Bart Steyaert

Bart Steyaert
Fedris

Phd

About

126
Publications
4,649
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1,049
Citations
Citations since 2016
26 Research Items
333 Citations
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201620172018201920202021202201020304050
201620172018201920202021202201020304050
201620172018201920202021202201020304050
Introduction
Skills and Expertise

Publications

Publications (126)
Chapter
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.
Chapter
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...
Chapter
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...
Chapter
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.
Chapter
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...
Chapter
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...
Chapter
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.
Chapter
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...
Chapter
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.
Chapter
This chapter is devoted to a stability analysis of regenerative queueing systems based on a renewal analysis technique. This approach allows us to obtain simple proofs for stability conditions for the stochastic processes that are considered. In order to illustrate the method, the chapter specifically focuses on the stability conditions of the well...
Chapter
Théorie des files d’attente 2 examine les pratiques établies et les tendances actuelles dans l’analyse et les applications des modèles de files d’attente. Ce second volume étudie l’analyse de stabilité de certains types de systèmes de files d’attente régénératives multiserveurs, l’analyse transitoire des systèmes de files d’attente markoviens se co...
Book
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...
Article
Full-text available
In multi-class telecommunications or manufacturing systems, customers belonging to the same class can often be processed together. This results in a service capacity that depends on the classes of the customers in the queue. In this paper, we analyse a discrete-time batch-service queue with two customer classes. The single batch server can group al...
Article
Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server’s capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capa...
Article
Full-text available
In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length...
Conference Paper
In manufacturing, a batch server groups multiple customers that require the same type of service based on a specific characteristic, such as temperature or destination. In this paper, we extend previous work with the analysis of the delay in a variable-capacity batch-service queueing system with general class-dependent service times and customer-ba...
Article
In this paper, we study a discrete-time queueing system with one server and two classes of customers. Customers enter the system according to a general independent arrival process. The classes of consecutive customers, however, are correlated in a Markovian way. The system uses a “global FCFS” service discipline, i.e., all arriving customers are ac...
Conference Paper
Full-text available
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...
Article
Full-text available
In this paper we use the burst factor of a packet stream, which is defined in a general setting, to quantify the long-term variability, or burstiness, of such a stream. We briefly review some existing results to show that this parameter plays an important role in the performance assessment and dimensioning of buffers in network nodes, even in a non...
Conference Paper
Due to their wide area of applications, queueing models with batch service, where the server can process several customers simultaneously, have been studied frequently. An important characteristic of such batch-service systems is the size of a batch, that is the number of customers that are processed simultaneously. In this paper, we analyse a two-...
Conference Paper
Exact analysis of tandem priority queues is a difficult problem. In this paper, we model the output process of the first stage as a three-state Markov chain and analyze the second stage. The arrival process of this second stage is the superposition of this output process and an uncorrelated arrival process. We calculate the joint probability genera...
Article
Full-text available
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...
Article
Full-text available
In this paper, we investigate a single-server discrete-time queueing system subject to two independent batch Bernoulli arrival processes, each supplying the queue with different customer classes. The two classes of customers have different priority levels in the queue, and different service-time distributions. The studied priority mechanism is time...
Article
Full-text available
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...
Article
This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server. We assume that customers all queue together and are served in the order of arrival, regardless of the class they belong to. This global FCFS service discipline creates a blocking effect: if a customer of one type is in...
Conference Paper
In this paper we consider a continuous-time queueing system with two different types (1 and 2) of customers with two dedicated servers (also named 1 and 2). This means server 1 (2) can only serve customers of type 1 (2). The goal of this paper is to study the boundary conditions for a system with global FCFS and presorting service discipline, i.e.,...
Article
When good items have to be separated from bad ones, significant reduction in costs can be achieved by screening the items in groups rather than individually. In this regard, the selection of an efficient group size is crucial. For several decades, a model from Robert Dorfman was the de facto standard to determine the optimal group size. However, mo...
Conference Paper
This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server with exponential service times. The system adopts a “global FCFS” service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. “Class clustering”, i.e., the fact...
Article
Full-text available
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...
Article
Full-text available
