Niek Baër
University of Twente
N.Baer@utwente.nl

Supervisor
Richard Boucherie

Title The PH/PH/1 multi-threshold queue
Abstract We consider a single server queue with infinite capacity in which service times and inter-arrival times are controlled by a threshold policy. This threshold policy will change the stage of the system once a particular queue length is reached. For each stage s the interarrival times are distributed and the service times are distributed. We model this queue as a Level Dependent Quasi-Birth-and-Death process and introduce a decomposition method to obtain the stationary queue length distribution.

Herman Blok
Leiden University
blokh1@math.leidenuniv.nl

Supervisor
Flora Spieksma

Title A generalized mu-c rule for the K-competing queues model with customer impatience
Abstract We consider a K-competing queues model with additional customer impatience. Our goal is to minimize the average holding costs. Without customer impatience it is well-known that it is optimal to allocate the server to a queue according to the mu-c rule. The mu-c rule gives priority to the highest cost reduction per unit time. With the additional feature of customer abondonments, the mu-c rule is not always optimal.

This system can be modelled as a Markov decision process, but it cannot be solved with the standard techniques. The customer abandonments impose unbounded jump rates and therefore we cannot apply uniformization. So far there has been no systematic way to analyse Markov decision processes with unbounded jump rates.

We developed a technique called Smoothed Rate Truncation, which enables us to analyze this system. We find a generalization of the mu-c rule. This generalized mu-c rule consists of three conditions, including the mu-c ratio and the recently introduced mu-c/beta ratio. If all conditions are satisfied, following this rule guarantees average optimality.

Harm Bossers
University of Twente
H.C.M.Bossers@utwente.nl

Supervisor
Johann Hurink, Gerard Smit

Title Integer Linear Programming approach for Selecting Tests for Outlier Detection in Testing of Integrated Circuits
Abstract Integrated circuits are tested thoroughly in order to meet the very high demands on quality. As an additional step, outlier detection is used to detect potential unreliable chips such that quality can be improved further. However, it is often unclear to which tests outlier detection should be applied and how the parameters must be set, such that outliers are detected and yield loss remains limited. In this paper we introduce an Integer Linear Programming model, that given a set of target devices, can select tests for outlier detection and set the parameters for each outlier detection method. We provide results on real world data and analyze the resulting yield loss and missed targets.

Aleida Braaksma
Academic Medical Center & University of Twente
A.Braaksma@utwente.nl

Supervisor
Richard Boucherie, Piet Bakker, Nikky Kortbeek

Title Integral resource capacity planning for inpatient care services
Abstract Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues, such as case mix, care unit partitioning and size, and staffing decisions. The inpatient care facility is a downstream department of which the workload is mainly determined by the patient outflow of the operating theater and the emergency department. Predicting this workload and staffing nurses accordingly, is essential for guaranteeing quality of care in a cost effective manner.

First, we present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule (MSS) and arrival patterns of emergency patients. Second, we introduce a stochastic method that uses these hourly census predictions to derive efficient nurse staffing policies. In particular, we explore the potential of flexible staffing policies which allow hospitals to dynamically respond to their fluctuating patient population by employing float nurses.

The methods are applied to a case study of the surgical inpatient clinic of the Academic Medical Center (AMC) Amsterdam. This case study demonstrates the methods' potential to study the complex interaction between staffing requirements and several interrelated planning issues. Inspired by the numerical results, the AMC decided that the methodologies will be incorporated in the redesign of the inpatient care operations during the upcoming years.

