Maria Vlasiou

University of Twente | UT · Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS)

While mean-field models of cellular operations have identified dominant processes at the macroscopic scale, stochastic models may provide further insight into mechanisms at the molecular scale. In order to identify plausible stochastic models, quantitative comparisons between the models and the experimental data are required. The data for these sys...

The Industrial and Applied Mathematics (IAM) master’s program at Eindhoven University of Technology received the INFORMS UPS George D. Smith Prize in 2022. This paper highlights the department’s history, the innovative aspects of the program, and its role in educating operations research practitioners. Eindhoven University of Technology emphasizes...

High-tech systems are typically produced in two stages: (1) production of components using specialized equipment and staff and (2) system assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of shortages of at least one component, which results in costly delays. Companies hedge this risk by strategic i...

The Asymmetric Inclusion Process (ASIP) tandem queue is a model of stations in series with a gate after each station. At a gate opening, all customers in that station instantaneously move to the next station unidirectionally. We enhance the ASIP model by introducing the capability for individual customers to independently move from one station to t...

It is with great pleasure that we present to you this publication, the proceedings of IFIP Performance 2023. This issue includes extended abstracts of all regular papers accepted at the conference and the full short papers. This year's program boasts a remarkable collection of contributions spanning various topics, including queuing theory, network...

The process of charging electric vehicles (EVs) within an electricity network is a complex stochastic process. Various factors contribute to this complexity, including the stochastic arrivals and demands of users at charging stations, the nonlinear nature of power flow in the network, and the need to uphold reliability constraints for the network’s...

While mean-field models of cellular operations have identified dominant processes at the macroscopic scale, stochastic models may provide further insight into mechanisms at the molecular scale. In order to identify plausible stochastic models, quantitative comparisons between the models and the experimental data are required. The data for these sys...

This paper introduces a AC stochastic optimal power flow (SOPF) for the flexibility management of electric vehicle (EV) charging pools in distribution networks under uncertainty. The AC SOPF considers discrete utility functions from charging pools as a compensation mechanism for eventual energy not served to their charging tasks. An application of...

We compare stability regions for different power flow models in the process of charging electric vehicles (EVs) by considering their random arrivals, their stochastic demand for energy at charging stations, and the characteristics of the electricity distribution network. We assume the distribution network is a line with charging stations located on...

This paper introduces a stochastic AC-OPF (SOPF) for the flexibility management of electric vehicle (EV) charging pools in distribution networks under uncertainty. The SOPF considers discrete utility functions from charging pools as a compensation mechanism for eventual energy not served to their charging tasks. An application of the proposed SOPF...

Interacting networks are different in nature to single networks. The study of queuing processes on interacting networks is underdeveloped. It presents new mathematical challenges and is of importance to applications. This area of operations research deserves careful study: queuing theory needs to incorporate high-order network interactions in the p...

We use simulation to compare different power flow models in the process of charging electric vehicles (EVs) by considering their random arrivals, their stochastic demand for energy at charging stations, and the characteristics of the electricity distribution network. We assume the distribution network is a line with charging stations located on it....

Emden-Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden-Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model....

In this paper, we study the maximum waiting time $\max_{i\leq N}W_i(\cdot)$ in an $N$-server fork-join queue with heavy-tailed services as $N\to\infty$. The service times are the product of two random variables. One random variable has a regularly varying tail probability and is the same among all $N$ servers, and one random variable is Weibull dis...

In this paper, we study the tail behavior of $\max_{i\leq N}\sup_{s>0}\left(W_i(s)+W_A(s)-\beta s\right)$ as $N\to\infty$, with $(W_i,i\leq N)$ i.i.d. Brownian motions and $W_A$ an independent Brownian motion. This random variable can be seen as the maximum of $N$ mutually dependent Brownian queues, which in turn can be interpreted as the backlog i...

Emden-Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden-Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model....

We develop and analyze a measure-valued fluid model keeping track of parking and charging requirements of electric vehicles in a local distribution grid. We show how this model arises as an accumulation point of an appropriately scaled sequence of stochastic network models. Our analysis incorporates load-flow models that describe the laws of electr...

We compare stability regions for different power flow models in the process of charging electric vehicles (EVs) by considering their random arrivals, their stochastic demand for energy at charging stations, and the characteristics of the electricity distribution network. We assume the distribution network is a line with charging stations located on...

In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as [Formula: see text]. This fluid limit depends on the initial number of tasks. In order to prove these results, we develop extreme value theory and diffusion approximations fo...

To reduce carbon emission in the transportation sector, there is currently a steady move taking place to an electrified transportation system. This brings about various issues for which a promising solution involves the construction and operation of a battery swapping infrastructure rather than in-vehicle charging of batteries. In this paper, we st...

We study extreme values in certain fork-join queueing networks: consider $N$ identical queues with a common arrival process and independent service processes. All arrival and service processes are deterministic with random perturbations following Brownian motions. We prove that as $N\rightarrow \infty$, the scaled maximum of $N$ steady-state queue...

