5.2 Telephone Terminology Relationships

Most of the mathematics used for sizing data communications equipment evolved out of work originally performed to solve the sizing problems of telephone networks. From a discussion of a few basic telephone network terms and concepts, we will see the similarities between the sizing problems associated with data communications equipment and facilities and the structure of the telephone network. Building on this foundation, we will learn how to apply the mathematical formulas developed for telephone network sizing to data communications network configurations.

To study the relationship between telephone network communications component sizing problems, let us examine a portion of the telephone network and study the structure and calling problems of a small segment formed by two cities, each assumed to contain 1000 telephone subscribers.

5.2.1 Telephone Network Structure

The standard method of providing an interconnection between subscribers in a local area is to connect each subscriber's telephone to what is known as the local telephone company exchange. Other synonymous terms for the local telephone company exchange include the "local exchange" and "telephone company central office." When one subscriber dials another connected to the same exchange, the subscriber's call is switched to the called party number through the switching facilities of the local exchange. If we assume that each city has one local exchange, then all calls originating in that city and to a destination located within that city will be routed through one common exchange.

Because our network segment selected for analysis consists of two cities, we have two telephone company exchanges ” one located in each city. To provide a path between cities for inter-city calling, a number of lines must be installed to link the exchanges in each city. The exchange in each city can then act as a switch, routing the local subscribers in each city to parties in the other city.

5.2.1.1 Trunks and Dimensioning

As shown in the top part of Figure 5.1, a majority of telephone traffic in the network segment consisting of the two cities will be among the subscribers of each city. Although there will be telephone traffic between the subscribers in each city, it normally will be considerably less than the amount of local traffic in each city. The path between the two cities connecting their telephone offices is known as a trunk.

Figure 5.1: Telephone Traffic Sizing Problems

One of the many problems in designing the telephone network is determining how many trunks should be installed between telephone company exchanges. A similar sizing problem occurs many times in each city at locations where private organizations desire to install switchboards . An example of the sizing problem with this type of equipment is illustrated in the lower portion of Figure 5.1. In effect, the switchboard functions as a small telephone exchange, routing calls carried over a number of trunks installed between the switchboard and the telephone company exchange to a larger number of subscriber lines connected to the switchboard. The determination of the number of trunks required to be installed between the telephone exchange and the switchboard is called dimensioning and is critical for the efficient operation of the facility. If insufficient trunks are available, company personnel will encounter an unacceptable number of busy signals when trying to place an outside telephone call. Once again, this will obviously affect productivity.

Returning to the inter-city calling problem, consider some of the problems that can occur in dimensioning the number of trunks between central offices located in the two cities. Assume that, based on a previously conducted study, it was determined that no more than 50 people would want to have simultaneous telephone conversations where the calling party was in one city and the called party in the other city. If 50 trunks were installed between cities and the number of inter-city callers never exceeded 50, at any moment the probability of a subscriber completing a call to the distant city would always be unity, always guaranteeing success. Although the service cost of providing 50 trunks is obviously more than providing a fewer number of trunks, no subscriber would encounter a busy signal.

Because some subscribers might postpone or choose not to place a long-distance call at a later time if a busy signal is encountered , a maximum level of service will produce a minimum level of lost revenue. If more than 50 subscribers tried to simultaneously call parties in the opposite city, some callers would encounter busy signals once all 50 trunks were in use. Under such circumstances, the level of service would be such that not all subscribers would be guaranteed access to the long distance trunks and the probability of making a long-distance call would be less than unity. Likewise, because the level of service is less than that required to provide all callers with access to the long-distance trunks, the service cost is less than the service cost associated with providing users with a probability of unity in accessing trunks. Similarly, as the probability of successfully accessing the long-distance trunk decreases, the amount of lost revenue or customer waiting costs will increase. Based on the preceding , a decision model factoring into consideration the level of service versus expected cost can be constructed as shown in Figure 5.2.

Figure 5.2: Using a Decision Model to Determine the Optimum Level of Service

5.2.1.2 The Decision Model

For the decision model illustrated in Figure 5.2, suppose the optimum number of trunks required to link the two cities is 40. The subscriber line-to-trunk ratio for this case would be 1000 lines to 40 trunks, for a 25:1 ratio.

To correctly dimension the optimum number of trunks linking the two cities requires an understanding of both economics and subscriber traffic. In dimensioning the number of trunks, a certain trade-off will result that relates the number of trunks or level of service to the cost of providing that service and the revenue lost by not having enough trunks to satisfy the condition when a maximum number of subscribers in one city dial subscribers in another. To determine the appropriate level of service, a decision model as illustrated in Figure 5.2 is required. Here, the probability of a subscriber successfully accessing a trunk corresponds to the level of service provided. As more trunks are added, the probability of access increases as does the cost of providing such access. Correspondingly, the waiting cost of the subscriber or the revenue loss to the telephone company decreases as the level of service increases , where the total cost represents the combination of service cost and waiting cost. The point where the cost is minimal represents the optimal number of trunks or level of service that should be provided to link the two cities.

From a LAN access perspective, a similar decision model can be constructed. However, instead of focusing on accessing trunks, our concern would be oriented toward providing access to a LAN via the switched telephone network. If the number of ports, modems, and business lines equals the number of employees or subscribers of the organization, nobody would experience a busy signal; however, the cost of providing this capacity level would be very high, and during a portion of the day, most of its capacity would more than likely be unused. As we reduce the number of ports, modems, and dial-in lines, the level of service decreases and eventually employee or subscriber waiting time results in either lost productivity or lost revenue. Thus, from a LAN access perspective, you would also seek to determine an optimum level of service.