Nico van Dijk

University of Amsterdam | UVA · Faculty of Economics and Econometrics

Objective To demonstrate the feasibility and effectiveness of extended matching of red blood cells (RBC) in practice. Background At present, alloimmunisation preventing matching strategies are only applied for specific transfusion recipient groups and include a limited number of RBC antigens. The general assumption is that providing fully matched...

Overflow mechanisms can be found in a variety of queueing models. This paper studies a simple and generic overflow system that allows the service times to be both job type and station dependent. This system does not exhibit a product form. To justify simple product form computations, two product form modifications are given, as by a so-called call...

Mass-scale red blood cell genotyping of donors and transfusion recipients increases the availability of extended antigen matched red blood cell units. Therefore, a new mathematical framework is developed that can be applied for general blood groups (i.e., beyond the ABO, RhD blood groups). It determines which red blood cell units should be issued f...

An approach is presented to compare two Markov Chains, particularly Continuous-Time Markov Chains (CTMC) such as to model Queueing Networks (QN). Here one may typically think of one CTMC or QN to be a solvable modification (e.g. a product form QN) of the other one, say the original, which is of practical interest but unsolvable. The approach is ess...

For rare blood groups the recruitment of donor relatives, for example siblings, is expected to be effective, since the probability of a similar rare blood group is likely. However, the likelihood differs between blood groups and is not commonly available. This paper provides a unified mathematical formulation to calculate such likelihoods. From a m...

Service systems often experience time-dependent aspects, typically due to time-dependent arrivals and capacities. Easy and quick to use queueing expressions generally do not apply to these situations, but are still used. At the same time a large number of computational papers exist that deal with queue length distributions for time-dependent queues...

Uniformization, also referred to as randomization, is a well-known performance evaluation technique to model and analyse continuous-time Markov chains via an easier to performance measures via iteration of the one-step transition matrix of the discrete-time Markov chain. The number of iterations has a Poisson distribution with rate dominating the m...

Sanquin, the organization responsible for blood collection in the Netherlands, aims to be donor-friendly. An important part of the perception of donor-friendliness is the experience of waiting times. At the same time, Sanquin needs to control the costs for blood collection. A significant step to shorten waiting times is to align walk-in arrivals, a...

A crucial challenge in future smart energy grids is the large-scale coordination of distributed energy generation and demand. In the last years several Demand Side Management approaches have been developed. A major drawback of these approaches is that they mainly focus on realtime control and not on planning, and hence cannot fully exploit the flex...

This paper illustrates how MDP or Stochastic Dynamic Programming (SDP) can be used in practice for blood management at blood banks; both to set regular production quantities for perishable blood products (platelets) and how to do so in irregular periods (as holidays). The state space is too large to solve most practical problems using SDP. Neverthe...

This book presents classical Markov Decision Processes (MDP) for real-life applications and optimization. MDP allows users to develop and formally support approximate and simple decision rules, and this book showcases state-of-the-art applications in which MDP was key to the solution approach. The book is divided into six parts. Part 1 is devoted t...

A crucial challenge in future smart energy grids is the large-scale coordination of distributed energy demand and generation. The well-known PowerMatcher is a promising approach that integrates demand and supply flexibility in the operation of the electricity system through dynamic pricing and a hierarchical bidding coordination scheme. However, as...

As blood donations are provided on a voluntary non-remunerated basis, blood donors should be treated as user-friendly as possible. Delays and waiting times within blood collection sites (donor centers) should thus be kept at acceptable levels. Waiting times are not incorporated directly other than by practical experience. A more rigorous approach i...

With the increased use of large-scale real-time embedded sensor networks, new control mechanisms are needed to avoid congestion and meet required Quality of Service (QoS) levels. In this paper, we propose a Markov Decision Problem (MDP) to prescribe an optimal query assignment strategy that achieves a trade-off between two QoS requirements: query r...

