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## Publications

Publications (118)

The paper is devoted to the tail asymptotics analysis of the steady-state waiting times in the queuing systems in which service times have Weibull distributions. We deduce conditions under which the service times in two different queueing systems are stochastically ordered. Then we show that, under the same conditions, the normalizing sequences of...

We consider the logarithmic asymptotics of the large deviation probability in a single-server queue with Poisson input, where server, after completion of service, seeks a customer in a virtual orbit (retrial customer) for the next service, unless new arrival captures server. This system is described by a regenerative process, and under stability as...

In this paper, the extremal behavior of the waiting time and queue size in some queueing systems is considered, based on the regenerative property of these systems. The basic properties of the extremal index of a stationary sequence are discussed, which further relate to the maximum waiting time and queue size processes. Simulation results are pres...

We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when one orbit is tight but the other orbit goes to infinity in probability. All theoretical results are illustrate...

In this chapter, we demonstrate the main steps of the regenerative stability analysis by considering the classical single-server GI/G/1 queueing system, as well as the multiserver GI/G/m system with \(m>1\) servers.

The purpose of this chapter is to derive the stability condition for another modification of the K-class retrial system considered in Chap. 7, with total input rate \(\lambda =\sum _{i=1}^K\lambda _i\) (with no balking), with a finite buffer of size \(G\ge 0\), and with m identical servers. Adopting most of the notations used in Chap. 7, we now con...

As became clear throughout the analysis presented in the previous chapter, the tightness property of stochastic processes plays an important role in the regenerative stability analysis of queuieng processes. Another topic that is important for the stability analysis presented in this book, is the monotonicity of the relevant processes in the queuei...

In this chapter, we apply the regenerative stability analysis to a number of queueing systems that belong to a class of state-dependent systems. In each of these systems, a mechanism is available that allows to control its dynamics, depending on the current state of the basic queueing processes describing the system.

Evidently, many more applications of the regenerative stability analysis technique can be considered. We address just some of these applications in this chapter, by respectively focusing on the stability analysis of an optical buffer model, on discrete-time queues, and on regenerative networks. We discuss only the new aspects of the related stabili...

In this chapter, we study the stability of a two-station queueing system with interacting servers that are able to join forces in one direction only, sometimes referred to as N-models [1, 2, 3]. Such a queueing system configuration has a lot in common with the notion of flexible servers [4], meaning that some service capacity may be transferred fro...

In a loss queueing system, a customer facing a busy server upon arrival (a blocked customer) leaves the system forever without waiting for service. However, in many applications, the blocked customers leaving the system may retry to enter service after some random time period.

In this chapter, we study the stability of some important extensions of the classical GI/G/m system : a multiserver system with non-identical servers (that was already in part discussed in Chap. 3), a finite-buffer system, a system with an infinite number of servers, and a system with a regenerative input flow. The multiserver system with non-ident...

In this chapter, we extend the analysis developed in Chap. 7 to more complicated retrial systems, in which the retrial rate of each orbit depends on a binary state of the other orbits. This setting is well-motivated and suited for modelling wireless multiple-access systems, see Sect. 8.4.

The stability analysis of stochastic models for telecommunication systems is an intensively studied topic. The analysis is, as a rule, a difficult problem requiring a refined mathematical technique, especially when one endeavors beyond the framework of Markovian models.
The primary purpose of this book is to present, in a unified way, research int...

The paper deals with a single-server model with constant retrial rate. If an arrival meets the server busy, it joins the infinite-capacity orbit and then tries to occupy the server again after generally distributed time interval. Unlike the classical retrial policy, the intensity of orbit customers does not depend on its number. To derive the stabi...

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 mod...

In this work, we consider an approximation of the so-called far-end-tail distribution of processes describing quality of service (QoS) performance of queueing systems. This approximation is based on the asymptotic equivalence between the excess distribution over a high threshold and the generalized Pareto distribution, for a wide class of the gover...

Mixture models arise when at least two different distributions of data sets are presented. In this paper, we introduce the upper and lower bounds for the steady-state performance of a multiserver model of the network node, with Exponential-Pareto mixture distribution of service times. We use the failure rate and stochastic comparison techniques tog...

In this paper, we consider a multiserver retrial queuing system with unreliable servers class-dependent retrial rates and N classes of customers following Poisson input processes. We analyze the distribution of the stationary generalized remaining service time which includes all unavailable periods (setup times) occurring during service of the cust...

We discuss the asymptotic of the large deviation probability in a single-server retrial queue with K classes of customers. The constant retrial rate policy is assumed. The input is assumed to be a general renewal process and the retrial attempts follow an exponential distribution. The system is described with a regenerative process. We are interest...

