Parallel algorithms for simulating continuous time Markov chains

We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors

Performance analysis of time-dependent queueing systems: survey and classification

Many queueing systems are subject to time-dependent changes in system parameters, such as the arrival rate or number of servers. Examples include time-dependent call volumes and agents at inbound call centers, time-varying air traffic at airports, time-dependent truck arrival rates at seaports, and cyclic message volumes in computer systems.There are several approaches for the performance analysis of queueing systems with deterministic parameter changes over time. In this survey, we develop a classification scheme that groups these approaches according to their underlying key ideas into (i) numerical and analytical solutions,(ii)approaches based on models with piecewise constant parameters, and (iii) approaches based on mod-ified system characteristics. Additionally, we identify links between the different approaches and provide a survey of applications that are categorized into service, road and air traffic, and IT systems

Bloody fast blood collection

This thesis consists of four parts: The first part contains an introduction, the second presents approaches for the evaluation of waiting times at blood collection sites, the third uses these to present approaches that improve waiting times at blood collection sites. The final part shows the application of two of the approaches to data from real blood collection sites, followed by the conclusions that can be drawn from this thesis. Part I: Introduction, contains two chapters. Chapter 1 introduces the context for this thesis: blood banks in general, the Dutch blood bank Sanquin and blood collection sites. The chapter sketches some of the challenges faced with respect to blood collection sites. As blood donors are voluntary and non-remunerated, delays and waiting times within blood collection sites should be kept at acceptable levels. However, waiting times are currently not incorporated in staff planning or in other decisions with respect to blood collection sites. These blood collection sites will be the primary focus of this thesis. This thesis provides methods that do take waiting times into account, aiming to decrease waiting times at blood collection sites and leveling work pressure for staff members, without the need for additional staff. Chapter 2 then presents a technical methods that will be used most of the chapters in this thesis: uniformization. Uniformization can be used to transform Continuous Time Markov Chains (CTMCs) — that are very hard to analyze — into Discrete Time Markov Chains (DTMCs) — that are much easier to analyze. The chapter shows how the method works, provides an extensive overview of the literature related to the method, the (technical) intuition behind the method as well as several extensions and applications. Although not all of the extensions and applications are necessary for this thesis, it does provide an overview of one of the most valuable methods for this thesis. Part II: Evaluation, contains two chapters that propose and adapt several methods to compute waiting times and queues at blood collection sites. A blood collection site is best modeled as a time-dependent queueing network, requiring non-standard approaches. Chapter 3 considers a stationary, i.e. not time-dependent model of blood collection sites as a first step. A blood collection site consists of three main stations: Registration, Interview and Donation. All three of the stations can have their own queue. This means that even the stationary model is non-trivial for some computations. However, for the stationary model, an analytic so-called product form expression is derived. Based on this product form, two more results are shown. The first result is that the standard waiting time distributions from M|M|s queues are applicable, as if the queue is in isolation. It is then concluded that no closed form expression exist for the total waiting or delay time distribution, as the distributions of the three stations in tandem are not independent. Therefore a numerical approach is presented to compute the total delay time distribution of a collection site. All of the results are supported by numerical examples based on a Dutch blood collection site. The approach for the computation of the total delay time distribution can also be combined with the approach from Chapter 4 for an extension to a time-dependent setting. Chapter 4 shows an approach to deal with these time-dependent aspects in queueing systems, as often experienced by blood collection sites and other service systems, typically due to time-dependent arrivals and capacities. Easy and quick to use queueing expressions generally do not apply to time-dependent situations. A large number of computational papers has been written about queue length distributions for time-dependent queues, but these are mostly theoretical and based on single queues. This chapter aims to combine computational methods with more realistic time-dependent queueing networks, with an approach based on uniformization. Although uniformization is generally perceived to be too computationally prohibitive, we show that our method is very effective for practical instances, as shown with an example of a Dutch blood collection site. The objective of the results is twofold: to show that a time-dependent queueing network approach can be beneficial and to evaluate possible improvements for Dutch blood collection sites that can only be properly assessed with a time-dependent queueing method. Part III: Optimization, contains four chapters that aim to improve service levels at Sanquin. The first three chapters focus on three different methods to decrease queues at blood collection sites. Chapters 5 and 6 focus on improving the service by optimizing staff allocation to shifts and stations. Chapter 7 focuses on improving the arrival process with the same goal. Chapter 8 is focused at improving inventory management of red blood cells. Donors do not arrive to blood collection sites uniformly throughout the day, but show clear preferences for certain times of the day. However, the arrival patterns that are shown by historical data, are not used for scheduling staff members at blood collection sites. As a first significant step to shorten waiting times we can align staff capacity and shifts with walk-in