Martijn van Brink
Maastricht University
m.vanbrink@maastrichtuniversity.nl

Supervisor
Alexander Grigoriev, Tjark Vredeveld

Title Express Package Delivery Problem
Abstract We consider a capacitated, fixed-charge, multicommodity flow problem with indivisible commodities. The commodities are transported with trucks, which all have the same capacity, and we assume there is an unlimited number of trucks. Two or more commodities that are transported over the same connection may share one or more trucks to save cost. However, this is only possible when these commodities traverse the connection at the same time. Therefore, timing plays an important role in this problem. First, we assume that each commodity needs to be delivered within a specified amount of time. In this case, we show that the problem is already NP-hard if we restrict the underlying network to a path. Second, we assume that for each commodity we have an unlimited amount of time available. We show that, unless P=NP, there cannot exist a polynomial time O(log K)- approximation algorithm, where K is the number of commodities. Applying LP-based randomized rounding, we obtain an approximation ratio of K+1, and we show that this ratio is tight. Next, we restrict the underlying network to cycles. We prove that the problem remains NP-hard and we develop a 6-approximation. Finally, we consider some computational results when the underlying network is restricted to cycles.

Kamiel Cornelissen
University of Twente
k.cornelissen@utwente.nl

Supervisor
Bodo Manthey

Title Smoothed Analysis of Belief Propagation for Minimum-Cost Flow and Matching
Abstract Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has applications in many areas, including machine learning, image processing, and computer vision. However, the theoretical understanding of the performance of BP is unsatisfactory. Recently, BP has been applied to combinatorial optimization

problems. It has been proved that BP can be used to compute maximum-weight matchings and minimum-cost flows for instances with a unique optimum. The number of iterations needed for this is pseudo-polynomial and hence BP is not efficient in general.

We study belief propagation in the framework of smoothed analysis and prove that with high probability the number of iterations needed to compute maximum-weight matchings and minimum-cost flows is bounded by a polynomial if the weights/costs of the edges are randomly perturbed. To prove our upper bounds, we use an isolation lemma by Beier and Vöcking (SIAM J. Comput., 2006) for matching and generalize an isolation lemma for min-cost flow by Gamarnik, Shah, and Wei (Oper. Res., 2012). We also prove almost matching lower tail bounds for the number of iterations that BP needs to converge.

Gergely Csapo
Maastricht University
g.csapo@maastrichtuniversity.nl

Supervisor
Rudolf Müller

Title Optimal mechanism design for the private supply of a public good
Abstract We study the problem of finding the profit-maximizing mechanism for a monopolistic provider of a single, non-excludable public good. This problem has been well studied for the case when agents' types are independently distributed, but the literature is almost silent about the case of general joint distributions.  We investigate the problem from an automated mechanism design perspective, meaning that we want to understand the algorithmic complexity of finding the optimal mechanism when we are given a finite set of type profiles and their distribution.

We show that the optimal deterministic, dominant strategy incentive compatible, ex-post individual rational mechanism can be computed in polynomial time by reducing the problem to finding a maximal weight closure in a directed graph. Node weights in the graph correspond to conditional virtual values. When valuations are independently distributed, the constructed mechanism is also optimal among all Bayes-Nash implementable and ex-interim individual rational mechanisms. In contrast, for dependent valuations strictly higher profit can be achieved if one allows for ex-interim individual rationality. By invoking techniques due to Cr{\'e}mer and McLean, we show that optimal deterministic, ex-interim individual rational, Bayes-Nash implementable or dominant strategy implementable mechanisms still can be found in polynomial time if the joint distribution of types satisfies certain regularity conditions.

Sihan Ding
CWI
S.Ding@cwi.nl

Supervisor
Rob van der Mei, Ger Koole

Title Estimation of retrial probabilities in call center data with incomplete information
Abstract This paper models an inbound call center as a multi-server queue with abandonments, redials (call backs after abandonment) and reconnects (call backs after being answered). We propose a model to estimate the redial or reconnect probabilities using call center data without customer identity information. We formulate this model as a minimization problem, where the minimum value is attained for the actual redial and reconnect probabilities.

We validate this estimation method using generated by discrete-event simulation, as by real call center data. We find out that our estimation of the redial probability is close to the real redial probability.