Queueing networks are studied with two stations: either in tandem or in parallel, and with a common service resource shared among the two stations. First, a necessary and sufficient criterion, called adjoint reversibility, is provided to decide whether the system possesses a product form or not. This criterion unifies both the parallel (a reversibl...

This paper is motivated by a case study to reduce the throughput times for radiotherapy treatment. The goal is to find a cost-effective way to meet future throughput targets. A combination of queuing theory and computer simulation was used. First, computer simulation to detect the bottleneck(s) in a multi-step radiotherapy process. Despite, the inv...

An interactive tool was developed for the ophthalmology department of the Academic Medical Center to quantitatively support management with strategic patient-mix decisions. The tool enables management to alter the number of patients in various patient groups and to see the consequences in terms of key performance indicators. In our case study, we f...

The shelf life of platelet concentrates (PCs) is a matter of days. Simultaneously, the demand is highly variable, shortages are not allowed, and producing too many results in outdating. Concurrently, younger PCs, implying an extended time till outdating (TTO), are preferred. Common PC inventory management relies on experience-based order-up-to rule...

This chapter presents an approach to compare two Queueing Networks. Here one may typically think of one network to be a solvable modification of another unsolvable one of practical interest. The approach is essentially based upon evaluating steady state performance measures by a cumulative reward structure and strongly relies upon the analytical es...

Do we have a product form? If so, how is it characterized? If not, how can product forms still be useful?

This paper examines whether urgent and regular patients waiting for a consultation at a radiotherapy outpatient department should be pooled or not. Both queuing theory and discrete event simulation were applied to a realistic case study. The theoretical approach shows that pooling is not always beneficial with regard to the waiting times of urgent...

In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss o...

The production and inventory management of blood products at blood banks and hospitals is a problem of general human interest. As a shortage may put lives at risk, shortages are to be kept to a minimum. As the supply is voluntary and costly, any spill of unused blood (products) is also to be minimized. Blood platelets (thrombocytes), which are the...

This note studies practical and theoretical scenarios to improve a completely pooled or unpooled scenario for two server groups (e.g. call center groups) with short and long jobs (e.g. calls). First, simple overflow (reported earlier) scenarios and priority rules are compared. Next, threshold rules are investigated for further practical improvement...

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are (i) classical circuit switch telephone networks (loss networks) and (ii) present-day wireless mobile networks. Performance measures of interest such as loss probabilities or throughputs can be obtained from the s...

The challenge of production and inventory management for blood platelets (PLTs) is the requirement to meet highly uncertain demands. Shortages are to be minimized, if not to be avoided at all. Overproduction, in turn, leads to high levels of outdating as PLTs have a limited "shelf life." Outdating is to be minimized for ethical and cost reasons. Op...

Finite loss queues with overflow naturally arise in a variety of communications structures. For these systems, there is no simple analytic expression for the loss probability. This paper proves and promotes easily computable bounds based on the so-called call packing principle. Under call packing, a standard product form expression is available.It...

This chapter aims to promote and illustrate the fruitful combination of classical operations research (OR) and computer simulation. First, a highly instructive example of parallel queues will be studied. This simple example already shows the necessary combination of OR (queueing) and simulation that appears to be of practical interest such as for c...

Should we pool capacities or not? This is a question that one can regularly be confronted with in operations and service management. It is a question that necessarily requires a combination of queueing (as OR discipline) and simulation (as evaluative tool). It is a question by which this combination leads to further steps for 'optimization'. This p...

Should service capacities (such as agent groups in call centers) be pooled or not? This paper will show that there is no single answer. For the simple but generic situation of two (strictly pooled or unpooled) server groups, it will provide (1) insights and approximate formulae, (2) numerical support, and (3) general conclusions for the waiting-tim...

This note is concerned with stochastic product line structures. It aims to promote that and how an analytic approach, known in the literature, can also be fruitful for the simulation of such structures. This approach is based on the modification of the system of interest so as to meet simple in = out principles. These principles, which can be check...

A computational and an analytic error bound are derived for the truncation of finite Jackson networks. Numerical support is provided for the special application of a cellular mobile communication network.

