trunking的概念：Trunking是一个系统可以承载的用户数量。但需要注意的是，此处的承载是统计意义上的承载，而不是系统饱和情况下所有服务台同时能够承载的用户数量。举一个简单的例子，银行有3个服务台，服务台一次只能为一个用户提供服务。则该银行系统同时只能为3个用户提供服务，但是用户到达服务台的分布在统计意义上服从泊松分布，因此在满足特定阻塞率（服务质量）的情况下，该系统可以承载10个用户。则该系统的Trunking为10。
推广至一般情况，令用户数量为$U$，服务台数量为$C$。当$U > C$时，一部分用户就会面临被阻塞的风险，发生阻塞的概率被称作阻塞概率（blocking probability），也常被叫做Grade of Service（GOS）。
Traffic Intensity
Traffic intensity measures the intensity of user activity. From a different point of view, it measures how often the system channels are occupied.
Traffic Intensity是衡量用户活跃程度的指标，也反映了信道被占用的频次。
Its unit, Erlang (Due to A. K. Erlang of Denmark), represents the amount of traffic intensity carried by a channel that is completely occupied.
Traffic Intensity的单位是Erlang，反映了当信道完全被占用时，所承载的Traffic Intensity数量。更具体的，原文给出了两个例子：
For example, if a user is on the phone 20% of the time, then the traffic offered by that user is 0.2 Erlang. From the perspective of channel utilization, if a channel is occupied thirty minutes out of an hour, then the traffic it carries is 0.5 Erlang.
Blocking Probability
$$Pr[Blocking] = \frac{A^c/C!}{\sum_{k=0}^CA^k/k!}$$
其中，$A$代表由用户产生的、系统要承担的offered Traffic Intensity，$C$代表信道数量。
Trunking Efficiency
A measure of efficiency for a trunked system is the maximum traffic intensity that is carried by the system subject to a given GoS.
原文给出的关于Trunking Efficiency的定义可以理解为：给定GoS时，系统所能承载的最大offered traffic intensity，也就是$A$的大小。
The capacity for C = 10 with GOS 0.01 is 4.46 Erlangs, while the apacity for C = 70 with GOS 0.01 is 56.1 Erlangs.
从上面给出的两个例子中可以得出：拥有大量服务资源的系统比拥有小量服务资源的系统更有效。