Jan-Pieter Dorsman
Eindhoven University of Technology
j.l.dorsman@tue.nl

Supervisor
Onno Boxma, Rob van der Mei, Maria Vlasiou

Title Evaluation and optimisation of an extended machine-repair model
Abstract In the classical machine-repair model, a machine subject to breakdowns typically faces competition for repair facilities with other machines. This leads to dependencies in their downtimes. What is oftentimes ignored in the MR-model is that the machines make products themselves. Due to the interdependency of the downtimes of the machines, caused by the fact that the machines share the same repairman, the queue lengths of the products in front of the machines are correlated. Therefore, the distribution of these queue lengths is hard to compute. In this presentation, we discuss methods for evaluating and optimising the queues of products in this model. In particular, we have a glance at how to derive approximate closed-form expressions, we provide a numerical algorithm to compute the exact distribution, we consider the optimal allocation of the repairman, and we discuss structural properties such as the behaviour of the system in heavy traffic.

Wendy Ellens
TNO
wendy.ellens@tno.nl

Supervisor
Michel Mandjes, Hans van den Berg

Title Statistical methods for anomaly detecttion
Abstract Anomaly detection is about the automatic detection of anomalies (irregularities) in big data sets. In applications, anomalies may correspond to system errors, service disruptions, hardware failures, fraud, changing behaviour, etc.
The problem under consideration is called the changepoint detection problem. A changepoint in a time series is the moment at which the underlying probability distribution changes. We are looking for methods that detect such a changepoint as soon as possible, while at the same time limiting the probability of a false alarm. The difficulty lies in the fact that outliers can be caused by statistical deviation or the underlying distribution may have changed.

Yuan Feng
University of Twente
Y.Feng@utwente.nl

Supervisor
Theo Driessen

Title A matrix approach to associated consistency of the generalized Shapley value
Abstract The talk is devoted to the Shapley value for cooperative games in generalized characteristic function form in which the players of coalitions are supposed to be ordered. An axiomatization of the generalized Shapley value is presented in terms of three properties, namely continuity, associated consistency, and inessential game property. The proof technique is based on fundamental matrix representations and the Diagonal Theorem for matrices. The rank, eigenvalues and eigenvectors for a certain representation matrix are treated to guarantee the application of the diagonalization.

Maria Frolkova
CWI
M.Frolkova@cwi.nl

Supervisor
Bert Zwart, Sergey Foss

Title Random fluid limit of an overloaded poling model
Abstract For many basic queueing systems, fluid limits are deterministic functions. In this work, we study a cyclic polling model under conditions that lead to a random fluid limit. These conditions are zero initial state and overload. We allow a wide class of service disciplines that guarantee the connection with branching processes. Exploiting this connection, we obtain a precise description of the fluid limit. Additionally, we suggest a method that establishes finiteness of moments of the busy period in an $M/G/1$ queue.

Jelmer van der Gaast
Erasmus University Rotterdam
jgaast@rsm.nl

Supervisor
Rene de Koster en Ivo Adan

Title Modeling and performance analysis of sequential zone picking systems
Abstract Sequential zone picking systems belong to the most popular internal transport and order picking systems in practice, due to their scalability, flexibility, high-throughput ability, and fit-for-use for a wide range of products and order profiles. The major disadvantage of such systems, though, is congestion and blocking under heavy use, leading to long order lead times. In order to diminish blocking and congestion most systems make use of a dynamic block-and-recirculate protocol. The various elements of the system, like conveyor lanes and the pick zones, are modeled as a network of queues with multiple order classes and with capacity constraints on subnetworks, including the dynamic block-and-recirculate protocol. Due to this protocol, however, the stationary distribution of the queueing network is highly intractable. Therefore, an innovative approximation method, using jump-over blocking is proposed to accurately assess key performance statistics such as throughput and recirculation. Multi-class jump-over networks admit a product-form stationary distribution, and can be efficiently evaluated by Mean Value Analysis (MVA) and use of Norton's theorem. The method is most suitable to support rapid and optimal design of complex zone picking systems, in terms of number of segments, number and length of zones, buffer capacities, and storage allocation of products to zones, in order to meet prespecified performance targets.

