Maciej Stasiak

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.

Server-side capacity dimensioning in operator-managed Over-The-Top (OTT) and Internet Protocol Television (IPTV) systems requires analytical methods that can account for heterogeneous traffic classes, differentiated subscription tiers, and strict grade-of-service (GoS) constraints. This paper proposes a capacity-planning framework based on a full-availability group (FAG) model and the Kaufman–Roberts recursion for evaluating class-specific blocking probabilities in multi-class OTT/IPTV delivery systems. The framework combines recursive occupancy-distribution computation with an incremental capacity search procedure to determine the minimum server-side delivery capacity satisfying differentiated blocking targets for free, standard, and premium subscription tiers. Three provisioning strategies are analysed within a unified model: dedicated server pools, a shared non-prioritised resource pool, and a shared prioritised resource pool. The analytical results are validated by discrete-event simulation and then used to compare the required capacities under the considered strategies. For the analysed six-class scenario, the shared server configuration reduces the required capacity by 3.82% compared with the dedicated architecture, while the prioritised shared configuration reduces it by 12.44%, while preserving stricter GoS protection for higher-priority traffic. The proposed framework provides network operators with a reproducible analytical tool for translating blocking-probability constraints into concrete server-capacity requirements and infrastructure-planning decisions.

This paper introduces a new analytical model of a multi-service system to which a heterogeneous mixture of stream, elastic, and adaptive traffic is offered, corresponding to data streams transmitted in real-world networks. The heterogeneity results from the coexistence of compressed and non-compressed traffic classes, where the compressed traffic is subject to a finite compression mechanism and includes both elastic and adaptive traffic. The model accounts for access constraints on resources for stream traffic, a strategy frequently used in modern ICT networks to manage the impact of high-rate data streams on overall system performance. The proposed model is developed based on an analysis of the service process within the system using multi-dimensional Markov processes. To assess the accuracy of the analytical model, a digital simulation is conducted. A comparative analysis of the results obtained from the analytical model and the simulation experiments confirms the high accuracy and robustness of the proposed approach, making it suitable for the design and optimization of modern ICT networks, including 5G systems.

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.

The article presents the results of a study on modeling cloud systems. In this research, the authors developed both analytical and simulation models. System analysis was conducted at the level of virtual machine support, corresponding to Infrastructure as a Service (IaaS). The models assumed that virtual machines of different sizes are offered as part of IaaS, reflecting the heterogeneous nature of modern systems. Additionally, it was assumed that due to limitations in access to physical server resources, only a portion of these resources could be used to create virtual machines. The model is based on Markov chain analysis for state-dependent systems. The system was divided into an external structure, represented by a collection of physical machines, and an internal structure, represented by a single physical machine. The authors developed a novel approach to determine the equivalent traffic, approximating the real traffic appearing at the input of a single physical machine under the assumptions of request distribution. As a result, it was possible to determine the actual request loss probability in the entire system. The results obtained from both models (simulation and analytical) were summarized in common graphs. The studies were related to the actual parameters of commercially offered physical and virtual machines. The conducted research confirmed the high accuracy of the analytical model and its independence from the number of different instances of virtual machines and the number of physical machines. Thus, the model can be used to dimension cloud systems.

This paper proposes an analytical method to determine the occupancy distribution in a group of links of elastic optical networks that service multiservice traffic streams. The method is based on a modification of the recursive Kaufman-Roberts equation, which allows one to take into account the influence of two system factors on the possibility of accepting calls of multiservice traffic streams. The first factor concerns the specific structure of the system, which is a group of links modeled as a limited-availability group. The second factor is related to the requirement of selecting adjacent frequency slot units. The proposed method, taking into account the dependencies mentioned above, relies on selecting a representative microstate for each macrostate, with its conditional transition probability closely approximating that of the given macrostate. To assess the precision of the proposed method and the underlying assumptions, tests were carried out for different capacity values of the system and different traffic values offered. The results of the research obtained show that, from an engineering point of view, the proposed model is characterized by satisfactory accuracy.

Cloud computing has become a major component of the modern IT ecosystem. A key contributor to this has been the development of Infrastructure as a Service (IaaS) architecture, in which users’ virtual machines (VMs) are run on the service provider’s physical infrastructure, making it possible to become independent of the need to purchase one’s own physical machines (PMs). One of the main aspects to consider when designing such systems is achieving the optimal utilization of individual resources, such as processor, RAM, disk, and available bandwidth. In response to these challenges, the authors developed an analytical model (the ARU method) to determine the average utilization levels of the aforementioned resources. The effectiveness of the proposed analytical model was evaluated by comparing the results obtained by utilizing the model with those obtained by conducting a digital simulation of the operation of a cloud system according to the IaaS paradigm. The results show the effectiveness of the model regardless of the structure of the emerging requests, the variability of the capacity of individual resources, and the number of physical machines in the system. This translates into the applicability of the model in the design process of cloud systems.

Handoff mechanisms are very important in fifth-generation (5G) mobile networks because of the cellular architecture employed to maximize spectrum utilization. Together with call admission control (CAC) mechanisms, they enable better optimization of bandwidth use. The primary objective of the research presented in this article is to analyze traffic levels, aiming to optimize traffic management and handling. This article considers the two most popular CAC mechanisms: the resource reservation mechanism and the threshold mechanism. It presents an analytical approach to occupancy distribution and blocking probability calculation in 5G mobile networks, incorporating connection handoff and CAC mechanisms for managing multiple traffic streams generated by multi-service sources. Due to the fact that the developed analytical model is an approximate model, its accuracy was also examined. For this purpose, the results of analytical calculations of the blocking probability in a group of 5G cells are compared with the simulation data. This paper is an extended version of our paper published in 17th ConTEL 2023.

The article presents a new analytical model for determining the probability of availability of a certain amount of well-defined free resources (e.g. a link) in a group of dedicated resources (e.g. a group of links) jointly serving a mixture of different classes of multiservice traffic. The presented method can be used to model access to resources in data centres, in particular in the software-defined networks, assuming -- for reliability reasons -- that the user should have access to a certain minimum number of specific separated resources. The proposed analytical model was verified by appropriate simulation experiments, which confirmed the satisfactory accuracy of the results obtained.

This article proposes a new analytical model of a queuing system to which a mixture of multi-service traffic is offered. The system under consideration has the advantage of servicing calls, in a shared server, of which only part will be placed in a queue when the server has no free resources (while the remaining part of the calls will be lost). In addition, this model also introduces the possibility for a compression mechanism to be applied for a selected number of data flows. The possibility of simultaneous analysis of the calls that can be placed in the queue as well as of those in which queuing is not implemented, while a certain number of them can be compressed, provides unquestionable advantage to the proposed model. The proposed model can be successfully applied to analyse and model 5G systems.