In this paper the focus is on “class clustering” in a continuous-time queueing model with two classes and dedicated servers. “Class clustering” means that customers of any given type may (or may not) have a tendency to “arrive back-to-back”. We believe this is a concept that is often neglected in literature and we want to show that it can have a co...
Article
Full-text available
In this paper, we investigate multi-class multi-server queueing systems with global FCFS policy, i.e., where customers requiring different types of service— provided by distinct servers— are accommodated in one common FCFS queue. In such scenarios, customers of one class (i.e., requiring a given type of service) may be hindered by customers of othe...
Article
In this contribution we introduce the burst factor, which is defined in a general setting, and quantifies the long-term variability, or burstiness, of a packet source. By means of a combination of analytic and simulation results, we will demonstrate that this parameter plays an important role in the calculation of the moments of the amount of work...
Article
We deduce approximations for the tail probabilities of the customer delay in a discrete-time queueing model with batch arrivals and batch service. As in telecommunications systems transmission times are dependent on packet sizes, we consider a general dependency between the service time of a batch and the number of customers within it. The model al...
Article
In the past, many researchers have analyzed queueing models with batch service. In such models, the server typically postpones service until the number of present customers reaches a service threshold, whereupon service is initiated of a batch consisting of several customers. In addition, correlation in the customer arrival process has been studied...
Article
Full-text available
In multi-core in-order processing systems, only one core can be utilised when the instruction at the head of the instruction queue produces data input for the next instruction in the queue. Although in-order processing has been studied in the past, the influence of data clustering, i.e. the extent to which subsequent instructions rely on each other...
Article
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...
Article
The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn’t actually determine what happens if multiple customers enter the system at the same time, which in the discrete-time paradigm translates into ‘during the same time-slot’. In other words, it doesn’t specify in which order such customers are served. When w...
Article
Batch servers are capable of processing batches of packets instead of individual packets. Although batch-service queueing models have been studied extensively during the past decades, the focus was mainly put on calculating performance measures related to the buffer content, whereas less attention has been paid to the packet delay. In this paper, w...
Article
Full-text available
For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian a...
Article
Full-text available
The paper we present here introduces a new priority mechanism in discrete-time queueing systems. It is a milder form of priority when compared to HoL priority, but it favors customers of one type over the other when compared to regular FCFS. It also provides an answer to the starvation problem that occurs in HoL priority systems. In this new priori...
Conference Paper
Full-text available
This paper considers a discrete-time queueing system with one server and two classes of customers. All arriving customers are ac-commodated in one queue, and are served in a First-Come-First-Served order, regardless of their classes. The total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distri-bution...
Article
We propose an algorithm for multivariate Markovian characterisation of H.264/SVC scalable video traces at the sub-GoP (Group of Pictures) level. A genetic algorithm yields Markov models with limited state space that accurately capture temporal and inter-layer correlation. Key to our approach is the covariance-based fitness function. In comparison w...
Article
Full-text available
This paper introduces a new priority mechanism in discrete-time queueing systems that compromises between first-come-first-served (FCFS) and head-of-line priority. In this scheduling discipline—which we dubbed slot-bound priority—customers of different priority classes entering the system during the same time-slot are served in order of their respe...
Article
In this paper, situations are investigated where customers requiring different types of service, each provided by distinct servers, are accommodated in one common queue. In such scenarios, customers of one class (i.e., requiring a given type of service) may be hindered ("blocked") by customers of other classes. For instance, if a road or a highway...
Article
Full-text available
In nodes where the arriving packets are stored in one common buffer, packets with a given destination may have to wait for the transmission of packets with other destina-tions, even when the corresponding output channel is free. Although this so-called blocking effect has attracted considerable attention in literature, the influence of the rel-ativ...
Article
For several specific discrete-time queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. This paper aims to show that this...
Article
Full-text available
A well-known problem with priority policies is starvation of delay-tolerant traffic. Additionally, insuffcient control over delay di erentiation (which is needed for modern network applications) has incited the develop-ment of sophisticated scheduling disciplines. The priority policy we present here has the benefit of being open to rigorous analysi...
Conference Paper
Full-text available
This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server. The system adopts a ‘‘global FCFS’’ service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. As a consequence of the ‘‘global FCFS’’ rule, customers of one...
Article
Full-text available
We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of t...
Conference Paper
Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only init...
Article
A well-known problem with priority policies is starvation of delay-tolerant traffic. Furthermore insufficient control over delay differentiation (which is needed for modern network applications) has incited the development of other scheduling disciplines. Processor sharing is one of many solutions to this problem. The priority policy we present her...
