This article proposes an analytical model of a multi-service hierarchical system with multi-service overflow traffic. To model the primary and secondary resources of this system, the state-dependent queue service discipline was used. In order to model the secondary resources with the dedicated queue for overflow traffic, the Hayward’s approach was generalized and applied. To evaluate its accuracy, the results of analytical modeling were compared with the data obtained during the simulation experiments carried out in the study. Both the data presented in the article and the results obtained by the present authors in numerous comparative studies clearly indicate that the proposed model makes it possible to evaluate the values of the blocking probability with the accuracy that provides its reliable practical application at the stage of network dimensioning. The overflow mechanism has particular significance in networks with limited resources, such as mobile networks.

This paper presents an analytical model for a railway mobile communications system. In line with recent trends, the system’s operation relies on 5G network resources (slices). It efficiently manages critical data streams (flows) that meet the stringent requirements of real-time systems (systems that handle hard and soft real-time services). Additionally, the proposed solution accommodates data with less stringent QoS parameters compared to real-time streams. The analytical model serves as an approximation of the process occurring in the system for servicing flows and has been developed based on the analysis of a Markov chain, where the states correspond to the states of the examined system. Due to the approximate nature of the analytical model, the results derived from it were compared with those obtained from the simulation experiment.

In this article, we present a new analytical model of one-sided (unilateral) multiservice switching structures. Structures of this type are more and more frequently implemented in network layout solutions in data centres as the so-called fat-tree topologies. The analytical model developed in the article enables the possibility of determining the blocking probability in switching structures composed of leaf/edge, aggregation, and spine/core switches. The results of the analytical model for a number of selected switching structures are compared in the article with corresponding results obtained for a simulation model. The study confirms high accuracy of the proposed model. This model can be used to evaluate traffic effectiveness in data centre structures that deploy fat-tree topologies.

The article proposes a new method of determining traffic characteristics of multiservice overflow systems that carry adaptive traffic. When the total offered load in primary resources exceeds a certain value, this type of traffic is admitted for service with lower bitrate. A particular attention is given in the article to a method for a determination of the parameters of traffic that overflows to secondary resources as well as to the way adaptive traffic is serviced. The method takes into consideration three possible types of traffic: Erlang, Engset, and Pascal traffic. It is based on a generalization of Hayward’s concept and its application to model systems with adaptive traffic with threshold compression. The method can be used for optimal dimensioning of logical networks (slices) in modern mobile systems due to possibility of analytical determination of grade of service parameters (blocking probability, carried traffic, and network load). To verify the accuracy of the proposed model the results of analytical calculations, obtained on the basis of the proposed model, are then compared with the results of simulation experiments for a number of selected structures of overflow systems that service adaptive traffic. The results of the study demonstrate high accuracy of the proposed theoretical model.

This article describes an approximate model of a group of cells in the LTE network with implemented load balancing mechanism. An appropriately modified model of Er-lang's Ideal Grading is used to model this group of cells. The model makes it possible to take into account limited availability of resources of individual cells to multi-rate traffic streams. The developed solution allows the basic traffic characteristics in the considered system to be determined, i.e. the occupancy distribution and the blocking/loss probability. Because of the approximate nature of the proposed model, the results obtained based on the model were compared with the results of a digital simulation. The present study validates the proposed model both in terms of the adopted assumptions and in terms of the simulation techniques.

The dynamic development of multiservice cellular networks has resulted in significant changes in the system architecture, which, in turn, has led to a broad distribution of many mechanisms and functions responsible for traffic management. These mechanisms take advantage of appropriate algorithms and analytic dependencies to ensure optimal quality of service that can be tailored to the objectives of the network operator. This paper proposes a new analytical model of a cellular network that supports multicast connections in a distributed environment. It is assumed that, in the cells participating in multicast connections, it is possible to apply different and independent traffic management mechanisms such as, for example, threshold mechanisms and resource reservation mechanisms. The proposed method can be used in an evaluation and scientific methods of research in the traffic effectiveness of multicast connections in given load conditions of a cellular network. An application of the method can have a particular significance in designing high-bit-rate multicast services to users in 4G networks. The analytical model proposed in this paper is verified on the basis of simulation examinations of cellular networks with multicast connections. The investigations confirm high accuracy of the model and the correctness of all theoretical assumptions adopted in the study.

The aim of this paper is the elaboration of a new analytical calculation method of the occupancy distribution and the blocking probability in multi-service switching networks with multi-service sources. The considered multi-stage switching networks operates according to point-to-group selection. The analytical results of the blocking probability in the switching networks with multi-service sources are compared with simulation data.

Video-on-Demand (VoD) system have become increasingly popular over time. Currently constructed systems offer to their users a vast array of multimedia content spanning movies, video clips, TV programs, etc. that is made available through many video servers. One of the very important parameters at the initial stage of the system design is the blocking probability that follow the instances of unavailability of service resulting from the lack of provision of access to a given content. This parameter can be defined by means of appropriate tools, i.e. analytical models of systems, that enable to determine the level of losses in a system under design in relation to offered access demand and usage. The paper presents a new method for modelling of distributed Video-on-Demand systems. The proposed method is based on Erlang's Ideal Grading (EIG) with differentiated availability. Until now, Erlang's ideal gradings have not been used in modelling systems such as VoD.

The paper proposes an analytical approach to blocking probability calculation in the UMTS network carrying a mixture of multi-rate traffic, under the assumption that the part of resources of the interface is dedicated for servicing handoff traffic. In the proposed method, handoff connections are modeled on the basis of the fixed point methodology and dynamic reservation. The results of analytical calculation of the blocking probability in the group of cells carrying a mixture of different multi-rate traffic streams are compared with the results of the simulation experiments, which confirms a rather high accuracy of the method. The described calculation scheme is applicable for cost-effective resource management in 3G mobile networks and can be easily applied to network capacity calculations.

A new approximate method of blocking probability calculation in multi-service switching networks carrying a mixture of different multi-rate unicast and multicast traffic streams is presented. Three algorithms of setting up multicast connections are considered and discussed. Special attention is paid to the methods for determining the effective availability parameter for multicast connections. The results of the analytical calculations of the blocking probability are compared with the data of discrete event simulations of the switching networks.

An approximate model of a multistage switching network carrying a mixture of different multichannel traffic streams is proposed. In the model the multistage switching network is reduced to a single-channel system, that is, to an Erlang ideal grading to which a mixture of different multichannel traffic is offered. An approximate method for recurrence determination of the distribution of being busy in such grading is presented. The determined distribution enables calculation of blocking probabilities for traffic streams of various classes. The derived formula is a generalization of Kaufman (1981) and Robert's (1981) recurrence formula covering a full-availability trunk group with various multichannel traffic streams, and it can be useful for the analysis of ISDN systems.>