hes and local plant involved with these calls. As we well know, many of the telephone company's subscribers would be unhappy because they would have to wait excessively to get calls through from X to Y. How, then, do we optimize a trunk route (or serving circuits) and keep the customers as satisfied with service as possible? Remember from Table 4.1, with an excellent grade of service of 0.001, that we relate grade of service to subscriber satisfaction (one element of quality of service) and that 47 trunks could carry 30.07 erlangs during the busy hour. Assuming the route did carry 30.07 erlangs, let's say at $1.00 per erlang, it would earn $30.07 for that hour. From a revenue viewpoint, that would be the best hour of the day. If the grade of service were reduced to 0.01, 47 trunks would bring in $35.21 (i.e., 35.21 erlangs) for the busy hour. Note the improvement in revenue at the cost of reducing grade of service. Here we are relating efficiency on trunk utilization. Trunks not carrying traffic do not bring in revenue. If we are only using some trunks during the busy hour only minutes a day to cover BH traffic peaks, the remainder of the day they are not used. That is highly inefficient. As we reduce the grade of service, the trunk utilization factor improves. For instance, 47 trunks will only carry 30.07 erlangs with a grade of service of 1 in 1000 (0.001), whereas if we reduce the grade of service to 1 in 20 (0.05), we carry 41.54 erlangs (see Table 4.1). Efficiency has improved notably. Quality of service, as a result, has decreased markedly. 4.2.4.1 Alternative Routing. One method to improve efficiency is to use alternative routing (called alternate routing in North America). Suppose we have three serving areas, X, Y, and Z, served by three switches (exchanges), X, Y, and Z, as illustrated in Figure 4.4. Let the grade of service be 0.005 (1 in 200 in Table 4.1). We find that it would require 48 trunks to carry 34.25 erlangs of traffic during the BH to meet that grade of service between X and Y. Suppose we re