Herwig Bruneel

• Ghent University

This paper considers a discrete-time single-server queueing system, with two classes of customers, named class 1 and class 2. We propose and analyze a novel threshold-based priority scheduling scheme that works as follows. Whenever the number of class-1 customers in the system exceeds a given threshold\documentclass[12pt]{minimal} \usepackage{amsma...

We investigate a discrete-time two-queue system with a single server. At the beginning of every time slot, the single server randomly selects either queue 1 or queue 2 to serve. The decision of the server to select either queue 1 or queue 2 in each time slot is independent of the state of the system and is determined by a single parameter. The serv...

We consider a system of two coupled parallel queues with infinite waiting rooms. The time setting is discrete. In either queue, the service of a customer requires exactly one discrete time slot. Arrivals of new customers occur independently from slot to slot, but the numbers of arrivals into both queues within a slot may be mutually dependent. Thei...

We consider a system of two coupled parallel queues, queue 1 and queue 2, with infinite waiting rooms. The time setting is discrete. In either queue, the service of a customer requires exactly one discrete time slot. Arrivals of new customers occur independently from slot to slot, but the numbers of arrivals of both types within a slot may be mutua...

We consider a system of two parallel discrete-time single-server queues, queue 1 and queue 2. The service time of any customer in either queue is equal to 1 time slot. Arrivals during consecutive slots occur independently from slot to slot. However, the arrival streams into both queues are possibly mutually interdependent, i.e., during any slot, th...

In this paper we look at queueing phenomena occurring at a traffic light. As opposed to the well-known and well-researched Fixed-cycle Traffic Light, we consider a traffic light with variable lengths for the red and green periods. More specifically we apply a method that allows the red and green periods to be according to a stochastic distribution....

We analyze a discrete-time queueing system, consisting of two queues and a single server. The server randomly distributes its time between the two queues. Service times of any customer of either queue are deterministically equal to 1 time slot. In general, the joint analysis of such a two-queue system turns out to be very hard. In this paper, we as...

We present the study of a non-classical discrete-time queuing system in which the customers each request a variable amount of service, called their “service demand”, from a system with multiple servers, each of which can provide a variable amount of service, called their “service capacity”, in each time slot. The service demands are independent fro...

This paper analyzes a finite-buffer queueing system, where customers arrive in batches and the accepted customers are served in batches by a single server. The service is assumed to be dependent on the batch-size and follows a general bulk service rule. The inter-arrival times of batches are assumed to be correlated and they are represented through...

This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server. The objective is to have a better grasp on the concept of a global first-come-first-served service discipline with presorting, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their...

We consider a discrete-time queueing system with two queues and one server. The server is allocated in each slot to the first queue with probability \(\alpha \) and to the second queue with probability \(1-\alpha \). The service times are equal to one time slot. The queues have exponentially bounded, but general, arrival distributions. The mathemat...

In this work we look at the delay analysis of a customer in a discrete-time queueing system with one permanent server and one occasional extra server. The arrival process is assumed to be general independent, the buffer size infinite and the service times deterministically equal to one slot. The system is assumed to be in one of two different state...

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Di...

This paper deals with a renewal input finite-buffer single-server queue, where the arrivals occur in batches and the server serves the customers singly. It is assumed that the inter-batch arrival times are generally distributed and the successive service times are correlated. The correlated single-service process is exhibited by a continuous-time M...

This article gives closed-form analytic expressions as well as a computational analysis of the stationary system-length distribution for the renewal-input, bulk-arrival, and multi-server continuous-time queueing model. The service times are equal to the constant D for any customer. The queueing model may be denoted as GIX/D/c queue. Using the stead...

jats:p>In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number...

Condition-based maintenance is a proactive maintenance strategy where the condition of machinery is monitored. A machine is preventively maintained when it shows signs of degradation, in which case the necessary spare parts are provided from stock. However, machines may occasionally suffer from sudden shocks, or they may fail before showing any sig...

In this work we look at a discrete-time multiserver queueing system where the number of available servers is distributed according to one of two geometrics. The arrival process is assumed to be general independent, the service times deterministically equal to one slot and the buffer capacity infinite. The queueing system resides in one of two state...

We present the study of a non-classical discrete-time queueing model in which the customers each request a variable amount of service, called their “service demand”, from a server which is able to execute a variable amount of work, called its “service capacity”, during each time slot. We assume that the numbers of arrivals in consecutive time slots...

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...

We analyze a discrete-time two-class queueing system with a single server which is alternately available for only one customer class. The server is each time allocated to a customer class for a geometrically distributed amount of time. Service times of the customers are deterministically equal to 1 time slot each. During each time slot, both classe...