In this paper, we introduce and study the relations between parameters of the two-component Hyperexponential, Exponential-Pareto and two-component Pareto mixture distributions which admit stochastic and failure rate comparisons. Then we apply the failure rate and stochastic ordering techniques to construct the upper and lower bounds for the steady-...

In this paper, a multiserver retrial system with constant retrial policy is considered. The input is assumed to be a general renewal process, service times are iid with a general distribution and the retrial attempts follow an exponential distribution. The system is described with a regenerative process, and we focus on the logarithmic asymptotics...

In this work, we discuss various (stochastic) orderings between random variables, with focus on the failure rate comparison. Then these results are applied to construct a coupling of random variables. In particular, it is shown how to compare the failure rates of various distributions, including Exponential, Weibull, Pareto and Burr distributions....

In this paper, a large deviation analysis of the retrial systems is developed. We consider both classical and constant retrial rate models. We focus on the (overflow) probability that the orbit size in the single-server system reaches a high level N within a regeneration period. Under natural assumptions, it is shown that, as N→∞, the overflow prob...

We study a multiclass single-server retrial system with independent Poisson inputs and the state-dependent retrial rates. Meeting busy server, a new class-i customer joins orbit i. Orbit i is working as a FIFO-type queueing system, in which the top customer retries to occupy server. The retrial times are exponentially distributed with a rate depend...

We consider a multiclass multiserver retrial queuing system with classical retrial discipline: the customers, meeting server busy, are blocked on the corresponding (virtual) orbit and then retry to occupy server independently. The retrial times have general class-dependent distributions. The input process is renewal and a new arrival is class-i cus...

In this paper, we consider a single-server retrial model with multiple classes of customers. Arrival of customers follow independent Poisson rule. A new customer, facing a busy server upon his arrival, may join the corresponding (class-dependent) orbit queue with a class-dependent probability, or leaves the system forever (balks). The orbit queues...

In this work, we investigate the stability conditions of a multiclass retrial system with coupled orbit queues and service interruptions. We consider a single server system accepting N classes of customers according to independent Poisson inputs and with class-dependent, arbitrarily distributed service times. An arriving customer who finds the serv...

For a fluid queue fed by superposition of fractional Brownian motion and alpha-stable Lévy process, the asymptotic lower bound of the overflow probability is obtained.

The paper deals with a Markovian retrial queueing system with a constant retrial rate and two servers. We present the detailed description of the model as well as establish the sufficient conditions for null ergodicity and strong ergodicity of the corresponding process and obtain the upper bounds on the rate of convergence for both situations.

We give a simple proof of the well-known property PASTA for the workload and queue size process in the queueing systems with Poisson input. The proof is based on a relation connecting the workload process at an arbitrary instants and the arrival instants of the customers and, in particular, yields famous Pollaczeck-Khintchine equality. It is then s...

In this work, we verify by simulation some recent theoretical
results describing the dynamics of the the retrial system with coupled
orbits. In such a system, retransmission rate of customers blocked in a
virtual orbit depends in general on the binary state, busy or idle, of other
orbits. We consider a system with N classes of customers, where an a...

In this paper, we apply a regenerative approach to reprove some recent steady-state results [1, 8, 9] for an orbit-queue (also known as retrial queue with a constant retrial rate) with outgoing calls. Stability conditions are discussed as well. Moreover, some generalizations of the model are also considered.

In this work, we use simulation to verify the stability conditions of the so-called N -model, which consists of two servers and two classes of external customers, both generated by Poisson inputs. Service times are server-dependent and, in each server, are i.i.d. When server 1 is occupied, and there are waiting customers in queue of server 1, then...

In this work we consider a single-server system accepting $N$ types of retrial customers, which arrive according to independent Poisson streams. In case of blocking, type $i$ customer, $i=1,2,...,N$ is routed to a separate type $i$ orbit queue of infinite capacity. Customers from the orbit queues try to access the server according to the constant r...

We consider a single-server system in which each customer is described by its service time and a random volume. The total volume of customers accepted by the system is upper bounded by a finite constant (system capacity) M. We give renewal-based approximations for a number of important stationary parameters of the system, in particular, the mean lo...

We consider a regenerative degradation process composed by a sum of the successive phases, where preventive repair is used to prevent an instantaneous failure. For an optimal control of such a systems, calculation of the failure probability, the average length of the regeneration cycle with or without failure, etc., is critically important. If the...

Long-term correlation is a key feature of traffic flows and has a deep impact on network performance. Indeed, the arrival rate can persist on relatively high values for a considerable amount of time, provoking long busy periods and possibly bursts of lost packets. The authors focus on Gaussian processes, well-recognized and flexible traffic models,...

