The Laplace-Stieltjes transformation of the distribution function of the peak age of information in a multichannel transmission group

This article continues the author’s cycle of works devoted to the problem of the Age of Information (AoI), a metric used in information systems for monitoring and managing remote sources of information from the control center. The theoretical analysis of information transmission systems requires a quantitative assessment of the “freshness” of information delivered to the control center. In this paper, we consider a model of a two-node transmission group consisting of an information source (sender node), a control center (recipient node) and several communication channels between them. It is assumed that the channel capacities may be different. At the same time, the network protocol requires that the information received by the recipient node be read in the same sequence as it was transmitted from the sending node. As a result, packets that violate the established order are delayed at the sending node for the time required to restore order. In this paper, the information transfer process is modeled using a multichannel queuing system with a limited storage, Poisson flow of applications, exponential maintenance and reordering of applications. At the same time, applications simulate packets of transmitted information, the system storage is a queue of packets for transmission, the service of applications on devices of varying intensity is the process of transmitting packets over communication channels. This model was used for the first time to estimate the age of information. As a result of the conducted research, expressions for the Laplace-Stieltjes transformation of the stationary distribution function and the initial moments of the maximum value of the information age, called the peak age, were obtained. A numerical study of system performance indicators has been conducted, including an analysis of the peak age of information at various system loads. The correctness of the analytical results is confirmed by the results of simulation modeling.