In this paper, we introduce a four-dimensional continuous-time Markov chain model to evaluate the performance of cognitive radio networks. In such networks, secondary (unlicensed) users may opportunistically use the frequency channels not currently occupied by primary (licensed) users in order to increase the utilization of the wireless spectrum. S...

Anticipating the impact of urgent emergency arrivals on operating room schedules remains methodologically and computationally challenging. This paper investigates a model for surgery scheduling, in which both surgery durations and emergency patient arrivals are stochastic. When an emergency patient arrives he enters the first available room. Given...

An accurate step length estimation can provide valuable information to different applications such as indoor positioning systems or it can be helpful when analyzing the gait of a user, which can then be used to detect various gait impairments that lead to a reduced step length (caused by e.g., Parkinson’s disease or multiple sclerosis). In this pap...

Generalized Processor Sharing is a notoriously hard model to analyze. In earlier work we derived an iterative procedure to calculate coefficients for a power series of the joint probability generating function of the stationary queue content. This procedure posed computational limitations on the possible number of coefficients calculable for the pe...

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...

In this work we look at the delay analysis of a customer in a discrete-time queueing system with one permanent server and one occasional extra server. The arrival process is assumed to be general independent, the buffer size infinite and the service times deterministically equal to one slot. The system resides in one of two different states defined...

We consider a discrete-time queueing system with one server and two types of customers, say type-1 and type-2 customers. The server serves customers of either type alternately according to a Bernoulli process. The service times of the customers are deterministically equal to 1 time slot. For this queueing system, we derive a functional equation for...

Cloud infrastructures are becoming a common platform for storage and workload operations for industries. With increasing rate of data generation, the cloud storage industry has already grown into a multi-billion dollar industry. This industry offers services with very strict service level agreements (SLAs) to insure a high Quality of Service (QoS)...

This paper investigates the problem of surgery sequencing under uncertain surgery durations, with the objective of minimizing the expected maximum waiting time that emergent patients may endure before an operating room becomes available. Given the sets of surgeries assigned to each operating room as well as the distribution of each surgery’s durati...

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...

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...

In optical packet/burst switched networks fiber loops provide a viable and compact means of contention resolution. For fixed size packets it is known that a basic void-avoiding schedule (VAS) can vastly outperform a more classical pre-reservation algorithm as FCFS. In this contribution we propose two novel forward-looking algorithms, WAS and XAS, t...

We analyse a priority queueing system with a normal queue (high priority) and an orbit (low priority). Only the first customer in orbit can retry during times that the queue and server are empty (constant retrial policy). In contrast with existing literature, we assume different service time distributions for the high- and low-priority customers. W...

We present the study of a non-classical discrete-time queueing model in which the customers each request a variable amount of service, called their “service demand”, from a server which is able to execute a variable amount of work, called its “service capacity”, during each time slot. We assume that the numbers of arrivals in consecutive time slots...

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...

Service differentiation is a basic requirement in every modern queueing system with multiple classes of customers. In this paper, we look at Hierarchical Generalized Processor Sharing (H-GPS), which is a discrete-time hierarchically-structured implementation of the well-known idealized Generalized Processor Sharing (GPS) scheduling discipline. We p...

Although ultra wideband (UWB) positioning is considered as one of the most promising solutions for indoor positioning due to its high positioning accuracy, the accuracy in situations with a large number of users will be reduced because the time between two UWB position updates can be very high. To obtain a position estimate in between these updates...

We study the tail probabilities of the customer delay for a buffer operating under a reservation-based scheduling discipline known as R-scheduling. Previous numerical work on this model has led to a hypothesized meta-model, which was tested using simulations but not proven analytically. In this paper, we prove the correctness of this meta-model ana...

We consider a discrete-time queueing system having two distinct servers: one server, the “regular” server, is permanently available, while the second server, referred to as the “extra” server, is only allocated to the system intermittently. Apart from their availability, the two servers are identical, in the sense that the customers have determinis...

We analyse the threshold-based exhaustive data backup scheduling mechanism by means of a queueing-theoretic approach. Data packets that have not yet been backed up are modelled by customers waiting for service (back-up). We obtain the probability generating function of the system content (backlog size) at random slot boundaries in steady state.

Cognitive radio networks use dynamic spectrum access of secondary users (SUs) to deal with the problem of radio spectrum scarcity . In this paper, we investigate the SU performance in cognitive radio networks with reactive-decision spectrum handoff. During transmission, a SU may get interrupted several times due to the arrival of primary (licensed)...