In this work, the fluid limit approach methodology is applied to find a sufficient and necessary stability condition for the Basic Collaboration (BC) system with feedback allowed, which is a generalization of the so-called W-model. In this queueing system, some customer classes need cooperation of a subset of (non-overlapping) servers. We assume th...

In this paper, we study a multiserver system in which each customer requires a random number of servers simultaneously and a random but identical service time at all occupied servers. This model describes the dynamics of modern high performance clusters. Stability criteria of this system (under exponential assumptions) have been proved earlier for...

We consider a multiserver retrial queueing system with a renewal input, $K$ classes of customers, and a finite buffer. Service times are class-dependent, however, for each class, are independent, identically distributed (iid). A new class-$i$ customer joins the primary system (servers and buffer), otherwise, if all servers and buffer are full, he j...

In this paper, we study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously and a random service time, identical at all occupied servers. We call it cluster model since it describes the dynamics of the modern multicore high performance clusters (HPC). Stability criterion of an...

In spite of their low frequency, rare events often play a major role in determining systems performance. In most cases they can be analysed only through simulation with ad-hoc techniques since traditional Monte Carlo approaches are quite inefficient in terms of simulation length and/or estimation accuracy. Among rare event simulation techniques, co...

We study a general multi-server system in which each customer has service time and a random volume. We consider two main cases: (i) the total volume of the present customers is unlimited and (ii) this volume is upper bounded by a finite constant. For this system, using the regenerative approach, we develop performance analysis. We establish a solid...

In this paper, we consider a model of communication system with state-dependent service rate. This mechanism allows to change service rate to increase the efficiency of the system. Motivation of such a system is discussed as well. Then we present the regenerative proof of the sufficient stability conditions of the system which is based on the negat...

In this paper we develop a novel approach to confidence estimation of the stationary measures in high performance multiserver queueing systems. This approach is based on construction of the two processes which are, respectively, upper and lower (stochastic) bounds for the trajectories of the basic queue size process in the original system. The main...

We study the stability of a single-server retrial queueing system with constant retrial rate, general input and service processes. First, we present a review of some relevant recent results related to the stability criteria of similar systems. Sufficient stability conditions were obtained by Avrachenkov and Morozov (2014), which hold for a rather g...

Due to the self-similar nature of broadband traffic, the arrival rate can persist on relatively high values for a considerable amount of time. Such a behavior, closely related to the duration of busy periods, has a deep impact on queueing performance in terms of loss probability and distribution of losses. In the paper we consider the probability t...

We study multi-class retrial queueing systems with Poisson inputs, general service times, and an arbitrary numbers of servers and waiting places. A class-i blocked customer joins orbit i and waits in the orbit for retrial. Orbit i works like a single-server (Formula presented.) queueing system with exponential retrial time regardless of the orbit s...

We continue to develop a novel approach for confidence estimation of the stationary measures in the model describing high performance multiserver queueing systems, such as high performance clusters (HPC). We call this model cluster model. This model is described by a stochastic process, and in the framework of the approach, we construct two envelop...

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 t...

We propose a new approach which allows to accelerate verification of the stability criterion of a multiserver
model with simultaneous service for large number of servers. This approach reduces a state space related to calculation of a basic normalization constant included in the stability condition. Moreover, this result allows to obtain a stable c...

We consider a single-server retrial system with one and several classes of customers. In the case of several classes, each class has its own orbit for retrying customers. The retrials from the orbits are generated with constant retrial rates. In the single class case, we are interested in finding an optimal retrial rate. Whereas in the multi-class...

In this paper, we consider
a state-dependent mechanism
which can be used to reduce mean power consumption in modern communication and computer systems. This mechanism allows to change flexibly the service rate so as to increase the energy efficiency of the system. We focus on computer systems with sojourn time dependent service rate, and present a...

In this paper, we define a class of asymptotically work – conserving service disciplines which, in particular, are used in some existing wireless systems. Then we describe a class of state-dependent queueing systems with focus on the workload-dependent and queue- dependent systems with asymptotically work-conserving discipline. We outline the regen...

We consider a Markovian single-server retrial queueing system with a constant
retrial rate. Conditions of null ergodicity and exponential ergodicity for the
correspondent process, as well as bounds on the rate of convergence are
obtained.

In this paper we apply regenerative method to estimate the required effective bandwidth (EB) of a station in an acyclic communication network. Earlier this problem for a tandem network has been addresses in [1]. We give a brief introduction to the EB theory and then discuss basic statistical methods for the EB estimation. For a queueing network des...

The paper studies the rate of convergence to stationarity of the fluid queueing system with a constant service rate which is fed by a Gaussian process with stationary increments. It is assumed that variance of the input process is regularly varying with index \(2H\in (1,\,2)\). It is proved that the convergence rate is exactly the same that has bee...

