Determination of Steady-State Characteristics of Three-Channel Queuing Systems with Erlangian Service Times

This article proposes a method for analyzing the following M/E₂/3/m queuing systems: the standard system and also systems with threshold and hysteresis strategies of random dropping of customers in order to control the input flow. Recurrence relations are obtained to compute the stationary distribution of the number of customers and steady-state characteristics. The constructed algorithms were tested on examples with the use of simulation models constructed with the help of GPSS World.     

Calculating Steady-State Characteristics of Single-Channel Queuing Systems Using Phase-Type Distributions

This paper analyzes the results of application of the hyperexponential and Erlang approximations with parameters of paradoxical and complex types for calculating steady-state characteristics of G /G /1/ m queuing systems by the fictitious phase method. The results are verified using simulation models.     

Recurrence Relations for Two-Channel Queuing Systems with Erlangian Service Time

We propose a method to investigate M / E_s / 2 / m and M / E_s / 2 /∞ queueing systems including the case of random dropping of customers. Recurrence relations are obtained for computing the stationary distribution of the number of customers in the system and its steady-state characteristics. The developed algorithms are tested on examples using simulation models constructed with the help of the GPSS World tools.     

Determining Stationary Characteristics of Two-Channel Queueing Systems with Erlangian Distribution of Service Time

The author proposes a method to study M/E₂/2/m and M/E₂/2/∞ queueing systems: standard systems and systems with the threshold and hysteretic strategies of random dropping of customers in order to control the input flow. Recurrence relations are obtained to compute the stationary distribution of the number of customers in the system and stationary characteristics. The constructed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools.     

Some Markovian Queuing Retrial Systems under Light-Traffic Conditions

The asymptotic behavior of the time of the first loss of a demand in Markovian single-channel and multichannel queuing retrial systems with a finite buffer and an external Markovian environment is analyzed. Two cases are studied: (a) the ratio of the input rate to the service rate tends to zero and (b) the ratio of the input rate to the service rate and the ratio of the input rate to the retrial rate tend to zero simultaneously. The method of so-called S-sets and the concept of a monotone structure introduced by Anisimov are used to prove the exponential approximation of the time of the first call loss and Poisson approximation of a flow of lost demands for both cases.     

Queuing Systems with Cyclic Control Processes

An analysis of queuing systems with control processes more general than cyclic ones is proposed. Conditions ensuring stochastic boundedness of cyclic systems and existence of their steady state are analyzed.__________Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 54–69, January–February 2005.     

Recurrence Relations for Multichannel Queueing Systems with Second-Order Erlangian Service Times

We propose a method to analyze queueing systems M / E₂ / n / m, M / E₂ / n / ∞, including the case of random dropping of customers. Recurrence relations are obtained to compute the steady-state distribution of the number of customers in the system and steady-state characteristics. The developed algorithms are tested on examples using simulation models constructed with the use of the GPSS World tools.     

Optimal Control of Queuing Systems with Channel Switching

Automation and Remote Control - We consider the problem of optimizing the operation of a queuing system in which the number of working service channels can be changed in a controlled manner at...     

Estimating the Parameters of Queuing Systems with Channel Switching

Automation and Remote Control - We consider the problem of estimating the queuing system structure and parameters when implementing the system of optimal switching of the main service channels at...     

Analysis of Queuing Systems for Random-Length Arrivals with Limited Cumulative Volume

Two queuing systems for variable-length customers, namely, a processor-sharing system and a multiline system without waiting places, are considered, for which arrivals are completely random, the joint arrival-length and service-time distribution is arbitrary, and the cumulative arrival volume is limited. For these systems, the stationary state probabilities and the arrival loss probability are determined.     

Analysis of Networks of the Resource Queuing Systems

Consideration was given to the model of a queuing network with resource queuing systems—the multi-server systems with losses where servicing of the accepted customer occupies random volumes of resources with the given distribution function depending on the customer class and the type of required servicing. Customer servicing in a node can be interrupted by a signal arriving at an exponential time from the start of servicing, and during the time of customer sojourn in the network it may be interrupted more than once. Analytical formulas for calculation of the fundamental probability-time model characteristics—including the joint distribution functions of the number of customers in the nodes and the volumes of resources occupied by them—were proposed on the assumption of the Poisson flows incoming to the nodes and arbitrary servicing.     

