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A single-server queueing system with n classes of customers, stationary superposed input processes, and general class-dependent service times is considered. An exponential splitting is proposed to construct classical regeneration in this (originally non-regenerative) system, provided that the component processes have heavy-tailed interarrival times. In particular, we focus on input processes with Pareto interarrival times. Moreover, an approximating G I / G / 1 -type system is considered, in which the independent identically distributed interarrival times follow the stationary Palm distribution corresponding to the stationary superposed input process. Finally, Monte Carlo and regenerative simulation techniques are applied to estimate and compare the stationary waiting time of a customer in the original and in the approximating systems, as well as to derive additional information on the regeneration cycles' structure. [ABSTRACT FROM AUTHOR]

We consider a general approach to establish the positive recurrence (stability) of regenerative stochastic systems. The approach is based on the renewal theory and a characterization of the remaining renewal time of the embedded renewal process generated by regeneration. We discuss how this analysis is simplified for some classes of the stochastic systems. The general approach is then illustrated by the stability analysis of a k-out-of-n repairable system containing n unreliable components with exponential lifetimes. Then we extend the stability analysis to the system with non-exponential lifetimes. [ABSTRACT FROM AUTHOR]

In this research, a single-server M-class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workloads in the classical M / G / 1 systems where the service time has M-component mixture distributions. This analysis is applied to establish the extreme behaviour of stationary workload in the retrial system with Pareto service-time distributions for all classes. [ABSTRACT FROM AUTHOR]

We consider a multiclass retrial system with classical retrials, and present a new short proof of the sufficient stability (positive recurrence) condition of the system. The proof is based on the analysis of the departures from the system and a balance equation between the arrived and departed work. Moreover, we apply the asymptotic results from the theory of renewal and regenerative processes. This analysis is then extended to the system with the outgoing calls. A few numerical examples illustrate theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper considers a modified Erlang loss system for cognitive wireless networks and related applications. A primary user has pre-emptive priority over secondary users, and the primary customer is lost if upon arrival all the channels are used by other primary users. Secondary users cognitively use idle channels, and they can stay (either in an infinite buffer or in an orbit) in cases where idle channels are not available upon arrival or they are interrupted by primary users. While the infinite buffer model represents the case with zero sensing time, the infinite orbit model represents the case with positive sensing time. We obtain an explicit stability condition for the cases where arrival processes of primary users and secondary users follow Poisson processes, and their service times follow two distinct arbitrary distributions. The stability condition is insensitive to the service time distributions and implies the maximal throughout of secondary users. Moreover, we extend the stability analysis to the system with outgoing calls. For a special case of exponential service time distributions, we analyze the buffered system in depth to show the effect of parameters on the delay performance and the mean number of interruptions of secondary users. Our simulations for distributions rather than exponential reveal that the mean number of terminations for secondary users is less sensitive to the service time distribution of primary users. [ABSTRACT FROM AUTHOR]

The modern technological process of timber harvesting is a complex system both technically and organizationally. Nowadays, the study of such systems and improvement of their efficiency is impossible without the use of mathematical modeling methods. The paper presents the methodology for the optimization of logging operations based on the queueing theory. We show the adapted queueing model, which characterizes the process of logging with the use of a harvesting set consisting of harvesters and forwarders. We also present the experimental verification of the designated model that confirmed mode's adequacy. The analysis of the effectiveness of the investigated harvesting set was conducted and the recommendations for its optimization were drawn. The research was conducted in the Pryazhinsky District in the Republic of Karelia. We showed that significant improvement of operational efficiency of the investigated harvesting set in the study area cannot be done by adjusting separate machine operations (i.e. by reducing the time of operations execution and their steadiness). However, a change in the number of machines allowed significant improvement in the operational efficiency. The most optimal harvesting set design for the experimental area consisted of two harvesters and two forwarders. [ABSTRACT FROM AUTHOR]

The backoff protocol is widely used for sharing a common channel among several stations in communication networks. The Binary Exponential Backoff (BEB) improves the system throughput but increases the capture effect, permitting a station to seize the channel for a long time. In this article, we introduce and analyze a new class of adaptive backoff protocols where a station changes its contention window after a successful transmission differently than BEB. The transitions between the contention window states are determined by a stochastic matrix which describes a finite, irreducible, aperiodic Markov chain. We derive a stationary distribution of an associated embedded Markov chain in an explicit form and then find the stationary distribution of the basic Markov chain explicitly. Preliminary simulation results show that our backoff protocol can reduce the capture effect in Ethernet and wireless networks significantly. [ABSTRACT FROM PUBLISHER]

We find an equilibrium in a single-server queueing system with retrials and strategic timing of the customers. We consider a set of customers, each of which must decide when to arrive to a queueing system during a fixed period of time. In this system, after completion of service, the server seeks a customer blocked in a virtual orbit (orbital customer) to be served next, unless a new customer captures the server. We develop, in detail, a setting with two and three customers in the set, and formulate and discuss the problem for the general case with an arbitrary number of customers. The numerical examples for the system with two and three customers included as well. [ABSTRACT FROM AUTHOR]

The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system model with two-component Pareto mixture distribution of service times. The theoretical results are illustrated by numerical simulation of the M / G / c systems while using the perfect sampling approach. [ABSTRACT FROM AUTHOR]