Fluid Limit For Cumulative Idle Time In Multiphase Queues

The object of this research in the queueing theory is the Functional-Strong-Law-of-Large-Numbers (FSLLN) under the conditions of heavy traffic in Multiphase Queueing Systems (MQS). A FSLLN is known as fluid limit or fluid approximation. In this paper, the FSLLN is proved for values of important probabilistic characteristic of the MQS investigated as well as the cumulative idle time of a customer

On the Total Queue Length in Multiphase Queues

The paper is designated to the analysis of queueing systems, arising in the network and communications theory (called multiphase queueing systems, tandem queues or series of queueing systems). The author investigated multiphase queueing systems and presents heavy traffic limit theorems for the total queue length of customers in multiphase queues. In this work, functional limit theorems are proved for values of important probability characteristics of the queueing system investigated as well as the total queue length of customers

On The Law Of The Iterated Logarithm In Open Queueing Networks

We investigated an open queueing network model in heavy traffic. The law of the iterated logarithm for the queue length of customers in an open queueing network has been proved

Fluid limits for the waiting time of a customer in multiphase queues

The object of this research in the queueing theory is the Functional-Strong-Law-of-Large-Numbers (FSLLN) under the conditions of heavy traffic in Multiphase Queueing Systems (MQS). FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN is proved for the values of important probabilistic characteristics of MQS investigated as well for the total waiting time of a customer and the waiting time of a custome

Heavy Traffic Limit For The Cumulative Idle Time In Multiphase Queues

The paper is designated to the analysis of queueing systems, arising in the networks theory and communications theory. This research present heavy traffic limit theorem for the cumulative idle time in multiphase queues

Fluid limits for the waiting time of a customer in multiphase queues

The object of this research in the queueing theory is the Functional-Strong-Law-of-Large-Numbers (FSLLN) under the conditions of heavy traffic in Multiphase Queueing Systems (MQS). FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN is proved for the values of important probabilistic characteristics of MQS investigated as well for the total waiting time of a customer and the waiting time of a custome

On global maxima in multiphase queues

The target of this research in the queueing theory is to prove the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems. In this paper, the LIL for global maxima is proved in the phases of a queueing system studied for an important probability characteristic of the system (total waiting time of a customer and waiting time of a customer)

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

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

On the Total Queue Length in Multiphase Queues

The paper is designated to the analysis of queueing systems, arising in the network and communications theory (called multiphase queueing systems, tandem queues or series of queueing systems). The author investigated multiphase queueing systems and presents heavy traffic limit theorems for the total queue length of customers in multiphase queues. In this work, functional limit theorems are proved for values of important probability characteristics of the queueing system investigated as well as the total queue length of customers