To modelling of monoservice multicast queueing systems with overlapping resource requirements

In this paper we consider random resources queueing system with multicasting designed for the performance analysis of modern telecommunication systems. This is a monoservice loss queueing system with random resource requirements, a finite number of servers and limited amount of resources. The term "overlapping resource requirements" reflects the multicast principle: all the customers in th system are served at the same amount of resourses dedicated to the first customer after idle period, as against unicast with providing individual amount for each subscriber accepted in the system. A newcomer never decreases the amount of resources occupied in the system but it can increase this amount in case when its random requirement exeeds the amount of resourses allocated to all its predecessors on the current busy period. Busy period starts when the first customer joins the sytem. When the service time of the first customer ends all the customers leave the system and the idle period starts. For this queueing system the stationary probabilities are obtained as a solution of the stationary equilibrium equations. We also propose the main performance characteristics of the system, i.e. the blocking probability and the mean number of customers in the system. © 2019 Author(s)

Analysis of multi-server queueing system with semi-Markovian input flow and negative customers acted upon queue end

The multi-server queueing system with a finite of an infinite buffer, with semi-Markovian input flow (for positive and negative customers) and with Markovian Service Process (for positive customers) whose the number of the states of the process and the intensities of the transitions between phases depend on the number of the customers in the system is considered. An arriving negative customer kills the one positive customer at the end of the queue. The relations and algorithms for computation of the steady-state probabilities and for calculation of the steadystate distribution of waiting time of positive customer are received. It is shown how the multiserver queueing system with semi-Markovian input flow, the servicing of the phase type and the above mentioned order of act of the negative customers can be bring to the general queuing system

Method of modeling interference characteristics in heterogeneous fifth generationwireless networks with device-to-device communications

The paper shows the construction of the model of the moving of interacting devices in heterogeneous wireless networks of the fifth generation with the help of the kinetic equation taking into account a given average speed of the devices, their spatial density, and the maximum allowable communication radius. A method for generating trajectories is proposed where the transceivers move randomly and the walk is not stationary in general. This is the feature of the study which distinguishes the proposedmodel frompreviously knownmodels. Interference characteristics, including signal-interference ratio (SIR), are studied in the form of a time-continuous random process, the problem of calculating these characteristics is proposed to be solved by simulations. It is shown that such analysis makes it possible to investigate the probabilistic characteristics of the interaction of devices such as signal interruption probability for the receiver-transmitter pair, the random variables for the duration of the availability period, and the period of absence of communication. © 2017 Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Development of mathematical models and methods of task distribution in distributed computing system

The article deals with certain aspects of Grid and Grid modeling. Grid is a distributed softwarehardware environment based on new computation and job flow management structure, principally. For analyzing the problems related to the logics of user-resource interaction, there has been developed a general model scheme. Within that scheme the authors consider the models that allow the formulation of concrete mathematical tasks. The ways of solving the assigned tasks are discussed as well

Decomposition of exponential G-networks, with dependent service and route change

Queueing networks with negative customers (G-networks), Poisson flow of positive customers, multi-server exponential nodes, and dependent service at the different nodes are studied. Every customer arriving at the network is defined by a set of random parameters: customer route, the length of customer route, customer volume and its service time at each route stage as well. The arrival of a negative customer to a queuing system causes one of the ordinary (or “positive”) customers to be removed (or “killed”) if any is present. However, the “killed” customer does not quit the network but continues his way along the new random route. For such G-networks, the multidimensional stationary distribution of the network state probabilities is shown to be representable in product form

Some Bayesian Queueing and Reliability Models

The Bayesian approach for certain tasks of queueing systems theory and reliability theory is introduced. The method provides the randomization of system characteristics with regard of a priori distributions of input parameters. This approach could be used, for instance, for calculating average values and for construction of confidential intervals applicable for performance and reliability characteristics of large groups of systems or devices

FSM based simulation for performance evaluation of SIP server loss-based overload control

The rapid development of services provided on SIP networks not only define the necessity of creating new equipment and standards but also requires the development of new methods and programming software tools for modeling and analyzing the effectiveness of the overload control mechanisms in SIP-server networks. The modeling process utilizes mathematical and simulation models as well as simulators. Only simulators or simulation tools make it possible to solve problems related to the analysis and optimization of the control parameters. The most appropriate modeler is the simulators reflecting the protocols and functions, which are fully or partially built into the original system. At present, there are no simulators for modeling the work of SIP servers in overload conditions with an application of mechanisms, which are currently under development by IETF SIP Overload Control workgroup. Simulation tool that supports the main SIP RFCs such as RFC 3261 are proposed in the paper. The architecture of SIP node is developed, and numerical example is presented. © ECMS Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova (Editors)

Simulation of the limited resources queuing system for performance analysis of wireless networks

Queuing systems with limited resources, in which customers require a device and a certain amount of limited resources for the duration of their service, proved their effectiveness in the performance analysis of modern wireless networks. However, the application of the queuing systems leads to complex computations. In this paper, we develop the simulation tool for the limited resources queuing systems and apply it to the analysis of M2M traffic characteristics in a LTE network cell. © ECMS Lars Nolle, Alexandra Burger, Christoph Tholen, Jens Werner, Jens Wellhause

Probabilistic model for the analysis of elastic session duration in wireless networks

In wireless networks, the bitrate received by a user session depends not only on the fraction of allocated resources of the base station but also on the number of factors affecting the signal-to-noise ratio. These factors include a distance between a mobile device and the base station, walls, buildings between them, etc. As a result, the bitrate of elastic sessions may differ tenfold. In this paper, we develop a probabilistic model that captures the main specifics of the data transmission through a wireless network by introducing the random serving rate coefficients concept. With the help of the model, we derived the cumulative distribution function of the elastic session duration. © 2021 Institute of Physics Publishing. All rights reserved

Polling system with threshold control for modeling of SIP server under overload

The main purpose of this research is the development of the methods for realizing an overload control mechanism on the Session Initiation Protocol servers by the application of polling systems with different service disciplines. The mathematical model is studied by means of numerical methods of the queuing theory and allows analyzing the behavior of different control parameters depending on the load in network of SIP servers. The polling system consists of two queues of finite capacity and implements the threshold control of loading by low-priority customers. The exhaustive and gated service disciplines are studied under Markov assumptions; formulas for calculation of the main probability measures of the polling system are derived. By performing simulations we demonstrate that the polling system with a threshold in the priority queue is a possible solution for loss-based overload control scheme at the SIP server. In some cases from the viewpoint of server utilization we found that the gated discipline is more preferable. © Springer International Publishing Switzerland 2014