Accelerated Simulation of the Steady-State Availability of Non-Markovian Systems

A general accelerated simulation method for evaluation of the steady-state availability of non-Markovian systems is proposed. It is applied to the investigation of a class of systems with repair. Numerical examples are given.     

Asymptotic Diffusion Analysis of $$MMPP|M|N$$ Queuing Systems with Feedback

Automation and Remote Control - We present the results of the study of an $$ N $$ -linear queuing system with feedback. The input flow is a Markov modulated Poisson process (MMPP). We use...     

Recovering High-Order Accuracy in WENO Computations of Steady-State Hyperbolic Systems

In this note we consider the application of the WENO scheme to simulations of steady-state flow in a converging diverging nozzle. We demonstrate the recovery of design accuracy through Gegenbauer postprocessing, despite the degradation of the order of accuracy for the numerical solution of the Euler equations to first-order in regions where the characteristics passed through the shock. We have shown a case in which the Gegenbauer postprocessing can recover the order of accuracy right up to the shock location. This suggests that high-order accurate information which crosses through the shock may not be irretrievably lost, and we can strive to recover it through various types of postprocessing.     

Stochastic Model for Communicating Retrial Queuing Systems with Cyclic Control in Random Environment1

The cybernetic approach is used to develop a mathematical model for communicating queuing systems. Conflicting input flows of the first queuing system and one of the input flows of the second queuing system are formed in a synchronous Markov random environment with a finite number of states. Another input flow of the second queuing system consists of retrials arriving from the first queuing system. The transition of a customer from the first queuing system to the second one takes a random amount of time. Servicing is performed by a cyclic algorithm with fixed duration.     

A Queuing Model for Evaluating the Transfer Latency of Peer-to-Peer Systems

This paper presents a queuing model to evaluate the latency associated with file transfers or replications in peer-to-peer (P2P) computer systems. The main contribution of this paper is a modeling framework for the peers that accounts for the file size distribution, the search time, load distribution at peers, and number of concurrent downloads allowed by a peer. We propose a queuing model that models the nodes or peers in such systems as M/G/1/K processor sharing queues. The model is extended to account for peers which alternate between online and offline states. The proposed queuing model for the peers is combined with a single class open queuing network for the routers interconnecting the peers to obtain the overall file transfer latency. We also show that in scenarios with multipart downloads from different peers, a rate proportional allocation strategy minimizes the download times.     

Power-Law Distributions of Component Size in General Software Systems

This paper begins by modeling general software systems using concepts from statistical mechanics which provide a framework for linking microscopic and macroscopic features of any complex system. This analysis provides a way of linking two features of particular interest in software systems: first the microscopic distribution of defects within components and second the macroscopic distribution of component sizes in a typical system. The former has been studied extensively, but the latter much less so. This paper shows that subject to an external constraint that the total number of defects is fixed in an equilibrium system, commonly used defect models for individual components directly imply that the distribution of component sizes in such a system will obey a power-law Pareto distribution. The paper continues by analyzing a large number of mature systems of different total sizes, different implementation languages, and very different application areas, and demonstrates that the component sizes do indeed appear to obey the predicted power-law distribution. Some possible implications of this are explored.     

The Quantization Property of Probability Distributions of the Characteristics of Dynamic Systems Observed in the Presence of Random Disturbances

The class of linear stochastic dynamic systems is defined, such that the laws of the probability distribution of values of output signals of a system are determined by its equations complying with the case of the absence of random disturbances. These distribution laws are found to be similar to the quantum laws of the distribution values of observable physical quantities. On this basis, a possibility of the definition of the quantum systems as systems of this class is investigated. It is shown that the theoretical proof of some axioms of quantum mechanics and new facts requiring the experimental verification follow from this definition.     

XML与消息队列的集成应用研究

在分析消息队列的基础上,提出了基于XML的消息队列,它可以统一消息的数据格式,方便地实现不同应用之间的数据交换。讨论了基于XML的消息和消息队列的相关问题,并给出了具体的实现方案。