In this note we prove that the speed of convergence of the workload of a L\'evy-driven queue to the quasi-stationary distribution is of order $1/t$. We identify also the Laplace transform of the measure giving this speed and provide some examples.

We develop and analyze a measure-valued fluid model keeping track of parking and charging requirements of electric vehicles in a local distribution grid. We show how this model arises as an accumulation point of an appropriately scaled sequence of stochastic network models. The invariant point of the fluid model encodes the electrical characteristi...

In this paper, we study an $N$ server fork-join queueing network with nearly deterministic arrivals and service times. Specifically, we aim to approximate the length of the largest of the $N$ queues in the network. From a practical point of view, this has interesting applications, such as modeling the delays in a large supply chain. We present a fl...

The rise of electric vehicles (EVs) is unstoppable due to factors such as the decreasing cost of batteries and various policy decisions. These vehicles need to be charged and will therefore cause congestion in local distribution grids in the future. Motivated by this, we consider a charging station with finitely many parking spaces, in which electr...

To reduce carbon emission in the transportation sector, there is currently a steady move taking place to an electrified transportation system. This brings about various issues for which a promising solution involves the construction and operation of a battery swapping infrastructure rather than in-vehicle charging of batteries. In this paper, we st...

The rise of electric vehicles (EVs) is unstoppable due to factors such as the decreasing cost of batteries and various policy decisions. These vehicles need to be charged and will therefore cause congestion in local distribution grids in the future. Motivated by this, we consider a charging station with finitely many parking spaces, in which electr...

We consider a distribution grid used to charge electric vehicles subject to voltage stability and various other constraints. We model this as a class of resource-sharing networks known as bandwidth-sharing networks in the communication network literature. Such networks have proved themselves to be an effective flow-level model of data traffic in wi...

We consider a distribution grid used to charge electric vehicles subject to voltage stability and various other constraints. We model this as a class of resource-sharing networks known as bandwidth-sharing networks in the communication network literature. Such networks have proved themselves to be an effective flow-level model of data traffic in wi...

The number of electric vehicles (EVs) is expected to increase. As a consequence, more EVs will need charging, potentially causing not only congestion at charging stations, but also in the distribution grid. Our goal is to illustrate how this gives rise to resource allocation and performance problems that are of interest to the Sigmetrics community.

Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times have general distributions. Customers are served according to their arrival order at each node and after finish...

We consider a system consisting of a single server serving a fixed number of stations. At each station, there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queueing networks, to an extension of polling systems and surprisingly to random graphs. We are interested in...

We study a network of parallel single-server queues, where the speeds of the servers are varying over time and governed by a single continuous-time Markov chain. We obtain heavy-traffic limits for the distributions of the joint workload, waiting-time and queue length processes. We do so by using a functional central limit theorem approach, which re...

Motivated by an application in wireless random-access networks, we study a class of polling systems with Markovian routing, in which the server visits the queues in an order governed by a discrete-time Markov chain. Assuming that the service disciplines at each of the queues fall in the class of branching-type service disciplines, we derive a funct...

Proportional fairness is a popular service allocation mechanism to describe and analyze the performance of data networks at flow level. Recently, several authors have shown that the invariant distribution of such networks admits a product form distribution under critical loading. Assuming exponential job size distributions, they leave the case of g...

This article considers an extension of the classic machine-repair problem. The machines, apart from receiving service from a single repairman, now also supply service themselves to queues of products. The extended model can be viewed as a two-layered queueing network, in which the queues of products in the first layer are generally correlated, due...

We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase...

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. Motivated by statistical analysis, we assume that the claim sizes are a mixture of a phase-type and a...

We consider a system consisting of a server alternating between two service points. At both service points there is an infinite queue of customers that have to undergo a preparation phase before being served. We are interested in the waiting time of the server. The waiting time of the server satisfies an equation very similar to Lindley's equation...

We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the elementary renewal theorem and avoids the technicalities in the proof that is presented in most textbooks. Moreover...

We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d.\ cycles. Although we focus on the classical definition, we present a more general definition that allows for some form of dependence between two adjacent cycles, and mention two further extensions of the second definition. We men...

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a spe...

We present analytic results for warehouse systems involving pairs of carousels. Specifically, for various picking strategies, we show that the sojourn time of the picker satisfies an integral equation that is a contraction mapping. As a result, numerical approximations for performance measures such as the throughput of the system are extremely accu...

We consider an extension of the classical machine-repair model, also known as the computer-terminal model or time-sharing model. As opposed to the classical model, we assume that the machines, apart from receiving service from the repairman, supply service themselves to queues of products. The extended model can be viewed as a two-layered queueing...