Bram Gorissen
Tilburg University
b.l.gorissen@tilburguniversity.edu

Supervisor
Dick den Hertog

Title A new method for deriving robust solutions of uncertain linear conic optimization problems having general convex uncertainty sets

Abstract We propose a new way to derive the tractable robust counterpart of a linear conic optimization problem.
For the dual of a robust optimization problem, it is known that the uncertain parameters of the primal problem become optimization variables in the dual problem ("primal worst is dual best''). We give a convex reformulation of the dual problem of a robust linear conic program. When this problem is bounded and satisfies the Slater condition, strong duality holds. We show how to construct the primal optimal solution from the dual optimal solution. Our result allows many new uncertainty regions to be considered that were previously intractable, e.g., the set of steady state probability vectors of a Markov chain with uncertain transition probabilities, or the set of vectors whose Bregman or phi-divergence distance to a given vector is restricted. Our result also makes it easy to construct the robust counterpart for intersections of uncertainty regions. The description of the uncertainty region is in the constraints of the dual optimization problem, so using intersections of uncertainty regions is as simple as adding constraints for all uncertainty regions involved. The results are illustrated by solving a multi-item newsvendor problem. We also propose a new globalized robust counterpart that is more flexible, and is tractable for general convex uncertainty sets and any convex distance function.

Ruben Hoeksma
University of Twente
r.p.hoeksma@utwente.nl

Supervisor
Marc Uetz

Title Two-Dimensional Optimal Mechanism Design for a Sequencing Problem
Abstract The design of optimal auctions is recognized as an intriguing issue in auction theory; first studied by Myerson (1981) for the case of single item auctions. In that setting, the goal is to maximize the seller's revenue. We study the design of optimal auctions (more precisely, mechanisms) in a setting where job-agents compete for being processed on a single machine that can only handle one job at a time. Each job has a service time and a weight representing the disutility for waiting. In this setting, it is folklore that the total disutility of the jobs is minimized by Smith's rule: schedule jobs in order of non-increasing ratios weight over service time.

We consider a setting for which the jobs' processing requirements as well as unit costs for waiting are private data. Given public priors for this private data, we seek to find an optimal mechanism, that is, a scheduling rule and incentive compatible payments that minimize the total expected payments to the jobs. Here, incentive compatible refers to a Bayes-Nash equilibrium.

While the problem can be efficiently solved when jobs have single dimensional private data along the lines of the seminal paper by Myerson, we here address the problem with two dimensional private data. We show that the problem can be solved in polynomial time by linear programming techniques. Our implementation is randomized and truthful in expectation. The main steps are a compactification of an exponential size linear program, and a combinatorial algorithm to compute from feasible interim schedules a convex combination of at most n deterministic schedules. In addition, in computational experiments with random instances, we generate some more theoretical insights.

Evelien van der Hurk
Erasmus University Rotterdam
EHurk@rsm.nl

Supervisor
Leo Kroon, Peter Vervest

Title Analyzing and forecasting passenger flow change due to major disruptions in public transport
Abstract Disruptions in public transport are at the center of attention in the winter season in the Netherlands. Though a large body of research exists on improving the logistic scheduling in case of a disruption, not much attention has been paid to how disruptions affect passengers. In this research we aim to provide insight into how passenger flows are affected by a major disruption and try to estimate the caused change in passenger flows.

We present a network reduction technique based on the change in paths of passengers due to the disruption. Thanks to detailed data like smart card data, the result of the network reduction can be used to derive forecasts of the number of passengers affected by a disruption. This leads to estimates of the change in demand over time and per train given the behavior of passengers. These forecasts form essential information for improving passenger service level in disruption management.

Presented results are based on a case study using real life smart card data of the Netherlands Railways (NS).