Blood platelets are precious, as voluntarily supplied by donors, and highly perishable, with limited lifetimes of 5–7 days. Demand is highly variable and uncertain. A practical production and inventory rule is strived for that minimizes shortages and spill. The demand and production are periodic, as varying over the seven days of the week. Demand f...

Due to a limited ICU capacity patients can be rejected at both the Operating Theater (OT) and at the Intensive Care Unit (ICU) within hospitals. The corresponding ICU-rejection probability is an important service factor for hospitals. A simple expression for this probability is not available. With c the ICU capacity (number of ICU beds), this paper...

As an extension of the discrete-time case, this note investigates the variance of the total cumulative reward for continuous-time Markov reward chains with finite state spaces. The results correspond to discrete-time results. In particular, the variance growth rate is shown to be asymptotically linear in time. Expressions are provided to compute th...

As an extension of the discrete-time case, this note investigates the variance of the total cumulative reward for continuous-time Markov reward chains with finite state spaces. The results correspond to discrete-time results. In particular, the variance growth rate is shown to be asymptotically linear in time. Expressions are provided to compute th...

This chapter describes a practical approach for the train-shunting problem. Solving the shunting problem is a daily difficult job for planners. This chapter reports on a practical train-shunting heuristic that shows similarities with Dynamic Programming (DP).

This paper presents and investigates a check-in problem for a twofold reason: i) as a problem of practical and novel scientific interest in itself and ii) as a problem which requires both a stochastic (simulation) and deterministic (integer programming) approach. First, simulation is used to determine minimal numbers of desks in order to meet a ser...

In these papers we study networks of queues with general routing- and service-characteristics. It is extensively analysed which models do satisfy a partial balance property, called the job-local-balance property. The key to our analysis is the adjoint process. Roughly speaking, the original process satisfies the job-local-balance property if and on...

This is an expository paper to promote the potential of OR (Operations Research) for simulation. Three applications will therefore be presented which in- clude call centers, check-in at airports, and performance bounds for production lines. The results indicate that (classical and new) OR results might still be most fruitful if not necessary for pr...

This second part, which follows Part I on the discrete-time case (see [Kybernetika 42, No. 1, 37–56 (2006; Zbl 1249.60168)]), deals with monotonicity and comparison results, as a generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete...

This second Part II, which follows a first Part I for the discrete-time case (see [3]), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no long...

This paper is written in honour to A. Hordijk. It establishes product form results for a generic and instructive multi-class tandem queue with blocking, to which A. Hordijk has directly and indirectly contributed. First, a sufficient and necessary product form characterization is provided. Next, three special cases are briefly presented. These ill...

Should we pool capacities or not? This is a question that one can regularly be confronted with in operations and service management. It is a question that necessarily requires a combination of queueing (as OR discipline) and simulation (as evaluative tool) and further steps for optimization. It was illustrated that a combined approach (SimOR) of si...

An error bound result is provided for the truncation of a finite Jackson network from which both a computational and analytic error bound can be concluded. The results are illustrated for a special application of a cellular mobile communication network.

Blood banks produce and store blood products in order to fulfil the uncertain demand at hospitals. Platelet pools are the most expensive and most perishable blood product having a shelf life of only four to six days. Production volumes need to be chosen carefully in order to reduce outdating while keeping the occurrence of shortages low. We invest...

A general framework is provided to derive analytic error bounds for the effect of perturbations and inaccuracies of nonexponential service or arrival distributions in single- and multiserver queues. The general framework is worked out in detail for the three types of finite or infinite buffer queues: GI/G/1/N, M/G/c/N, and GI/M/c/N. First, for the...

This note studies the variance of total cumulative rewards for Markov reward chains in both discrete and continuous time. It is shown that parallel results can be obtained for both cases. First, explicit formulae are presented for the variance within finite time. Next, the infinite time horizon is considered. Most notably, it is concluded that the...