In Cognitive Radio Networks (CRNs), spectrum sensing is performed by secondary (unlicensed) users to utilize transmission opportunities, so-called white spaces or spectrum holes, in the primary (licensed) frequency bands. Secondary users (SUs) perform sensing upon arrival to find an idle channel for transmission as well as during transmission to av...

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...

In this paper, we study a non-classical discrete-time queueing model with variable service demands and variable service capacities. Specifically, we consider the case where the service capacities of the system, i.e., the numbers of work units that the system can perform during each slot, are independent from slot to slot and have an identical gener...

In this paper, we analyze a non-classical discrete-time queueing model where customers demand variable amounts of work from a server that is able to perform this work at a varying rate. The service demands of the customers are integer numbers of work units. They are assumed to be independent and identically distributed (i.i.d.) random variables. Th...

We consider a system where two queues share one server. In case of conflict, the first (second) queue is served with probability β (1−β respectively). We prove strict monotonicity and continuity w.r.t. β of the mean unfinished work in queues 1 and 2. Restrictive assumptions are avoided as much as possible, by only assuming that the total unfinished...

We analyze the delay experienced in a discrete-time priority queue with a train-arrival process. An infinite user population is considered. Each user occasionally sends packets in the form of trains: a variable number of fixed-length packets is generated and these packets arrive to the queue at the rate of one packet per slot. This is an adequate a...

In this paper, we analyze a discrete-time queueing model with two types (classes) of customers and two servers, one for each customer class. Although each server can only process one type of customers, all customers are accommodated in one single queue and served in their order of arrival, irrespective of their types. The numbers of customers arriv...

With ever-increasing demand for bandwidth, both optical packet switching and optical burst switching are proposed as alternatives to increase the capacity of optical networks in the future. In these packet-based switching techniques, Fiber Delay Lines (for delay assignments) and wavelength conversion (for channel assignments) are used to avoid cont...

This paper considers a discrete-time single-server infinite-capacity queue with two classes of packet arrivals, either delay-sensitive (class 1) or delay-tolerant (class 2), and a reservation-based priority scheduling mechanism. The objective is to provide a better quality of service to delay-sensitive packets at the cost of allowing higher delays...

In this paper, we study the delay characteristics of a discrete-time queue with a reservation-based scheduling mechanism. The objective is to provide a better quality of service to delay-sensitive packets at the cost of allowing higher delays for the best-effort packets. We consider a single-server infinite-capacity queue with general independent p...

With ever-increasing demand for bandwidth, both optical packet switching and optical burst switching are proposed as alternatives to increase the capacity of optical networks in the future. In these packet-based switching techniques, Fiber Delay Lines are used to avoid contention between packets on a single wavelength. The involved scheduling algor...

Numerous scheduling policies are designed to differentiate quality of service for different applications. Service differentiation can in fact be formulated as a generalized resource allocation optimization towards the minimization of some important system characteristics. For complex scheduling policies, however, optimization can be a demanding tas...

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-...

Buffer overflow in intermediate network routers is the prime cause of packet loss in wired communication networks. Packet loss is usually quantified by the packet loss ratio , the fraction of packets that are lost in a buffer. While this measure captures part of the loss performance of the buffer, we show that it is insufficient to quantify the eff...

We analyze a discrete-time queueing model where two types of customers, each having their own dedicated server, are accommodated in one single FCFS queue. Service times are deterministically equal to \(s \ge 1\) time slots each. New customers enter the system according to a general independent arrival process, but the types of consecutive customers...

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...

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...

We present the analysis of a non-classical discrete-time queueing model where customers demand variable amounts of work from a server that is able to perform this work at a varying rate. The service demands of the customers are integer numbers of work units. They are assumed to be independent and identically distributed (i.i.d.). The service capaci...

We establish a statistical framework for investigating the influence of correlated random displacements of antenna elements in a uniform circular antenna array (UCA) on the distribution of direction-of-arrival (DOA) estimates. More specifically, we apply a stochastic collocation method formodeling the sparse UCA root-MUSIC-DOA estimates as polynomi...

This paper analyzes a single-server discrete-time queueing model with general independent arrivals, where the service process of the server is characterized in two steps. Specifically, the model assumes that (1) each customer represents a random, arbitrarily distributed, amount of work for the server, the service demand, and (2) the server disposes...

In this paper, we study a discrete-time single-server queueing system where the arriving traffic consists of both delay-sensitive and delay-tolerant streams. We analyze the effects of a reservation-based scheduling discipline on the delay characteristics of both types of traffic. Under this discipline, a placeholder packet is inserted in the queue...