Frank Karsten
Eindhoven University of Technology
F.J.P.Karsten@tue.nl

Supervisor
Marco Slikker and Geert-Jan van Houtum

Title Resource pooling and cost allocation among independent service providers
Abstract We consider a number of independent service providers who may pool their resources and customer streams into a joint service system for efficiency. These service providers may represent such diverse organizations as hospitals that pool beds or maintenance firms that pool repairmen. We model the service systems as Erlang delay systems (M/M/s queues) that face a fixed cost rate per server and homogeneous delay costs for waiting customers. Our key result is that participants can allocate the total costs of their pooled system amongst themselves in a stable way. That is, the corresponding cooperative game has a non-empty core. In the process of proving this, we derive new structural properties of a continuous extension of the classic Erlang delay function.

Bart de Keijzer
CWI
B.de.Keijzer@cwi.nl

Supervisor
Guido Schaefer

Title Housing Markets with Indifferences: A Tale of Two Mechanisms
Abstract The (Shapley-Scarf) housing market is a well-studied and fundamental model of an exchange economy. Each agent owns a single house and the goal is to reallocate the houses to the agents in a mutually beneficial and stable manner. Recently, Alcalde-Unzu and Molis [2011] and Jaramillo and Manjunath [2011] independently examined housing markets in which agents can express indifferences among houses. They proposed two important families of mechanisms, known as TTAS and TCR respectively. We formulate a family of mechanisms which not only includes TTAS and TCR but also satisfies many desirable properties of both families. As a corollary, we show that TCR mechanisms satisfies the desirable property of strict core selectingness (in case the strict core is non-empty). Finally, we settle negatively the open question whether the TTAS mechanism runs in polynomial time. This is joint work with Haris Aziz.

Mihaela Mitici
University of Twente
m.a.mitici@utwente.nl

Supervisor
Richard Boucherie, Maurits de Graaf

Title A Quality of Service Optimal Query Assignment Strategy for Wireless Sensor Networks
Abstract The added computing capabilities of modern sensors have enabled Wireless

Sensor Networks(WSN) to become an integrated platform, where local processing is possible. Consequently, the WSN is able not only to communicate the measurements to the Database(DB )for storage, but also to respond to queries with sensed data.

A challenge of the WSN seen as an integrated platform involves meeting Quality of Service(QoS) requirements such as response time, scalability, data freshness. A balance between QoS requirements is difficult to achieve, especially in the case of conflicting requirements. This gives rise to new types of models that trade-off between QoS requirements.

This paper addresses the trade-off between query waiting time and data freshness. If all queries are assigned to the WSN, they receive recently sensed data. Hence, data freshness requirements are met. But their waiting time increases as more queries are send to the WSN. The alternative is to assign the queries to the DB. They are immediately answered with stored data, which might be outdated. In this case, waiting time is minimized, but the data freshness requirement is not met. We are interested in finding query assignment policies that address the trade-o_ between the two QoS requirements in a scalable and cost-efficient way.

We propose a model in which a central query controller assigns incoming queries either to the WSN or to the Database (DB) such that the data freshness requirement is met against minimal waiting time. We use stochastic dynamic programming to derive an optimal query assignment policy.

Firstly, we analyze how different tolerance thresholds for data freshness impact the query assignment policies. Secondly, we compare our MDP-based assignment strategy with an heuristic, currently used in practice. Simulation results show that our proposed model outperforms the heuristic in terms of average assignment costs and DB utilization.