Should we pool or not? This is a question of general interest for call center management. The general perception seems to exist that pooling is always beneficial either in terms of performance (mean waiting times and service levels) or agent capacity savings. This paper aims to show that also at practical call center level a more detailed answer is...

"Should we pool separate queues into a single queue or not?" A question as practical as for daily-life situations such as at a bank, a hospital or a service center as well as for technical applications such as in manufacturing or call centers. A question that involves fundamental insights of queuing theory. A question that can only be answered in a...

This paper presents and investigates a check-in problem for a twofold reason: i) as a problem of practical and novel scientific interest in itself and ii) as a problem which requires both a stochastic (simulation) and deterministic (integer programming) approach. First, simulation is used to determine minimal numbers of desks in order to meet a ser...

The performance of new railway networks cannot be measured or simulated, as no detailed train schedules are available. Railway infrastructure and capacities are to be determined long before the actual traffic is known. This paper therefore proposes a solvable queueing network model to compute performance measures of interest without requiring train...

This paper aims to and illustrate that simulation and queuing theory can and should go hand in hand for a variety of practical problems, both in daily-life and industry, which are still open for fundamental research. To this end, it will highlight real-life cases taken from: Dailylife situations (postal office or bank), administrative logistics (re...

By studying performance measures via reward structures, on-line error bounds are obtained by successive approximation. These bounds indicate when to terminate computation with guaranteed accuracy; hence, they provide insight into steady-state convergence. The method therefore presents a viable alternative to steady-state computer simulation where t...

The purpose of the paper is to describe: (a) why simulation is necessary to evaluate check-in, (b) a simulation toolbox for check-in counters and (c) two case studies for Amsterdam Airport Schiphol. First, it is discussed why queuing theory results are too limited but nevertheless useful to predict queuing times for check-in counters at airports. N...

Monotonicity and comparison results are known to be most useful for the qualitative analysis of Markov chain applications. In this paper, the extension of such results will be studied for the more general class of dynamic systems governed by nonnegative matrices. Both the discrete-time and continuous-time case will be investigated. It will be shown...

Queueing networks are studied with finite capacity constraints for clusters of stations. First, by an instructive tandem cluster example it is shown how a product-form modification method for networks with finite stations can be extended to networks with finite clusters. Next, a general result is established by which networks with finite clusters c...

The classical technique of uniformization (or randomization) for bounded continuous-time Markov chains and Markov reward structures is extended to dynamic systems generated by arbitrary non-negative generators. Most notably, these include so-called input-output models in economic analysis. The results are of practical interest for both computationa...

The classical technique of uniformization (or randomization) for bounded continuous-time Markov chains and Markov reward structures is extended to dynamic systems generated by arbitrary non-negative generators. Most notably, these include so-called input-output models in economic analysis. The results are of practical interest for both computationa...

This work presents an estimate of the error on a cumulative reward function until the entrance time of a continuous-time Markov chain into a set, when the infinitesimal generator of this chain is perturbed. The derivation of an error bound constitutes the first part of the paper while the second part deals with an application where the time until s...

This work presents an estimate of the error on a cumulative reward function until the entrance time of a continuous-time Markov chain into a set, when the infinitesimal generator of this chain is perturbed. The derivation of an error bound constitutes the first part of the paper while the second part deals with an application where the time until s...

This paper describes how a combined queueing and simulation study was successfully executed for the design of a toll plaza. The objectives of the study were twofold: . to configure the types of toll booths with multiple payment functionalities (cash, credit cards, and electronic payment). . to determine the number of toll booths for each type. The...

This paper presents a queueing network description of a cellular mobile communications network. These cellular networks are characterised by the call lengths, the fresh call arrival rate, and the handover rates, as well as the capacity restrictions on the number of calls because of limited bandwidth. In the resulting queueing network the routing pr...

This paper aims to illustrate that simulation and queueing theory can and should go hand in hand for a variety of practical problems, both in daily-life and industry, which are still open for fundamental research. To this end, it highlights real-life cases taken from: daily-life situations (postal office or bank), administrative logistics (reengine...

