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Excerpt from Reducing the Variance of Sojourn Times in Multiclass Queueing Systems Consider a single server queue visited by K customer classes who arrive according to independent renewal processes with average arrival rates M. K 1, Each customer class has a general service time distribution with mean mi. And finite variance, and each customer exits the system after receiving service. Therefore, the traffic intensity of the queueing system is p 2: l Akmk. Let Qk(t) be the number of class 1: customers in the system at time t, and let I(i) be the cumulative amount of time that the server is idle up to time t. The Brownian model assumes the existence of a large integer n such that u p) is positive and of moderate size; a representative example is p 9 and n 100. The system parameter n is used to define the rescaled processes Z (zk) and U by Zk(t) and eu) for t 2 0, and the Brownian control problem is obtained by letting the parameter n approach infinity. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.