Judith Mulder
Erasmus University Rotterdam
mulder@ese.eur.nl

Supervisor
Rommert Dekker

Title Designing robust liner shipping schedules: Optimizing recovery actions and buffer times
Abstract In liner shipping ships follow a fixed route within a fixed time schedule. Additional costs are incurred when ships are delayed. Delay can be handled in two different ways: prevention and recovery. To prevent ships to incur delay, buffer times can be added to the schedule. The buffer time will then be used to capture (a part of) the obtained delay. However, ships that arrive on time have to wait until their scheduled departure time before they can leave the port. On the other hand, ships can perform recovery actions, such as increasing the sailing speed, to reduce the amount of delay. The objective of this research is to determine a recovery policy that minimizes the costs associated to delays and recovery actions for a given liner shipping route with variable buffer times. When the buffer times are fixed, the problem can be formulated as a Markov decision process. However, when we allow the buffer times to be variable, the Markov property is violated. Therefore, we adjust the formulation for the variable buffer times and propose heuristics to solve the problem. We compare the solutions of our heuristics to the optimal solutions.

Xian Qiu
University of Twente
X.Qiu@utwente.nl

Supervisor
Walter Kern, Marc Uetz

Title Fractional programming in cooperative games
Abstract We study the integrality gap of certain kinds of 0-1 integer program under the framework of cooperative games. In particular, we consider bin packing games of the following kind: The player set N consists of k bins of capacities b_1,...,b_k, and n items of sizes a_1,...,a_n. The value of a coalition which contains bins and items is the maximum size of items of the coalition that can be packed to the bins of the coalition. The total value of N can be regarded as the total earning of all players. The usual goal in cooperative games is how to 'fairly' allocate total earnings among all players. However, a fair allocation may not always exist. We investigate the approximate allocation for bin packing games.

Daniël Reijsbergen
University of Twente
D.P.Reijsbergen@utwente.nl

Supervisor
Werner Scheinhardt

Title Automated Rare Event Simulation for Stochastic Petri Nets
Abstract We introduce an automated approach for applying rare event simulation to stochastic Petri net models of highly reliable Markovian systems. Rare event simulation can be much faster than standard simulation because it is able to exploit information about the typical behaviour of the system. Previously, such information came from heuristics, human insight, or analysis on the full state space. We present a formal algorithm that obtains the required information from the high-level description as a stochastic Petri net, without generating the full state space. Essentially, our algorithm reduces the state space of the model into a (much smaller) graph in which each node represents a set of states for which the most likely path to failure has the same form. We empirically demonstrate the efficiency of the method in two case studies.

Ward Romeijnders
University of Groningen
w.romeijnders@rug.nl

Supervisor
M.H. van der Vlerk, W.K. Klein Haneveld

Title On the Performance of a Class of Convex Approximations for Integer Recourse Models
Abstract We consider the performance of the convex approximations introduced by Van der Vlerk (2004) for the class of integer recourse problems with totally unimodular (TU) recourse matrices. We show that the main theorem in Van der Vlerk (2004) needs stronger assumptions. As a result, a performance guarantee for the convex approximations is lacking in general. In order to obtain such a performance guarantee, we first analyze the approximations for simple integer recourse models. Using a new approach we improve the existing error bound for these models by a factor 2. We use insights from this analysis to obtain an error bound for complete integer recourse problems with TU recourse matrices. This error bound ensures that the performance of the approximations is good as long as the dispersion of the random variables in the model is large enough.

Laurens Smit
Leiden University
laurens@pipe.nl

Supervisor
Floske Spieksma

Title The Class of Quasi--‐Skip Free Processes: Stability and Explicit Solutions when Successively Lumpable
Abstract We consider the class of Quasi-skip-free (QSF) processes, a generalization of the quasi-birth-and-death (QBD) processes. They are Markov processes with states that can be specified by tuples of the form (m,i) where m represents the 'current' level of the state. In addition, their probability state transition law does not permit transitions to a state in a level two or more units away from the current state's level in one direction. Such processes have applications in many areas of applied probability including queuing theory, reliability, computer science and the theory of branching processes. 

We discuss stability conditions for QSF processes and provide a simple condition under which a QSF process is successively lumpable (SL-QSF). We use this successive lumpability property to derive explicit solutions and bounds for the steady state probabilities of general state space SL-QSFs, and to obtain a number of simplified derivations for results that are much more difficult to establish otherwise. Finally, we present explicit solutions for the well known PH/M/n and M/PH/n queues, which are both SL-QSFs.

