C, và khi p là đủ lớn, họ sẽ muốn mua ít mà C. Theo đó, p tăng từ 0, tổng số tiền của băng thông P rằng khách hàng muốn mua hàng, cụ thể là i xi. / p, giảm từ một giá trị trên PNC đối với 0, và tại một số giá trị, p D p, chúng ta có i xi. p / D C. Bằng cách thiết lập các giá N p nhà điều hành bảo đảm rằng | SOME EXAMPLES 95 approximation of the true acceptance region for a given finite N. It becomes more exact as N increases. Practical experiments show excellent results for N of the order of 100. Suppose X is the operating point in A and gt X y is the constraint that is binding at this point. Then t achieves the supremum in . Let s be the infimizer in the right hand side of . Then @gt @Xj X X stUj s t and so as above gt X y has a linear approximation in the neighbourhood of xN of k k st 2x Uj s t s jij Uj s t s Ct C B y j 1 j 1 Dividing by st we have X XjUj s t C where C C C 1 b - j 1 t s The linear constraint in gives a good approximation to the boundary of the acceptance region near xN if the values of s and t which are optimizing in do not change very much as x varies in the neighbourhood of xN . We can extend this idea further to obtain an approximation for the entire acceptance region by approximating it locally at a number of boundary points. Optimizing the selection of such points may be a highly nontrivial task. A simple heuristic when the s and t do not vary widely over the boundary of the acceptance region is to use a single point approximation. One should choose this point to be in the interesting part of the acceptance region . in the part where we expect the actual operating point to be. Otherwise one may choose some centrally located point such as the intersection of the acceptance region with the ray 1 1 . 1 . In practice points on the acceptance region and their corresponding s and t can be computed using . We start with some initial point x near 0 and keep increasing all its components proportionally until the target CLP is reached. Let us summarize this section. We have considered the problem of determining the number of contracts that can be handled by a single switch if a certain QoS constraint is to be satisfied. We take a model of a switch that has a buffer of size B and serves C cells per second in a first come .
