 Now, we are going to go in a little more detail to discuss the architecture of PSTNs. Specifically, we'd see how these PSTNs comprise certain modules with specific jobs and what are exchanges because this is the most widely used terminology in PSTNs. The components which essentially play very important roles in PSTNs include the multiplexers, the concentrators, the private automatic branch exchanges and these technologies are realized in a hierarchical manner that we call the network hierarchy and the usage of the number of devices in this hierarchy is determined by the network dimensioning that has been done by statistical engineers. Let's look at the PSTNs in a very broad environment. We see that we have telephones which are connected all over. These telephones are connected to the exchange a.k.a. the switching system either through concentrators or through multiplexers or through private exchanges and we also see the telephone lines which are directly terminating that you see on the top. Let's start each one of them one by one. When we look at the telephones on the left hand side which are connected to the exchange through concentrators they all terminate into the concentrator and from the concentrator a single line that we call the trunk emanates. This trunk carries the aggregate traffic of all these telephones. That is where the use of statistical multiplexing comes into play. If we look at the analog telephone lines it is pretty straightforward. These telephones are connected directly into the exchange. On the right hand side we see that we have telephones which are connected through multiplexers. Multiplexers as we shall shortly see are the digital devices which connect these telephones over digital lines. So here these telephones are connected in the subscriber loop in a digital manner and here on the bottom right we see that we have private branch exchange that is providing intra PBX connectivity to the telephone save for a certain company and then the traffic which is sent out from this particular private branch exchange is sent again using trunks. Now the switching system or the exchange is in turn connected through the transmission system towards other exchanges. With an understanding of PSTNs let's move on. Of course the most important concept that we have earlier discussed is the hierarchy. This hierarchy is predominantly controlled by the telecommunication companies or the telecom operators known as the telcos. These basically comprise a series of switches and exchanges which are connected to each other in kind of a tree model. Now these exchanges are connected to each other via transmission lines. The bandwidth provided by these transmission lines also varies and it is determined by the network hierarchy that you wish to choose. The factors which affect the hierarchy are based on the number of users in a certain geographical area that wish to connect to the exchange number one and number two the overall number of areas. With a focus and consideration to these two parameters the hierarchy is realised. Another important aspect that we have just looked at in that general environment is the role of multiplexing. As we said in our initial lectures that sometimes in the subscriber loop the telephones are connected to the exchange via the digital means. So if the local loop is digital so we have the provision to actually look at the digital transmission coming from the telephone to the exchange as comprising ones and zeros. So there is a possibility to use the digital device that we know as the multiplexer. The multiplexer works with another sister device called the demultiplexer together called demux. So the availability of a multiplexer on one end and another multiplexer on the other end has to be taken into consideration to provide the multiplexing capability for digital lines. The importance of concentrator cannot be over emphasized. Basically what it does is it understands that the number of telephones usually are not active. Some of these have activity periods. Some of these are not active. As we already know that the number of users in a certain geographic area comprise men, women and children. These men may be professionals working mostly in the daytime at their offices. The women folk which is staying back may not be active users of the telephone. And likewise the students or the children are mostly away from for most of the daytime. That actually means that there could be a relationship which could be seen that exists between the number of users in a certain geographical area and the total number of transmission lines or I would say the frequencies or the number of time slots which need to be carried from the local subscriber level to the exchange. So concentrator is a device that groups or aggregates all such traffic from the subscribers. And of course what usually we would see is that the number of users is much more than what the overall transmission capability of a certain trunk is. So what happens is the trunk could get busy when all the users are active. Well that is the cost which has to be paid. Now we would look at concentrator in a little more detail. For now we just finish the discussion on concentrator by just typifying concentrators to be either the remote exchange concentrators which connect the traffic from one exchange to the other or these could be line concentrators which take individual telephones on a certain trunk by aggregating their traffic. The topic of network dimension as I was just mentioning is very important to realize what should be the capacity of the outgoing trunk from the concentrator. Now the concentrators actually exploit the activity inactivity. It actually means that depending on the number of telephones is in a certain area and the total traffic coming from each telephone added up together we would determine the bandwidth required from the trunk. Now this would not be a constant phenomenon it would be varying across different times of the day. Let's take an example. Let's see in a certain geographical area the number of users is 100. If we say that at an average if at one point in time the number of active users is no more than 20% so for 100 users that's going to be around 20. In real case if we just could assume that all the users are active all the time the actual lines needed would be 100. But statistically planning using certain formulae known as the Erlang B and Erlang C formulae which are used in traffic engineering we would be actually providing connectivity of 30 trunk lines that is for 100 users we are just providing 30 trunk lines. It means that 70 users would not be able to access the exchange when they need it. Well through statistical analysis it can be proven that at an average each user would only see the network busy for 1% of the time. That is if a user makes a call so all 900 calls made for 99% of the time the calls would be through and for only 1% the calls would not be realized. Another important concept that has been discussed in the figure we have seen is the private branch exchanges. These exchanges are also connected to the central exchange or the switching elements. These exchanges are used by the private companies. As long as the traffic remains local within a certain company the traffic is not sent to the exchange of the telecom company because the private company has the PBX meant to actually regulate and confine its traffic to its own premises. But when the traffic is bound for another network or say outside the PBX only then the traffic is sent out of the PBX using the concentrator. So basically what it does is it saves the revenue of sending a traffic from one party within the company to another party within the same company.