Abstracts presentations phd students
BOEF, EDGAR DEN
Philips Research Laboratories &
Eindhoven University of Technology
Prof. Holstlaan 4
5656 AA Eindhoven
denboef@natlab.research.philips.com
Supervisor
Aarts
Title
Optimal bus and buffer allocation for a set of
leaky-bucket-controlled streams
Abstract
In an in-home digital network (IHDN) it may be expected that several
variable-bit-rate streams (audio, video) run simultaneously over a
shared communication device, e.g. a bus. In this presentation we
consider a single bus to which several buffers are connected. A set of
variable-bit-rate streams is given, where each stream runs over the bus
between two of the connected buffers. Each stream is controlled by one
or more leaky buckets. This implies that the supply of data of a stream
is bounded by a piecewise-linear, concave function f. We show how
allocations of the bus capacity and the buffer sizes can be obtained
for all streams, such that for each stream a feasible transmission
strategy exists.
First, we model the problem as a linear program (LP). Then we show that
to obtain a feasible solution to the problem, we may take the function
f of a stream as its actual supply function. We briefly describe how
the Dantzig-Wolfe decomposition can be applied to the LP. This leads to
a master LP and several single-stream problems that need to be solved
repeatedly. For these single-stream problems we derive four constraints
that do not involve the transmission strategy. We show that these
constraints are sufficient for any feasible solution of the
single-stream problems. Using these four constraints, we can obtain
optimal solutions to the single-stream problems efficiently.
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BOER, CSABA
Faculty of Economics
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
acboer@few.eur.nl
Supervisors
De Bruin / Verbraeck / de Swaan Arons
Title
Distributed e-services for road container transport simulation
Abstract
This paper describes a recently carried out project that aims to
improve the handling process of trucks at new container terminals. One
of the difficulties that terminals are faced with is the handling of
the truck arrivals. The current situation sometimes results in large
number of trucks waiting in excessively long queues, as they arrive
more frequently than they are served. This situation especially arises
in peak hours and in particular days when the number of trucks
drastically increases. Due to the limited number of serving cranes and
the limited capacity of parking places these trucks are confronted with
delays and a costly situation.
In order to find out how to avoid the difficulties enumerated and to
improve the effectiveness of complex systems, simulation models are
developed. Monolithic complex simulation models of terminals already
exist, but as they provide a simplified truck arrival generator, do not
take into account several aspects, such as negotiation with the truck
companies or delays during the driving process, that might influence
the arrival frequency of the trucks at the container terminal. In this
paper we introduce a distributed model that aims to improve the
handling process of trucks at container terminals by integrating
several different models. This integration enables to consider several
additional aspects that were ignored by the monolithic approach. We
develop a real planning system for scheduling the arriving time of the
trucks at the terminal. The new planning system requires the truck
companies to register the trucks at the terminal administration before
delivering or picking up a container. The terminal administration
together with the administration of the truck companies negotiate an
arrival time that is acceptable for both sides. We deal with two main
problems: negotiation from both sides and the interoperability of the
systems of the negotiating parties.
The distributed modelling approach allows for the integration of
several independent models coming from different background
disciplines. Different participants (organizations) can individually
develop their own model without sharing their business logic. In this
way the internal information in the models can remain hidden for the
other partners as they only share the relevant information for the
interoperability process. Further, the distributed approach allows for
reusability and parallel work.
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BUDAI, GABRIELLA
Department of Econometrics
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
budai@few.eur.nl
Supervisor
Dekker
Title
A dynamic approach for planning preventive railway maintenance
activities
Abstract
Statistics have shown that the demand for railway transport has
increased considerably in the last few years. In order to satisfy the
demand, there is a need especially for a high quality and modern
railway infrastructure, for reliable service, for more trains per hour,
for railway safety and improved punctuality. However, increasing the
number of trains (and their speed) leads to an increase of
deterioration of infrastructure. Hence, more intensive maintenance and
renewal works are needed. This means that the infrastructure possession
time for these maintenance activities will increase as well. Therefore,
it is more and more difficult to find an optimal timetable for those
possession intervals in such of way that it does not cause severe
disruptions of the railway traffic.
