We study the problem of classification when the set of classes is a sigma-compact metric space, by means of surrogate cost minimization. We give a natural sufficient condition for the optimal classifier to be of the form Tf when the function f minimizes a surrogate for the actual loss defined on pairs of classes. Sequences of functions whose expectations converge to the infimum of the expectations of all such functions can then be found by minimizing the sample averages of training sets. In particular, we show how to use surrogate cost minimization when the set of classes is countable and give an example.

Consider a switching component in a packet-switching network, where messages from several incoming channels arrive and are routed to appropriate outgoing ports according to a service policy. One requirement in the design of such a system is to determine the buffer storage necessary at the input of each channel and the policy for serving these buffers that will prevent buffer overflow and the corresponding loss of messages. In this paper, a class of buffer service policies, called Least Time to Reach Bound (LTRB), is introduced that guarantees no overflow, and for which the buffer size required at each input channel is independent of the number of channels and their relative speeds. Further, the storage requirement is only twice the maximal length of a message in all cases, and as a consequence the class is shown to be optimal in the sense that any nonoverflowing policy requires at least as much storage as LTRB.

The problem of selecting a single route for each class of service and each pair of communicating nodes in an SNA network is considered. The nodes, links, sets of candidate routes, and traffic characteristics are given. The goal is to select a set of routes which minimizes the expected network end-to-end queueing and transmission delay. Queueing is modeled as a network ofM/M/1queues which leads to a nonlinear combinatorial optimization problem. Using Lagrangean relaxation and subgradient optimization techniques, we obtain a tight lower bound on the minimal expected delay as well as sets of feasible solutions for the problem. An experimental interactive system has been used to evaluate the procedure; very favorable results have been obtained on a variety of networks.