Simulation modeling of HM-networks with consideration of positive and negative messages

In the article an open Queueing Network (QN) with positive and negative messages and incomes, which can be used in modeling of the behavior of viruses at the Information Systems and Networks (ISN), and also at forecasting costs taking into account virus penetration, was analyzed. Some numerical and analytical results were described on the analysis of exponential QN of the above type. It was given an algorithm of simulation modeling (SM) of HM-networks with positive and negative messages, based on the 0-point, which allows you to find incomes in such networks with arbitrary distribution of service times of positive messages. The results of the SM have been compared with the proposed analytical and numerical results. Sufficiently high accuracy of these methods was shown

Application of HM-networks with inpatient claims in finding the memory capacity in information systems

To solve the problem of determining the memory capacity of the information systems (IS), the use of the stochastic model is proposed, based on the use of НМ (Howard-Matalytski) - queueing networks with revenues. This model allows one to take into account time dependencies of the message processing from their capacities, the possibility changes of the messages capacities over time and also the possibility of leaving messages from queues in nodes of IS, without getting into them appropriate processing. The expressions for the mean (expected) values of total message capacities in the IS nodes have been obtained

Analysis of Markov HM-Queueing Networks with FIFO discipline at the transient regime and its application

In the paper Markov Queueing Networks (QN) are considered with the same types and different types of customers and incomes, FIFO discipline, which are probabilistic models of different Information Nets and Systems (INS). The incomes from the state transition of the network depend on servicing times of customers in the Queueing Systems (QS). The purpose of the research are design and development of methods and techniques of finding the probability-cost characteristics in such QN as effective analysis tools of INS. A closed Markov HM-network with the same types of customers has been investigated. Approximate expressions for the expected incomes of the QS were obtained. The method of finding the mean number of the customers was proposed. The analysis of an open HM-network with different types of customers and many-server queues has been carried out in the second part of the paper. Customers during the transition between QS can change its type. Approximate expressions for the expected incomes of the QS for each type of customer have been also obtained. A method for finding the mean number of servicing lines was described

About one method of finding expected incomes in HM-queueing network with positive customers and signals

In the paper an open Markov HM(Howard-Matalytski)-Queueing Network (QN) with incomes, positive customers and signals (G(Gelenbe)-QN with signals) is investigated. The case is researched, when incomes from the transitions between the states of the network are random variables (RV) with given mean values. In the main part of the paper a description is given of G-network with signals and incomes, all kinds of transition probabilities and incomes from the transitions between the states of the network. The method of finding expected incomes of the researched network was proposed, which is based on using of found approximate and exact expressions for the mean values of random incomes. The variances of incomes of queueing systems (QS) was also found. A calculation example, which illustrates the differences of expected incomes of HM-networks with negative customers and QN without them and also with signals, has been given. The practical significance of these results consist of that they can be used at forecasting incomes in computer systems and networks (CSN) taking into account virus penetration into it and also at load control in such networks

Analysis of Markov HM-Queueing Networks with FIFO discipline at the transient regime and its application

In the paper Markov Queueing Networks (QN) are considered with the same types and different types of customers and incomes, FIFO discipline, which are probabilistic models of different Information Nets and Systems (INS). The incomes from the state transition of the network depend on servicing times of customers in the Queueing Systems (QS). The purpose of the research are design and development of methods and techniques of finding the probability-cost characteristics in such QN as effective analysis tools of INS. A closed Markov HM-network with the same types of customers has been investigated. Approximate expressions for the expected incomes of the QS were obtained. The method of finding the mean number of the customers was proposed. The analysis of an open HM-network with different types of customers and many-server queues has been carried out in the second part of the paper. Customers during the transition between QS can change its type. Approximate expressions for the expected incomes of the QS for each type of customer have been also obtained. A method for finding the mean number of servicing lines was described

Nonstationary analysis of the queueing network with bypass of systems of multi-type and absolute priority messages

This paper contains an investigation of an open exponential network with bypass of systems of multi-type messages with absolute priority in transient behavior. Messages with priority received by the node with the probability depending on the state system and the type of incoming messages are for service, forcing messages that are serviced or instant changes in the following system, and can leave the network. Network settings: the intensity of the incoming flow and the intensity of service of different types of messages in single-line systems and the conditional probabilities of transitions of messages between the systems are dependent on the time. We obtained a system difference-differential equations for the state probabilities of the network. To find the state probabilities of the network in the transitional behavior applied a methodology based on the use of the apparatus of multidimensional generating functions

The analysis of the three-level HM-network and its application for the incomes forecasting of a logistic transport system

Investigation of the closed three-level HM-network, which is the model of the production transportation in a logistic transport system, is conducted in this article. The approximated expression for the expected income of the central system and the system of the nonhomogeneous differential equations for an average number of messages in network systems, when the incomes from transitions between network’s states are random variables with the set moments of the first two orders, is received. The relation for variance of the income of the central system of network (system of the top level) is also received