The purpose of this paper is to provide some useful methods for finding
optimal track possession intervals for carrying out preventive
maintenance works. The maintenance schedule is made in such a way that
the inconvenience for the train operators, the disruption to and from
the scheduled trains and the infrastructure possession time for
maintenance is minimized. The maintenance activities are performed as
much as possible in train free periods or in hours with less impact to
the operators and the number of hours required for these works is
minimized, by clustering as much as possible the preventive maintenance
activities. Our approach takes also into consideration the situation
when these train free periods are not long enough for carrying out the
track maintenance works. This is the case if longer projects have to be
performed. Since it is not always possible to interrupt the maintenance
work by letting some trains to pass by, train cancellation is needed or
one has to arrange alternative transport, e.g. using buses. In this
paper we are focusing on the infrastructure maintenance, excluding the
rolling stock from our research area.
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CHAERANI, DIAH
Optimization Technology Group
Department of Information System and Algorithm
Faculty of Electrical Engineering, Mathematics and Computer Science
Delft University of Technology
Mekelweg 4
2628 CD Delft
d.chaerani@ewi.tudelft.nl
Supervisor
Roos
Title
The robust shortest path with ellipsoidal uncertainty set
Motivated by some recent papers on the robust shortest path problem, with box uncertainty sets (see Karasan et al [1], Bertsimas et al [2], [3], and Montemanni et al [4]), in this paper we investigate the robust shortest path problem with ellipsoidal uncertainty set as proposed by Ben-Tal and Nemirovski (see [5]). With this approach, the robust counterpart of the shortest path problem can be modelled as a conic quadratic optimization problem. As our model, like the Karasan model, contains binary variables, we use a branch and bound scheme to solve the model. We present some examples and compare the robust paths obtained from the Karasan model and our model, respectively.
References
[1] O.E. Karasan, M.C. Pinar and H.Yaman: The Robust Shortest Path Problem with Interval Data, Optimization Online, 2001.
[2] D. Bertsimas and M. Sim: Robust Discrete Optimization and Network Flows, Mathematical Programming (to appear}.
[3] D. Bertsimas and M. Sim: Price of Robustness, Operations Research (to appear}.
[4] R. Montemanni, L.M. Gambardella and A.V. Donati: A branch and bound algorithm for the robust shortest path problem with interval data, Operations Research Letters (to appear).
[5] A. Ben-Tal and A. Nemirovski: Robust optimization - methodology and applications, Mathematical Programming 92 (2002) 453 - 480.
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CHEUNG, SING KONG
Stochastic Operations Reserarch Group
Department of Applied Mathematics
University of Twente
P.O. Box 217
7500 AE Enschede
s.k.cheung@utwente.nl
Supervisors
Boucherie / van den Berg
Title
On the sojourn time distribution in the M/G/1 processor sharing queue
We consider the M/G/1 processor-sharing queue and the sojourn time as a classical performance measure. Determining the sojourn time distribution turned out be a very difficult problem. The distribution is known by several different complex expressions (in terms of contour integrals) of its Laplace-Stieltjes transforms. A relatively easy expression has been derived by Zwart and Boxma [1]. Using this result we derive new properties for the (conditional) sojourn time distribution. In particular, we are interested in all the moments of the sojourn time distribution and show that they can be bounded in special structure.
References
[1] Zwart, A.P. & Boxma, O.J.: Sojourn times aymptotics in the M/G/1 processor sharing queue, Queueing Systems 35 (2000) 141-166.
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CRUIJSSEN, FRANS
CentER Applied Research
Tilburg University
P.O. Box 90153
5000 LE Tilburg
frans.cruijssen@uvt.nl
Supervisor
Fleuren
Title
Order sharing in transportation
In this presentation we discuss the sharing of transportation order in single depot, homogeneous fleet routing environment. In the traditional situation, all transportation companies had their own clients and their own set of transportation orders. In a situation with order sharing, transportation companies mutually share their data on transportation orders. This gives them the opportunity to select transportation orders from a much larger set of orders than in the traditional situation. In this presentation we discuss the economic and other advantages of order sharing. Furthermore, we will point out the disadvantages of order sharing. The conclusions are based on both a simulation study and a real-life case. The simulation study shows that transportation costs may decrease by 5 to 15 percent and sometimes even more due to order sharing. The results can also be used as a proxy for the benefits of a merger between multiple transportation companies.
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DIEKER, TON
CWI
P.O. Box 94079
1090 GB Amsterdam
ton.dieker@cwi.nl
Supervisor
Mandjes
Title
On the buffer content and length of a busy period in a queue with
Gaussian input
We consider a buffered queueing system that is fed by a Gaussian source and drained at a constant rate. The system input is modeled by a Gaussian process with stationary increments and regularly varying variance function.