Maximiliano Udenino
Eindhoven University of Technology
M.Udenio@tue.nl

Supervisor
Jan C. Fransoo, Nico Dellaert

Title An analysis of the effect of response speed on the Bullwhip effect using control theory
Abstract In this paper, we use linear control theory to analyze the performance of a firm operating under a generalized APIOBPCS decision support system (a variant of the order-up-to rule): such a firm will generate material orders as a function of the difference between actual inventories and their specific targets (with independent controllers for on-hand, and pipeline inventories). We contribute to the existing literature by explicitly modeling managerial behavior: we allow fractional -instead of full- adjustments to be performed in each period, thus introducing a proxy to the firms' reactiveness to changes.
We show that when these behavioral factors are taken into account, supply chain stability can no longer be guaranteed. Furthermore, we show that the necessary conditions for stability in such a system depend not only on the behavioral parameters, but also on the procurement lead times. Following this, we quantify the performance of the system by analyzing the effect of different demand signals on order and inventory variations. In particular, we study the transient response to a step change in demand; the magnitude of amplification under cyclical demands; and the steady-state performance as measured by the ratio of stationary order and demand variances (bullwhip measure).
Finally, we illustrate the practical importance of this research by positioning available empirical, and experimental, data in the context of this research, and the consequent managerial insights. 

Eleni Vatamidou
Eindhoven University of Technology
e.vatamidou@tue.nl

Supervisor
Ivo Adan, Maria Vlasiou, Bert Zwart

Title Improved approximations for the M/G/1 queue
Abstract Great attention is given in evaluating numerically the waiting time distribution of an M/G/1 or a G/G/1 queue. An important method is by approximating the service times with a phase-type distribution, which provides very accurate approximations for the waiting time distribution when the service times originate from light-tailed distributions. However, in the presence of heavy-tailed service times the phase-type approximations are incapable of capturing the tail behavior of the exact waiting time distribution. In this presentation, supported by statistical analysis, we assume that the service times are a mixture of a phase-type and a heavy-tailed distribution. Using this mixture model, we derive a complete series expansion for the waiting time distribution. We prove that the first two terms of the power series constitute an approximation that captures the heavy-tailed behavior of the exact waiting time distribution and gives a small relative error. For this approximation, we also provide error bounds. Finally, in a mixture model for which the waiting time distribution can be found explicitly, we compare our approximation with the exact results.

Maartje van de Vrugt
University of Twente
N.M.vandeVrugt@utwente.nl

Supervisor
Richard Boucherie

Title Blocking probabilities in Erlang loss queues with advance reservation
Abstract We consider an Erlang loss queue in which resources can be claimed a random time in advance. For a special deterministic case, we derive the stationary distribution of this model. Our analytical and numerical results indicate that advance reservation can both increase and decrease blocking probabilities.

Qiushi Zhu
Eindhoven University of Technology
Q.Zhu@tue.nl

Supervisor
G. van Houtum

Title A condition-based maintenance policy for mult-component systems with optimal control limits and maintenance intervals
Abstract Condition-based maintenance (CBM) is becoming increasingly important due to the development of advanced sensor technology. We propose a new CBM policy for multi-component systems with stochastic and continuous deteriorations. To reduce the setup cost of maintenance actions, we propose a joint maintenance interval in the mathematical model. The optimal maintenance control limits of all the degrading components in a system and the optimal joint maintenance interval are determined by minimizing the average long-run cost rate related to maintenance and downtime. In order to optimize the maintenance policy for a system with large amounts of component, we develop a model to decompose the system optimization to individual component level firstly and optimize the system on aggregate level. Moreover, a numerical study with a case of wind farm maintenance is performed based on the data and parameters from literature. At last, our policy is evaluated in comparison with a 'corrective-maintenance-only' policy.