Investigation of the law of the iterated logarithm for extreme queue length in multiphase queues

Abstract

Interest in the field of multiphase queueing sys-tems has been stimulated by the theoretical values of the results as well as by their possible applications in informa-tion and computing systems, communication networks, and automated technological processes. The object of this re-search in queueing theory is the law of the iterated loga-rithm (LIL) under the conditions of heavy traffic in multi-phase queueing systems (MQS). In this paper, the LIL is proved for extreme values of important probabilistic cha-racteristics of the MQS investigated as well as maxima of the summary queue length of customers and maxima of the queue length of customers.