(a) Star network (b) Area with single TE and multi TE

Fig. 9.3. Star topology.

If the number of stations served by a TE increases, they are divided into smaller network, each served by its TE. Fig. 9.3(b) shows the star network with splitted setup. This configuration reduces the line cost but increases the exchange costs. With the star arrangement the outer centres require fewer trunk terminations, but the trunk centre has greatly increased number of terminations. So, the star arrangement reduces the design requirements on all but one of the switching centres. It needs larger, and more powerful trunk centre. As only one larger centre is required, star arrangement preferable. Note that the exchange area indicates that all the calls in that area are considered to be local calls.

Hierarchical networks. Many star networks may be inter connected by using an additional tandom exchange, leading to two level star network. An orderly construction of multilevel star networks leads to hierarchical networks. Fig. 1.11 shows the two types of hierarchical structures of AT & T and ITU-T. Hierarchical networks are capable of handling heavy traffic with minimal number of trunk groups. The hierarchical network requires more switching nodes, but achieves significant savings in the number of trunks. Determination of the total number of trunk circuits in entire network is necessarily a function of the amount of traffic between each pair of switching nodes. The efficiency of circuit utilization is the basic motivation for hierarchical switching structures.

In Fig. 1.11, it is shown that, if there is a high traffic intensity between any pair of exchanges, direct trunk groups may be established between any pair of exchanges (dotted lines or trunks of AT & T hierarchical network). These direct routes are known as high usage routes or trunks. In a strictly hierarchical network, traffic from subscriber A to B and vice versa flows through the highest level of hierarchy. A traffic route via the highest level of hierarchy is known as the final route. Whenever high usage route exists, route is primiarily routed through them. The overflow traffic is routed through hierarchical network. Traffic is always routed through the lowest available level of the nework.

In addition to the high usage trunks, the tandom switches which is employed at the lowest level (not part of toll network) is augmented. The term tandom refers specifically to intermediate switching within the exchange area. The exchange area is an area within which all calls are considered to be local calls. The basic function of a tandom office is to interconnect those central offices (or class 5 or local exchanges) within an exchange area having insufficient interoffice traffic volumes to justify direct trunks. Tandom exchanges also provide alternate routes for exchange area call get blocked on direct routes between end offices.

To calculate whether a direct route is cheaper than a tandom route, the cost ratio (CR) is defined as

Cost of provision of a tandom connection between two centres

Cost of provision of direct circuit between two centres

The costs are usually measured interms of the present value of annual charges. Routing via a tandom switching centre is always more economic if the cost ratio is less than or equal to one. But the non-linear relationship between number of trunks and traffic carried can make tandom rather than direct routing more economic even for values of X greater than unity. As a general rule, increasing the capacity of an existing trunk route always requires fewer additional trunks than the provision of a new direct trunk route.

9.3.2. Alternative Routing

Based on the assumption that the routing is made only by direct routing or tandom routing, it is found that to route a stream of traffic, tandom route is more economical. In fact, even greater economics are often possible if just a proportion of the traffic is routed directly. This approach is known as alternative routing.

In alternative routing, connections should use the direct trunks (referred as high usage route), because direct route provides better transmission quality and use fewer network facilities. If all the direct trunks are busy, calls are routed via a tandom exchanges or alternate routes to maintain suitably low blocking probabilities. Thus, the networks are designed to allocate a limited number of heavily utilized trunks in the direct route and provides alternate routes for over flow.

If the high usage route consists of N tunks and the offered traffic is A erlangs, the probability of all trunks busy is given by the Erlangs-B formula (equation 8.54). The traffic carried on high usage route AH is given by

the overflow traffic is A = AB(N, A) erlangs ...(9.3)

The Erlang-B formula is a good representation of the traffic on a high usage route because blocked calls are diverted to the alternative route and does not reappear. But the number of circuits required by a final route to carry the overflow traffic should not be calculated from Erlang's-B formula, because this traffic is not poissonian. The characteristic of traffic for high usage route with overflow is shown in Fig. 9.4.

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