We study a network of parallel single-server queues, where the service speeds are governed by a continuous-time Markov chain. This generic model finds applications in many areas such as communication systems, computer systems and manufacturing systems. We obtain heavy-traffic approximations for the joint workload, delay and queue length processes b...

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. Motivated by statistical analysis, we assume that the claim sizes are a mixture of a phase-type and a...

In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload distribution of the MAP/G/1 queue that capture the tail behavior of the exact workload distribution and provide a small...

We consider a system consisting of a server serving in sequence a fixed number of stations. At each station there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queuing networks, to an extension of polling systems, and surprisingly to random graphs. We are intereste...

We present analytic results for warehouse systems involving pairs of carousels. Specifically, for various picking strategies, we show that the sojourn time of the picker satisfies an integral equation that is a contraction mapping. As a result, numerical approximations for performance measures such as the throughput of the system are extremely accu...

We consider a system consisting of a server serving in sequence a fixed number of stations. At each station there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queuing networks, to an extension of polling systems, and surprisingly to random graphs. We are intereste...

We consider an extension of the classical machine-repair model. As opposed to the classical model, we assume that the machines, apart from receiving service from the repairman, also supply service themselves to queues of products. The extended model can be viewed as a layered queueing network (LQN), where the first layer consists of two separate qu...

We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the environment $i$ equals 0 or 1. When the exponential clock $e_q^{(i)}$ ends, the workload, as well as the L\'evy input pr...

We investigate a computer network consisting of two layers occurring in, for example, application servers. The first layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network. At the second layer, active servers at these nodes act now as customers who are served by a common CPU. Our m...

This paper gives an overview of recent research on the performance evaluation and design of carousel systems. We discuss picking strategies for problems involving one carousel, consider the throughput of the system for problems involving two carousels, give an overview of related problems in this area and present an extensive literature review. Emp...

We investigate the tail behaviour of the steady-state distribution of a stochastic recursion that generalises Lindley's recursion. This recursion arises in queueing systems with dependent interarrival and service times, and includes alternating service systems and carousel storage systems as special cases. We obtain precise tail asymptotics in thre...

We discuss a single-server multi-station alternating queue where the preparation times and the service times are auto- and cross-correlated. We examine two cases. In the first case, preparation and service times depend on a common discrete time Markov chain. In the second case, we assume that the service times depend on the previous preparation tim...

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers according to a spectrally positive Lévy process Y(t) which is reflected at 0. When the exponential clock ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to at epoch for some random nonnegati...

We discuss a single-server multi-station alternating queue where the preparation times and the service times are auto- and cross-correlated. We examine two cases. In the first case, preparation and service times depend on a common discrete time Markov chain. In the second case, we assume that the service times depend on the previous preparation tim...

We investigate the tail behaviour of the steady state distribution of a stochastic recursion that generalises Lindley's recursion. This recursion arises in queuing systems with dependent interarrival and service times, and includes alternating service systems and carousel storage systems as special cases. We obtain precise tail asymptotics in three...

We consider a polling system where a group of an infinite number of servers visits sequen- tially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and service time of each individual customer is drawn from a general probability distribution function. Thus, each of the queues c...

We consider an extension of the standard G/G/1 queue, described by the equation W= Dmaxmax{0,B-A+YW}W\stackrel{ \mathcal {D}}{=}\max\mathrm{max}\,\{0,B-A+YW\} , where ℙ[Y=1]=p and ℙ[Y=−1]=1−p. For p=1 this model reduces to the classical Lindley equation for the waiting time in the G/G/1 queue, whereas for p=0 it describes the waiting time of the s...

In this paper we study the Lindley-type equation W=max {0,B−A−W}. Its main characteristic is that it is a non-increasing monotone function in its main argument W. Our main goal is to derive a closed-form expression of the steady-state distribution of W. In general this is not possible, so we shall state a sufficient condition that allows us to do s...

We derive the limiting waiting-time distribution FWFW of a model described by the Lindley-type equation W=max{0,B-A-W}W=max{0,B-A-W}, where B has a polynomial distribution. This exact solution is applied to derive approximations of FWFW when B is generally distributed on a finite support. We provide error bounds for these approximations.

We derive the limiting waiting-time distribution FW of a model described by the Lindley-type equation W = max{0,B A W}, where B has a polynomial distribution. This exact solution is applied to derive approximations of FW when B is generally distributed on a finite support. We provide error bounds for these approximations.

We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit expressions for its time-dependent waiting-time distribution, the correlation between waiting times, and the dist...

Thesis (doctoral)--Technische Universiteit Eindhoven, 2006. Includes bibliographical references (p. 173-186).

We consider a system consisting of a server alternating between two service points. At both service points, there is an infinite queue of customers that have to undergo a preparation phase before being served. We are interested in the waiting time of the server. The waiting time of the server satisfies an equation very similar to Lindley's equa...

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the...

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the...

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly,located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Impor- tant performance characteristics are the waiting time of the picker and th...