In the talk, we investigate how a high buffer level is achieved and how a long busy period occurs. We do this by presenting conditional limit theorems that result from a large deviation analysis. In addition, we establish logarithmic asymptotics for the probability that the buffer content exceeds u as u → ∞, and we find the logarithmic asymptotics for the probability that the length of the busy period exceeds T as T → ∞.
If time permits, we discuss some issues that arise when establishing exact asymptotics for the probability of a high buffer content.
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EL GHAMI, MOHAMED
Optimization Technology Group
Department of Information System and Algorithm
Faculty of Electrical Engineering, Mathematics and Computer Science
Delft University of Technology
Mekelweg 4
2628 CD Delft
m.elghami@ewi.tudelft.nl
Supervisor
Roos
Title
A new class of barrier functions for primal-dual interior-point
methods in linear optimization
Abstract
Recently, Peng, Roos, and Terlaky introduced so-called
self-regular barrier functions for primal-dual interior point
methods (IPMs) for linear optimization. Each such barrier function
is determined by its (univariate) self-regular kernel function. In
this paper we present a new class of barrier functions. The
proposed class is defined by some simple conditions on the kernel
function and its first three derivatives. In spite of this, the
best iteration bound of large-update interior-point methods based
on these functions is shown to be O([log
n][log n/ε]√n),
and for
small-update methods O([log n/ε]√n)
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ENDRAYANTO, IRWAN
Stochastic Operations Reserarch Group
Department of Applied Mathematics
University of Twente
P.O. Box 217
7500 AE Enschede
a.i.endrayanto@math.utwente.nl
Supervisor
Boucherie
Title
An analytical model for CDMA downlink rate optimization taking into
account uplink coverage restriction
Abstract
This paper models and analyzes downlink and uplink power assignment
in
Code Division Multiple Access (CDMA) mobile networks. By discretizing
the area into small segments, the power requirements are characterized
via a
matrix representation that separates user and system characteristics.
We
obtain a closed-form analytical expression of the so-called
Perron-Frobenius eigenvalue of
that matrix, which provides a quick assessment of the feasibility of
the power
assignment for each distribution of calls over the segments. Our
results allow for a fast
evaluation of outage and blocking probabilities. The result also
enables a quick
evaluation of feasibility that may be used for capacity allocation. Our
combined
downlink and uplink feasibility model is applied to determine maximal
system throughput in
terms of downlink rates.
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ESTÉVEZ -FERNÁNDEZ, M. ARÁNZAZU
Department of Econometrics and Operations Research
University of Tilburg
P. O. Box 90153
5000 LE Tilburg
a.e.frenandez@uvt.nl
Supervisors
Borm / Hamers
Title
On the core of multiple longest traveling salesman games
Abstract
In this paper we introduce multiple longest traveling salesman
(MLTS) games. An MLTS game arises from a
network in which a salesman has to visit each node (player) precisely
once, except its home location, in an order that maximizes the total
reward. First it is shown that the value of a coalition of an MLTS game
is determined by taking the maximum of suitable combinations
of one and two person coalitions. Secondly it is shown that MLTS games
with five or less players have a nonempty core. However, a six players
MLTS game may have an empty core. For the special instance where the
reward between a pair of nodes is equal to 0 or 1, we provide relations
between the structure of the core and the underlying network.
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HEUVEL, WILCO VAN DEN
Department of Econometrics
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
wvandenheuvel@few.eur.nl
Supervisor
Title
A polynomial time algorithm for a deterministic joint pricing and inventory model
Abstract
We consider the uncapacitated economic lot-size model, where demand is a deterministic function of price. In the model a single price need to be set for all periods. The objective is to find an optimal price and ordering decisions simultaneously. Kunreuther and Schrage (1973) proposed an heuristic algorithm to solve this problem. Our contribution is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Second, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time.
Reference:
Kunreuther, H. and L. Schrage: Joint pricing and inventory decisions for constant priced items, Management Science 19 (1973) 732–738.
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LE ANH, TUAN
Rotterdam School of Management
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
ltuan@fbk.eur.nl
Supervisor
De Koster
Title
Online dispatching rules for vehicle-based internal transport
systems
Abstract
On-line vehicles dispatching rules are widely used in many facilities
such as warehouses to control vehicles' movements. Single-attribute
dispatching rules, which dispatch vehicles based on only one parameter,
are used commonly. However, multi-attribute dispatching rules prove to
be better in general. In this study, we introduce new dispatching rules
and evaluate their performance compared to several good dispatching
rules in literature, using the experimental design of a real case
study.