Queueing networks are used widely as modelling and evaluation tools in manufacturing, telecommunications, computer networking, and related areas. Much of the research effort has been devoted to so-called Jackson networks, that is, networks with Poisson arrivals, exponential service times and routing independent of the state of the system and the hi...

The extension of Markov reward models to dynamic models with nonnegative matrices is motivated by practical applications, such as economic input–output, employment, or population models. This paper studies the generalization of error bound theorems for Markov reward structures to dynamic reward structures with arbitrary nonnegative matrices. Both i...

This paper describes how a combined queueing and simulation study was successfully executed for the design of a toll plaza. The objectives of the study were twofold: ∞ to configure the types of toll booths with multiple payment functionalities (cash, credit cards, and electronic payment). ∞ to determine the number of toll booths for each type. The...

Queueing networks are known to provide a useful modelling and evaluation tool in computer and telecommunications. Unfortunately, realistic features like finite capacities, link failures, dynamic routing and non-exponentiality usually prohibit analytic solutions.Numerical and approximate computations as well assimplifications and performance boundsf...

Systems of heterogeneous parallel processing are studied such as arising in parallel programs executed on distributed systems. A lower and an upper bound model are suggested to obtain secure lower and upper bounds on the performance of these systems. The bounding models are solved by using a matrix-geometric algorithmic approach. Formal proofs of t...

We consider a class of models for multicomponent systems in which components can break down and be repaired in a dependent manner and where breakdown and repair times can be arbitrarily distributed. The problem of calculating the equilibrium distribution and, from this, the expected performability for these models is intractable unless certain assu...

Queueing networks are an important means to model and evaluate a variety of practical systems. Unfortunately, analytic results are often not available. Numerical computation may then have to be employed. Or, system modifications might be suggested to obtain simple bounds or computationally easy approximations. Formal analytic support for the accuar...

We consider the problem of cost optimal railway line allocation for passenger trains for the Dutch railway system. At present, the allocation of passenger lines by Dutch Railways is based on maximizing the number of direct travelers. This paper develops an alternative approach that takes operating costs into account. A mathematical programming mode...

The technique of uniformization, introduced by Jensen [3] and also known as randomization, is widely known as a fruitful tool to transform (homogeneous) continuous-time Markov chains into discrete-time Markov chains, both for theoretical and computational purposes, most notably to evaluate performance measure such as arising in manufacturing, telec...

A simple practical approximation is studied for a two-stage tandem queue with a finite first station. Explicit small error bounds are obtained for the mean queue length and the tail probabilities of the second queue. These error bounds are based on a new application of an existing error bound theorem for comparing Markov chains. The extension requi...

In this paper we treat a discrete-time generalized semi-Markov process in which simultaneous deaths of more than one lifetime and simultaneous arrivals are permitted and service scheduling is probabilistic. Necessary and sufficient conditions for insensitivity are derived and a simple algorithmic procedure provided whereby the equilibrium probabili...

This tutorial aims to address and illustrate that queuing theory has a wider potential than generally perceived, while at the same time a variety of practical problems, both in daily-life and industry, are open for fundamental research. To this end, it will: (i) Highlightbasic queuing insights for daily-life purposes. (ii) Provideexact and bounding...

The arrival theorem is known to be valid for product form queueing networks that do not have capacity constraints at the queues. This paper investigates the validity of the arrival theorem for open and closed queueing networks with finite queues under product form conditions, and derives a necessary and sufficient condition for the validity of the...

This note studies the comparison of finite-buffer and nonexponential batch arrival systems of the form Gx/M/c/c + N with the corresponding systems, with N replaced by N', where N' can be smaller, larger, or infinite. If N' = ∞ the service times can be arbitrarily distributed. Both comparison and error bounds are obtained for performance measures su...

A discrete time queue is studied with simultaneous service completions per time slot. By truncating the state space an approximate recursive solution is proposed. An explicit error bound for the accuracy of this truncation is derived. This error bound is of order ϱL, where ϱ is the traffic load and L the truncation size.