We analyse a scheduling system in which users announce requests for information from a server some time before they actually need this information. Each constituent of the requested information has its own specific deadline, which is characteristic for applications that gradually consume a stream of information (e.g., video). For that purpose, a re...

Today, telecommunication networks host a wide range of heterogeneous services. Some demand strict delay minima, while others only need a best-effort kind of service. To achieve service differentiation, network traffic is partitioned in several classes which is then transmitted according to a flexible and fair scheduling mechanism. Telecommunication...

Abstract This letter focuses on the waiting time of customers in a single-server queueing system, served according to one of two well-known scheduling disciplines, Random-Order-of-Service (ROS) and First-Come-First-Served (FCFS). Arrivals are modeled with a Markov-Modulated Poisson Process (MMPP); service times are exponential. For two basic settin...

With ever-increasing demand for bandwidth, optical packet/burst switching is proposed to utilize more of the available capacity of optical networks in the future. In these packet-based switching techniques, packet contention on a single wavelength is resolved effectively by means of Fiber Delay Lines. The involved scheduling algorithms are typicall...

In this paper, we study a hybrid scheduling mechanism in discrete-time. This mechanism combines the well-known Generalized Processor Sharing (GPS) scheduling with strict priority. We assume three customer classes with one class having strict priority over the other classes, whereby each customer requires a single slot of service. The latter share t...

With ever-increasing demands for bandwidth, optical packet/burst switching is used to utilize more of the available capacity of optical networks. In existing prototypes of optical switches, packet contention is resolved by combining time and wavelength multiplexing by means of fiber delay lines and wavelength converters. Although optical switches d...

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.,...

In operations research and networking problems, random-order-of-service (ROS) provides a well-known alternative to the classic first-come-first-served (FCFS) policy. Models with ROS policy are typically harder to analyze than their FCFS counterparts, with some performance measures notoriously hard to obtain. While significant progress has been real...

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the “deadline” of the customer. More specifically, we model the deadlines of the consecutive customers as independent and geometrically distributed random variables. Customers enter the system according to a genera...

We develop an optimization model for a supply chain, integrating both location and inventory decision making. The supply chain consists of one supplier, multiple distribution centers and multiple retailers, and is subject to stochastic customer demand and supply lead times. The objective is to simultaneously optimize the locations of distribution c...

In multi-class queueing systems, customers of different classes can enter the system. When studying such systems, it is traditionally assumed that the different classes of customers occur randomly and independently in the arrival stream of customers in the system. This is often in contrast to the actual situation. Therefore, we study a multi-class...

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...

We consider the problem of evaluating and constructing appointment schedules for patients in a health care facility where a single physician treats patients in a consecutive manner, as is common for general practitioners, clinics and for outpatients in hospitals. Specifically, given a fixed-length session during which a physician sees K patients, e...

In optical packet/burst switching, fiber delay line (FDL) optical buffers provide an effective means of contention resolution. In many implementations, a single-stage buffer is assumed. In this contribution, however, we analyze a multi-stage setting, with the second stage consisting of only a single small delay line. For the stability analysis, we...

In optical packet/burst switching, packet contention on a single wavelength is resolved effectively by means of Fiber Delay Lines. The involved scheduling algorithm is typically designed to minimize packet loss, by filling so-called voids, and trying to keep the so-called gaps small. We propose a new type of algorithm that selectively creates voids...

This paper analyzes a single-server discrete-time queueing model with general independent arrivals, where the service process of the server is characterized in two steps. Specifically, the model assumes that (i) each customer represents a random, arbitrarily distributed, amount of work for the server, the service demand, and (ii) the server dispose...

In this paper, we present a mechanism for scheduling multi-class traffic in a node of a packet-based communication network. We focus in particular on the output queues used for contention resolution at the output links of a network node. The mechanism, referred to as R-scheduling, is based on the use of in-queue reservations for future arriving dat...

We perform an analysis of the transient delay in a discrete-time FIFO buffer with batch arrivals. As transient delay is an ambiguous concept, we first discuss different possible definitions of the term (delay of the kth customer, delay of a customer arriving at time t, etc.). In this paper, we focus on the analysis of the delay of a customer arrivi...

This paper considers the detection of coded phase-shift keying signals subjected to additive white Gaussian noise and oscillator phase noise. We propose a detector that partitions the received frame into smaller blocks and models the unknown phasor variations over each block as a truncated discrete cosine transform (DCT) expansion. Detection and de...