![]() The limit system, corresponding to $ a = 0 $, This relation allows the approximate calculation of $ w ( x) $ ![]() ![]() Here the distribution of the time intervals $ \tau _ 0 $. Of calls which arrived up to the same time. ![]() If it exists), of the ratios $ r ( t) / e ( t) $ One of the main aims of research in this area is the choice of a preferable organization for a queueing system.įor example, for a typical object of queueing theory such as an automatic telephone exchange (see Queue with refusals) one of the basic characteristics is the proportion of calls lost, that is, the limit $ p $, The fundamental problems of queueing theory usually are these: Based on "local" properties of the random processes under discussion, study their stationary characteristics (if they exist) or the behaviour of these characteristics over a long period of time. Queueing theory mainly uses the apparatus of probability theory. The definitions of these processes are most often descriptive, since their formal construction is very complicated and not always effective. These models are presented as random processes of a special form, sometimes called service processes. The branch of probability theory in which one studies mathematical models of various kinds of real queues (cf.
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