The performance criteria are minimizing the average load waiting time
while keeping the maximum load waiting time as small as possible and
better utilize vehicles. The experiments show that newly introduced
hybrid dispatching rule yields the best performance overall
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LENNARTZ, PETER
Institute for Information and Computing Sciences
Utrecht University
Padualaan 14
3584 CH Utrecht
peterl@cs.uu.nl
Supervisor
Hoogeveen
Title
The relation between the no-wait job shop problem and the traveling
salesman problem
Abstract
We consider the No-Wait Job Shop Problem (JSP) which is defined
as follows. Given a number of jobs to execute we have to assign
starting times to the jobs (= finding a feasible schedule) such
that the point in time when the last job finishes its execution is as
soon as possible (that is to minimize the makespan). Here, a job
consists of a number of operations, which have to start a fixed amount
of time after the job starts (this amount of time may depend on the
operation, but is given in advance). Furthermore, each operation is to
be executed for an uninterrupted interval of specific length on a
specified machine.
In this talk we take a closer look at a subset of these JSP instances,
namely the ones where each pair of jobs do not intertwine - the so
called 2-compact job shops.
For an instance out of this subset we model a graph where the length
of an arc (u,v) is defined to be the minimal amount of time that is
needed to execute v after u. Here, we mean by `after' that the job
associated with $v$ is not scheduled before the one associated with
u.
We will see during the talk that if we have the triangle inequality in
this graph an optimal TSP tour gives us the optimal schedule. And we
will see what to do if the triangle inequality does not hold.
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MOONEN, LINDA
Catholic University of Leuven
Naamsestraat 69
B-3000 Leuven
Belgium
linda.moonen@econ.kuleuven.ac.be
Supervisor
Spieksma
Title
Partitioning a permutation graph: algorithms and an application
Abstract
We discuss the problem of partitioning a permutation graph into cliques
of bounded size. We describe a real-life application of this problem
encountered at a manufacturing company in the Netherlands and we
present two exact algorithms for solving this problem. The first
algorithm is a branch-and-price algorithm, based on an integer
programming formulation. The pricing problem can be formulated as a
longest path problem and can be solved efficiently by dynamic
programming. The second algorithm is an enumeration algorithm based on
the concept of bounded clique-width. This algorithm was motivated by a
special structure that is present in the real-life instances that were
used for computational experiments. Both algorithms are tested on a
number of real-life instances and randomly generated instances. From
the computational results we conclude that both the real-life and the
random instances can be solved satisfactorily by the branch-and-price
algorithm. The enumeration algorithm performs really well in case of
the real-life instances (99% of the instances are solved within a
second), but the random instances cannot be solved efficiently, due to
the large number of different lengths in the input. From these results
we also see that the LP-relaxation provides us with a good lower bound
on the integer optimum.
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NICOLAI, ROBIN
Department of Econometrics
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
rnicolai@few.eur.nl
Supervisor
Dekker
Title
Modelling the deterioration of high voltage poles: a comparison of
methods
Abstract
There are several thousands high voltage poles in the Netherlands. They
facilitate the transportation of electricity from the power plant to
companies and houses. To guarantee a continuous electricity supply the
poles have to be inspected and, when necessary, maintained. This paper
focuses on the deterioration process of the organic coating layer that
protects the steel structure from corrosion. Only if there is
sufficient knowledge of the condition of the coating on the poles,
maintenance actions can be done in the most efficient way. Therefore
the deterioration process of the coating has to be estimated
accurately. We do this for high voltage poles in a given environment
using three different stochastic processes. The Brownian motion with
non-linear drift, the Gamma process with non-linear shape function and
the simulation of a physical process are compared. Expert judgement is
used to obtain parameter estimates. It is found that the Brownian
motion with non-linear drift describes the stochastic deterioration
process better than the Gamma process. Moreover, the estimation of the
parameters of the Brownian motion with non-linear drift is more
efficient in terms of computing time. The simulation process is
inferior to the other 2 processes with respect to goodness-of-fit and
computing time. However, it gives a better understanding of the
deterioration process in reality, since it is based on expert opinions.
Moreover, the simulation can be visualised.