arrivals. Chapter 5 aims to optimize shift scheduling for blood collection sites. The chapter proposes a two-step procedure. First, the arrival patterns and methods from queueing theory are used to determine the required number of staff members for every half hour. Second, an integer linear program is used to compute optimal shift lengths and starting times, based on the required number of staff members. The chapter is concluded with numerical experiments that show, depending on the scenario, a reduction of waiting times, a reduction of staff members or a combination of both. At a blood collection site three stations (Registration, Interview and Donation) can roughly be distinguished. Staff members at Dutch blood collection sites are often trained to work at any of these stations, but are usually allocated to one of the stations for large fractions of a shift. If staff members change their allocation this is based on an ad hoc decision. Chapter 6 aims to take advantage of this mostly unused allocation flexibility to reduce queues at blood collection sites. As a collection site is a highly stochastic process, both in arrivals and services, an optimal allocation of staff members to the three stations is unknown, constantly changing and a challenge to determine. Chapter 6 provides and applies a so-called Markov Decision Process (MDP) to compute optimal staff assignments. Extensive numerical and simulation experiments show the potential reductions of queues when the reallocation algorithm would be implemented. Based on Dutch blood collection sites, reductions of 40 to 80% on the number of waiting donors seem attainable, depending on the scenario. Chapter 7 also aims to align the arrival of donors with scheduled staff, similarly to Chapter 5. Chapter 7 tries to achieve this by changing the arrivals of donors. By introducing appointments for an additional part of donors, arrivals can be redirected from the busiest times of the day to quiet times. An extended numerical queueing model with priorities is introduced for blood collection sites, as Sanquin wants to incentive donors to make appointments by prioritizing donors with appointments over donors without appointments. Appointment slots are added if the average queue drops below certain limits. The correct values for these limits, i.e. the values that plan the correct number of appointments, are then determined by binary search. Numerical results show that the method succeeds in decreasing excessive queues. However, the proposed priorities might result in unacceptably high waiting times for donors without appointments, and caution is therefore required before implementation. Although this thesis mainly focuses on blood collection sites, many more logistical challenges are present at a blood bank. One of these challenges arises from the expectation that Sanquin can supply hospitals with extensively typed red blood cell units directly from stock. Chapter 8 deals with this challenge. Currently, all units are issued according to the first-in-first-out principle, irrespective of their specific typing. These kind of issuing policies lead to shortages for rare blood units. Shortages for rare units could be avoided by keeping them in stock for longer, but this could also lead to unnecessary wastage. Therefore, to avoid both wastage and shortages, a trade-off between the age and rarity of a specific unit in stock should be made. For this purpose, we modeled the allocation of the inventory as a circulation flow problem, in which decisions about which units to issue are based on both the age and rarity of the units in stock. We evaluated the model for several settings of the input parameters. It turns out that, especially if only a few donors are typed for some combinations of antigens, shortages can be avoided by saving rare blood products. Moreover, the average issuing age remains unchanged. Part IV: Practice and Outlook concludes this thesis. The first of two chapters in this part shows the combined application of two approaches from this thesis to data from three collection sites in the Netherlands. The final chapter of this thesis presents the conclusions that can be drawn from this thesis and discusses an outlook for further research. Chapter 9 shows the combined application of the methods in Chapters 5 and 6 to three real collection sites in Dutch cities: Nijmegen, Leiden and Almelo. The collection sites in Nijmegen and Leiden are both large fixed collection sites. The collection site in Almelo is a mobile collection site. The application of each one of the methods individually reduce waiting times significantly, and the combined application of the methods reduces waiting times even further. Simultaneously, small reductions in the number of staff hours are attainable. The results from Chapter 9 summarize the main message of this thesis: waiting time for blood donors at blood collection sites can be reduced without the need for more staff members when the working times of staff members are used more effectively and efficiently, and controlling the arrival process of donors. The approaches presented in this thesis can be used for this purpose. This is not only beneficial for blood donors, but will also result in more balanced workload for staff members, as fluctuations in this workload are reduced significantly

Extended Abstracts: PMCCS3: Third International Workshop on Performability Modeling of Computer and Communication Systems

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryThe pages of the front matter that are missing from the PDF were blank

Analysis of buffer allocations in time-dependent and stochastic flow lines

This thesis reviews and classifies the literature on the Buffer Allocation Problem under steady-state conditions and on performance evaluation approaches for queueing systems with time-dependent parameters. Subsequently, new performance evaluation approaches are developed. Finally, a local search algorithm for the derivation of time-dependent buffer allocations is proposed. The algorithm is based on numerically observed monotonicity properties of the system performance in the time-dependent buffer allocations. Numerical examples illustrate that time-dependent buffer allocations represent an adequate way of minimizing the average WIP in the flow line while achieving a desired service level

The application of Approximate Dynamic Programming techniques

Koole, G.M. [Promotor]Bhulai, S. [Copromotor