Some recent results presented at Aalto University, including the stability criterion and it’s accelerated version, exact solution for a single-server green computing model, some tasks in the volunteer computing research

We investigate flow-level stability of schedulers in parallel-service wireless systems, which is important for maximizing the base station's capacity to serve the heterogeneous flows that are within the base station's power range. We model such a system as a multi-class queueing system with multiple preemptive servers, in which flows of different c...

We consider the effective bandwidth (EB) estimation in the networks with the regenerative input. Based on the Lindley's-type recursion for the workload process in discrete and continuous time, we apply a large deviation approach to construct a regenerative estimate of the required EB in the nodes of tandem queuing networks. Simulation shows that th...

The inspection (or renewal time) paradox is one of the basic results of the renewal theory. It expresses the mean stationary forward renewal time by means of the two first moments of the interrenewal time. We consider a single-server system with optical buffers and apply the inspection paradox to obtain more tight stability condition for the equidi...

In this work, the fluid approach methodology is first applied to find a sufficient stability condition for a two-station cascade network: customers that are awaiting service at the first queue can move to the second station, whenever it is free, to be served there immediately, but the opposite is not allowed. Each station is fed by a renewal input...

The paper studies a general multiserver queue in which the service time of an arriving customer and the next interarrival period may depend on both the current waiting time and the server assigned to the arriving customer. Stability of the system is proved under general assumptions on the predetermined distributions describing the model. The proof...

A special speed-up simulation technique based on a combination of splitting and regenerative approach is developed to estimate a rare event probability. A consistent estimation of the probability that the workload process in M/G/1 and GI/G/1 queues exceeds a high level within a regeneration cycle is considered. A similar problem is studied for the...

In this work, the fluid limit approach is applied to find stability conditions of two models of queueing networks with interacting servers. We first consider a two-station queueing model with two customer classes in which customers that are awaiting service at any queue can move to the other station, whenever it is free, to be served there immediat...

In the paper, we consider a single-server loss system in which each customer has both service time and a random volume. The total volume of the customers present in the system is limited by a finite constant (the system’s capacity). For this system, we apply renewal theory and regenerative processes to establish a relation which connects the statio...

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate ) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance...

Thanks to their flexibility and compact characterization, Gaussian processes have emerged as popular models to describe the traffic dynamics in a wide class of the modern telecommunication networks. A relatively new characterization of traffic flows is based on the effective envelopes, which represent a probabilistic generalization of the arrival c...

We consider a FCFS multiclass, multiserver queueing system with class-dependent and server-dependent service times. We find stability criterion of such a system using the regenerative approach. The key idea is to consider the basic queue-size process in the saturated system. Then we use renewal theory and a characterization of the limiting remainin...

We consider a two-station cascade network, where the first station has Poisson input and the second station has renewal input, with i.i.d. service times at both stations. The following partial interaction exists between stations: whenever the second station becomes empty while customers are awaiting service at the first one, one customer can jump t...

In this paper we discuss the estimation of the loss probability in a queueing system with finite buffer fed by Brownian traffic, the Gaussian counterpart of the well-known Poisson process. The independence among arrivals in consecutive time slots allows the application of regenerative simulation technique, combined with the so-called Delta-method t...

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 paper, we introduce and analyze a new class of adaptive backoff pr...

For many queueing systems, the server is not continuously available. Service interruptions may result from repair times after server failures, planned maintenance periods or periods during which customers from other queues are being served. These service interruptions cause an overall performance degradation which is most striking when interruption...

This contribution presents the first stability analysis of multiwavelength queueing systems. Results are obtained for a wide class of implementable scheduling disciplines referred to as delay-oriented disciplines, a class to which for example join the shortest queue belongs. Scheduling is applied as contention resolution in optical switches accommo...

We discuss the application of the regenerative simulation of estimate the loss probability in a queueing system with finite buffer which is fed by a Gaussian input. We mainly consider queue with Brownian input. Stability analysis is discussed and some numerical examples are also included.

We consider the estimation of effective bandwidths in single-server queue- ing networks with finite buffers and regenerative input process. Drawbacks of batch means estimators in simulation practice are discussed and a new regenerative estimator is suggested.

We give a short survey of the moment properties of the basic regenerative queueing processes. Moreover, we show applicability of the regenerative simulation to estimate a steady-state performance measure of the positive recurrent basic process possessing long-range dependence. The moment properties of the embedded renewal process of regenerations p...

We consider a GI/G/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has $c$ identical servers and can accommodate the maximal number of $K$ jobs. If a newly arriving job finds the full primary queue, it joins the orbit. The original primary jobs arrive to the s...