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OLIEMAN, NIELS
Operations Research and Logistics
Wageningen University
Hollandseweg 1
6706 KN Wageningen
niels.olieman@wur.nl
Supervisor
Hendrix
Title
Optimal robust product design
Abstract
We call quantitative models that predict product characteristics as
a
function of product design "product models". We use product models to
find optimal product designs, which minimise costs, while fulfilling
all product specifications.
Product models that contain estimated model parameters have some degree
of uncertainty in predicting the product characteristics. This leads to
the multiple objective problem to minimise costs and maximise the
chance of fulfilling all product specifications.
We formulate this optimal robust product design problem as a
probabilistic goal-programming problem and introduce two methods to
optimise this problem. The first method deals with maximising a
robustness lower-bound measure given an upper bound for the cost
function. The second method deals with maximising a robustness
approximation measure given an upper bound for the cost function.
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OOTEGHEM, DENNIS VAN
Department of Mathematics and Computer Science
Eindhoven University of Technology
P.O. Box 513
5600 MB Eindhoven
d.t.m.b.ooteghem@tue.nl
Supervisors
Boxma / Borst
Title
Tail asymptotics for discrimininatory processor-sharing queues with heavy-tailed service requirements.
Abstract
Over the past few years, the Processor-Sharing (PS) discipline has been widely adopted as a convenient paradigm for modelling the bandwidth sharing among dynamically interacting TCP flows in the Internet. However, the applicability of the PS discipline relies on the assumption that the service capacity is shared in an egalitarian manner. As the Internet evolves to support an ever increasing range of services, there is a growing need for some form of service differentiation to satisfy the diverse requirements of heterogeneous applications. The Discriminatory Processor-Sharing (DPS) discipline provides a natural approach for modelling the flow-level performance of differentiated bandwidth-sharing mechanisms. DPS is a multi-class extension of the ordinary egalitarian PS policy, where the various customer classes are assigned positive weight factors. The service capacity is shared among all users present in proportion to the respective class-dependent weight factors.
In the presentation, we derive the sojourn time asymptotics for a multi-class G/G/1 queue with regularly varying service requirements operating under the DPS discipline. Under certain assumptions, we prove that the service requirement and sojourn time of a given class have similar tail behaviour, independent of the specific values of the DPS weights. As a by-product, we obtain an extension of the tail equivalence for ordinary PS queues to non-Poisson arrivals. The results suggest that DPS offers a potential instrument for effectuating preferential treatment to high-priority classes, without inflicting excessive delays on low-priority classes.
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OUWEHAND, PIM
Department of Technology Management
Eindhoven University of Technology
P.O. Box 513
5600 MB Eindhoven
p.ouwehand@tm.tue.nl
Supervisors
De Kok / Van Donselaar
Title
Sales forecasting through aggregation
Abstract
Standard forecasting methods which are designed to cope with seasonal demand often are no longer applicable in practice. Due to growing assortments and shorter product life cycles there simply may not be enough sales data available anymore to construct reliable forecast models at the individual item level. In this article we present alternative forecasting methods, which are based on the concepts of forecasting at a higher aggregation level and combining forecasts. Sales data from two prominent Dutch wholesalers are used to illustrate the drawbacks of the standard forecasting methods and to demonstrate the potential of the new methods. The average reduction in forecast error (in terms of MSE) turns out to be three times as large as reported in earlier studies on common seasonal patterns.
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PORRAS, ERIC
Department of Econometrics
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
porrasmusalem@few.eur.nl
Supervisor
Dekker
Title
An efficient optimal solution method for the joint replenishment
problem with minimum order quantities
Abstract
We study the joint replenishment problem (JRP) for m items under
deterministic demand, with a minimum order quantity constraint for each
item in the replenishment order. We first study an iterative procedure
that proves to be not efficient in this case. Further, we derive bounds
on the basic cycle time and propose an efficient global optimisation
procedure to solve the JRP with constraints. A real example is
evaluated.
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SÁIZ PÉREZ, ELENA
Operations Research and Logistics
Wageningen University
Hollandseweg 1
6706 KN Wageningen
elena.saiz@wur.nl
Supervisor
Hendrix
Title
Facility-pricing location game
Abstract
Two classic competitive location models in the literature are: model of
price choice and model of location choice. Game theory is playing an
important role in solution concepts for years. In the so-called
"pricing game" firms choose prices for given locations; in the
so-called "location game" prices are fixed and the firms choose the
locations. We consider a two-stage game with N known participants
deciding where to locate and what price to offer the product. The
objective is to find a Nash equilibrium in prices and location in order
to get stable coalition structures maximising benefits.
