The purpose of this research in the queueing theory is the theorem about the law of the iterated logarithm in multiphase queueing systems and its application to the mathematical model of the message switching system. First the law of the iterated logarithm is proved for the cumulative idle time of a customer. Finally we present an application of the proved theorem for the model of the message s...

Let [Formula: see text] be a stationary LNQD sequence of random variables with zero means and finite variance. In this paper, by the Kolmogorov type maximal inequality and Stein's method, we establish the result of the law of the iterated logarithm for LNQD sequence with less restriction of moment conditions. We also prove the law of the iterated logarithm for a linear process generated by an L...

An open queueing network model in light traffic has been developed. The theorem on the law of the iterated logarithm for the idle time process of customers in an open queueing network has been presented. Finally, we present an application of the theorem a idle time model from computer network practice. Key–Words: mathematical models of technical systems, reliability theory, queueing theory, ope...

In [6], Walter Philipp wrote that “. . . the law of the iterated logarithm holds for any process for which the Borel-Cantelli Lemma, the central limit theorem with a reasonably good remainder and a certain maximal inequality are valid.” Many authors [1, 2, 4, 5, 9] have followed this plan in proving the law of the iterated logarithm for sequences (or fields) of dependent random variables. We ca...