Article
After completing the basic technical Logistics Readiness Officer (LRO) course, the LRO returns to their assigned base and begins core competency on-the-job training. In order to become qualified, the LRO must be assigned to at least one proficiency in each of the three core competencies (material management, distribution management, and contingency...
Article
In this paper, a method is developed to analyze the evolution of the traffic characteristics of information streams crossing the consecutive stages of an ATM multistage switching structure. Specifically, we develop a generic model for characterizing the traffic streams at the input of the consecutive stages, based on the assumption that the queuein...
Article
Full-text available
A digital subscriber line access multiplexer that multiplexes streaming packetised telephony and/or video-on-demand traffic is studied. To this end, the distribution of the amount of work in a discrete-time single-server queuing model with heterogeneous sources and general packet lengths is calculated. Obtaining actual data concerning the distribut...
Article
A critical component in the delivery of VBR streaming video over packet-based networks, is the playout buffer at the receiver side. As packets will incur a variable delay within the network, a mechanism is needed to dejitter the stream and assure that packets are played out at exactly the same rate at which they were generated by the sender. Packe...
Conference Paper
In this paper, a multivariate Markovian traffic model is proposed to characterise H.264/SVC scalable video traces. Parametrisation by a genetic algorithm results in models with a limited state space which accurately capture both the temporal and the inter-layer correlation of the traces. A simulation study further shows that the model is capable of...
Article
Full-text available
In this paper, we analyze a discrete-time preemptive resume priority queue. We consider two classes of customers which have to be served, where customers of one class have preemptive resume priority over customers of the other. Both classes contain customers with generally distributed service times. We show that the use of probability generating fu...
Thesis
Full-text available
De kwaliteit van de multimediadiensten die worden aangeboden over de huidige breedband-communicatienetwerken, wordt in hoge mate bepaald door de performantie van de buffers die zich in de diverse netwerkele-menten (zoals schakelknooppunten, routers, modems, toegangsmultiplexers, netwerkinter- faces, ...) bevinden. In dit proefschrift bestuderen we...
Article
We assess the performance of a bottleneck buffer in a multimedia network. The buffer temporarily stores packets of different video streams, awaiting for transmission on a single output link. These streams are encoded in a scalable way such that the bottleneck buffer may drop packets of enhancement layers to ensure delivery of base layer packets. In...
Article
The authors consider an integrated switching element with a shared buffer memory and a constant hardware delay. This hardware delay is caused by the hardware operations required to process the routing information of incoming cells. A general uncorrelated cell arrival process in the switch, an independent and uniform routing process of cells from th...
Article
Full-text available
In this paper, we analyze a discrete-time preemptive repeat priority queue with resampling. High-priority packets have preemptive repeat priority, and interrupted low-priority packets are subjected to independent retransmission attempts. Both classes contain packets with generally distributed transmission times. We show that the use of generating f...
Article
In this paper, we study the loss and delay of data bursts in an optical buffer. We assume that this buffer consists of a number of fiber delay lines (FDLs). In order to guarantee quality of service (QoS) differentiation in such a buffer, we investigate analytically an offset-time based scheduling mechanism. We consider a system with C QoS classes,...
Article
Full-text available
Priority scheduling for packets is a hot topic, as interactive (voice,video) services are be- ing integrated in existing data networks. In this paper, we consider a discrete-time queueing system with a non-preemptive (or Head-Of-the-Line) priority scheduling discipline and a gen- eral number of priority classes. Packets of variable length arrive in...
Conference Paper
Full-text available
Priority scheduling for packets is a hot topic, as interactive (voice,video) services are being integrated in existing data networks. In this paper, we consider a discrete-time queueing system with non-preemptive (or Head-Of-the-Line) priority scheduling and a general num-ber of priority classes. Packets of variable length arrive in the queueing sy...
Article
Full-text available
Abstract In this paper, we analyze a discrete-time GI-G1; Geo2-1 preemptive resume priority queue. We consider two classes of packets which have to be served, where one class has preemp- tive resume priority over the other. The high-priority class contains packets with generally distributed service times while the low-priority packets are assumed t...
Article
In this paper, we investigate the evolution of the interarrival and interdeparture times between voice packets when they are proceeding through a number of network nodes. We model the arrival process in a node as the superposition of a single tagged stream and an independent background process that aggregates the remaining traffic sources. Because...
Article
In this paper, we analyze a discrete-time GI-Geo-1 preemptive resume priority queue. We consider two classes of packets which have to be served, where one class has preemptive resume priority over the other. We show that the use of generating functions is beneficial for analyzing the system contents and packet delay of both classes. Moments and (ap...
Conference Paper
Full-text available
We derive a methodology to determine the effect of per service session admission control on the resource usage in an aggregation network for the delivery of video services. Given the network capacity and the characteristics of the service, we determine the number of subscribers that can be served in the scenarios with and without admission control....