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TURKENSTEEN, MARCEL
Faculty of Economics
University of Groningen
P.O. Box 800
9700 AV Groningen
m.turkensteen@eco.rug.nl
Supervisors
Sierksma / Van der Veen
Title
Common arcs in optimal assignments and shortest tours
Abstract
The Asymmetric Traveling Salesman Problem (ATSP) is a well known NP-hard problem with a large number of practical applications. Its most common relaxation is the Assignment Problem (AP). Many Branch-and-Bound algorithms delete high arcs from an optimal AP solution F to obtain a shortest ATSP tour T. In this paper, we investigate whether it is more effective to delete arcs with small tolerance values. The computational experiments show that the fraction of arcs from F that also appear in a shortest tour T is approximately 40% to 80%, depending on the instance type. Moreover, an arc from F with small upper tolerance value is less likely to appear in T than an arc with high cost value, i.e. predictions are more accurate when tolerances are used.
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VLASIOU, MARIA
Department of Mathematics and Computer Science
Eindhoven University of Technology
P.O. Box 513
5600 MB Eindhoven
vlasiou@eurandom.tue.nl
Supervisor
Adan
Title
Throughput analysis of two carousels
Abstract
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 throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley's equation for the waiting time in the PH/U/1 queue. Although the latter equation has no simple solution, it appears that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the PH/U/1 queue strongly depends on the coefficient of variation of the inter-arrival time. Numerical results show that, for the carousel system, the mean waiting time and throughput are not very sensitive to the coefficient of variation of the pick-time.
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VROMANS, MICHIEL
Rotterdam School of Management
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
mvromans@fbk.eur.nl
Supervisors
Kroon / Dekker / van Nunen
Title
Homogenization and railway timetabling norms
Abstract
The Netherlands has one of the highest utilized national railway
networks in the world. Accordingly, a high reliability is needed. On
one hand this can be achieved by high quality maintenance of the
infrastructure and rolling stock. On the other hand, a less vulnerable
use of the available capacity also plays a key role. For the latter,
smart guidelines for the logistic planning of railway traffic are
needed. This research aims at the development of such guidelines.
Speed differences between local trains and intercity or high-speed
services are one of the main causes for the high utilization rate, and
therefore for the sensitivity of the railway system. Several
theoretical and practical cases are evaluated, where more homogeneous
cases are compared with more heterogeneous ones.
Speed differences can be decreased in two ways: fast trains are slowed
down or slower trains are accelerated. Deceleration of the system leads
to a range of consequences. High-speed travelers will experience an
increased traveling time, but short-distance travelers may attain more
–and faster– travel opportunities. When trains require longer traveling
times, the demand for rolling stock and personnel will also increase.
Acceleration of the system often leads to less traveling possibilities
between minor stations –and detours may be required for certain
journeys– but travel times between a minor station on one side and a
major station on the other side will often go down. Therewith, the
overall impact on travelers depends heavily on the desired trips.
Homogenization has a positive impact on punctuality. However, the
positive impact of the homogenization on the robustness has to be
compared with other features of the different scenarios, such as
planned travel times for passengers and frequencies. A good balance
between these features is needed.
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VUUREN, MARCEL VAN
Department of Mathematics and Computer Science
Eindhoven University of Technology
P.O. Box 513
5600 MB Eindhoven
m.v.vuuren@tue.nl
Supervisor
Adan
Title
Compact Markovian arrival processes for the description of multiple arrival streams
Abstract
We propose a class of Markovian Arrival Processes (MAPs) to efficiently describe multiple arrival streams. The size of the state space of the MAPs is kept small, while preserving the main characteristics of the arrival streams. Each of the arrival streams has Erlangk-1,k distributed inter-arrival times. The main idea is to reduce the state-space by aggregating the states in which the total number of completed phases is the same. This method is used to approximate the performance of a SGi/G/1 queue, as well as an inventory control model. The results are also compared with a two-moment fit and the method of Whitt [1] and Albin [2] to approximate multiple arrival streams. Simulation results show that this method is very accurate and it works better than the other ones.
References
[1] W. Whitt: Approximating a Point Process by a Renewal Process, I: Two Basic Methods, Operations Research 30 (1982) 125-147.
[2] S. L. Albin: Approximating a Point Process by a Renewal Process, 2: Superposition of Arrival Processes to Queues, Operations Research 32 (1984) 1133-1162.
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