57 research outputs found

    Unreliable Retrial Queues in a Random Environment

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    This dissertation investigates stability conditions and approximate steady-state performance measures for unreliable, single-server retrial queues operating in a randomly evolving environment. In such systems, arriving customers that find the server busy or failed join a retrial queue from which they attempt to regain access to the server at random intervals. Such models are useful for the performance evaluation of communications and computer networks which are characterized by time-varying arrival, service and failure rates. To model this time-varying behavior, we study systems whose parameters are modulated by a finite Markov process. Two distinct cases are analyzed. The first considers systems with Markov-modulated arrival, service, retrial, failure and repair rates assuming all interevent and service times are exponentially distributed. The joint process of the orbit size, environment state, and server status is shown to be a tri-layered, level-dependent quasi-birth-and-death (LDQBD) process, and we provide a necessary and sufficient condition for the positive recurrence of LDQBDs using classical techniques. Moreover, we apply efficient numerical algorithms, designed to exploit the matrix-geometric structure of the model, to compute the approximate steady-state orbit size distribution and mean congestion and delay measures. The second case assumes that customers bring generally distributed service requirements while all other processes are identical to the first case. We show that the joint process of orbit size, environment state and server status is a level-dependent, M/G/1-type stochastic process. By employing regenerative theory, and exploiting the M/G/1-type structure, we derive a necessary and sufficient condition for stability of the system. Finally, for the exponential model, we illustrate how the main results may be used to simultaneously select mean time customers spend in orbit, subject to bound and stability constraints

    Stability Problems for Stochastic Models: Theory and Applications II

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    Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21Β­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

    Queues: Flows, Systems, Networks

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    Π’ сборникС ΠΈΠ·Π»Π°Π³Π°ΡŽΡ‚ΡΡ Π½ΠΎΠ²Ρ‹Π΅ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ Π½Π°ΡƒΡ‡Π½Ρ‹Ρ… исслСдований Π² области Ρ€Π°Π·Ρ€Π°Π±ΠΎΡ‚ΠΊΠΈ ΠΈ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ процСссов ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ Π² Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… сСтях с использованиСм Π°ΠΏΠΏΠ°Ρ€Π°Ρ‚Π° Ρ‚Π΅ΠΎΡ€ΠΈΠΈ систСм ΠΈ сСтСй массового обслуТивания. ΠŸΡ€Π΅Π΄Π½Π°Π·Π½Π°Ρ‡Π΅Π½ спСциалистам Π² области вСроятностного Π°Π½Π°Π»ΠΈΠ·Π°, случайных процСссов, матСматичСского модСлирования, ΠΈ матСматичСской статистики, Π° Ρ‚Π°ΠΊΠΆΠ΅ спСциалистам Π² области проСктирования ΠΈ эксплуатации сСтСй связи ΠΈ ΠΊΠΎΠΌΠΏΡŒΡŽΡ‚Π΅Ρ€Π½Ρ‹Ρ… сСтСй

    Bloody fast blood collection

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    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) β€” that are very hard to analyze β€” into Discrete Time Markov Chains (DTMCs) β€” 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

    The influence of legal language upon Supreme Court voting in civil liberties cases.

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    Scholars such as Jeffrey Segal and Harold Spaeth contend that U.S. Supreme Court decisions are based primarily upon the ideological beliefs of the justices. However, in this work I show that this conclusion is exaggerated. The aggregation of votes into a summary statistic (the percent liberal rating) and its use by Segal and Spaeth in a regression having only 21 cases creates misleading results. The truth is that political ideology is a fluctuating influence upon the Court. In some areas of civil liberties voting, ideology is a poor explanation of how cases are decided (e.g., core political speech). But in other areas, ideology is a much stronger explanation (e.g., search and seizure). In this work, I investigate whether the clarity of legal commands can explain why the influence of ideology fluctuates so much. My hypothesis is that value voting is inversely related to how clearly a right is designated by legal commands. That is, where statutes or constitutional language clearly designates a claim to liberty, ideology is a weak predictor of votes, but where law is vague and indeterminate in its nomenclature, value-voting rules. This dissertation has both a qualitative and quantitative component. It also relies upon literature that is multi-disciplinary. It accomplishes following: (1) constructs a criteria for rigidity in legal language; (2) selects cases for content analysis that meet the criteria; (3) assesses the relationship between values and votes within the selection using logistic regression analysis; (4) assesses the influence of textual rigidity upon votes cast by each individual justice for all selected cases using logistic regression analysis and (5) re-assess the attitudinal model\u27s goodness of fit for all civil liberties cases in a way that avoids ecological problems and micronumerous cases. The results of this work will show that the influence of political ideology upon judging in the Supreme Court has been overstated in the literature, and that command rigidity is a statistical predictor of judicial votes. In short, law matters

    Holder in Due Course in Consumer Transactions Requiem Revival or Reformation

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    No area of consumer protection has produced as much near religious ferment in recent years as that collection of rules which insulate third party financers from product-related claims or defenses of consumer purchasers. Courts, legislatures, agencies, commissions, and commentators 6 have assailed the holder in due course idea from all directions, so far as its application in consumer transactions is concerned. The cloud of rhetoric thus raised has tended to obscure the complexity of the subject, state only imperfectly the significant considerations, and oversimplify the appropriate legal responses. Moreover, the focus of much of this recent discussion has been on traditional notions of holder in due course. There are now important new developments in the form of the recommendations of the National Commission on Consumer Finance, a completely redrafted 1974 Uniform Consumer Credit Code, a new Model Consumer Credit Act drafted by the National Consumer Law Center, the possibly imminent promulgation of a holder in due course Trade Regulation Rule by the Federal Trade Commission, and, most recently, the enactment of a federal statute limiting holder in due course application in credit card transactions.This Article takes up the changing shape of the holder in due course controversy and outlines grounds for consensus as to future legislative policy

    Holder in Due Course in Consumer Transactions: Requiem, Revival, or Reformation?

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    No area of consumer protection has produced as much near religious ferment in recent years as that collection of rules which insulate third party financers from product-related claims or defenses of consumer purchasers. Courts, legislatures, agencies, commissions, and commentators 6 have assailed the holder in due course idea from all directions, so far as its application in consumer transactions is concerned. The cloud of rhetoric thus raised has tended to obscure the complexity of the subject, state only imperfectly the significant considerations, and oversimplify the appropriate legal responses. Moreover, the focus of much of this recent discussion has been on traditional notions of holder in due course. There are now important new developments in the form of the recommendations of the National Commission on Consumer Finance, a completely redrafted 1974 Uniform Consumer Credit Code, a new Model Consumer Credit Act drafted by the National Consumer Law Center, the possibly imminent promulgation of a holder in due course Trade Regulation Rule by the Federal Trade Commission, and, most recently, the enactment of a federal statute limiting holder in due course application in credit card transactions.This Article takes up the changing shape of the holder in due course controversy and outlines grounds for consensus as to future legislative policy

    Holder in Due Course in Consumer Transactions Requiem Revival or Reformation

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    Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

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    The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

    The Popular Policeman and Other Cases

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    In this compelling title, two distinguished scholars share their experiences as expert witnesses in cases ranging from eyewitness testimony, person identification and recovered memories, to false confessions, collaborative storytelling and causal attribution, in the context of various interrogation techniques and their ability to deliver reliable results. Each chapter describes in lucid, entertaining prose a representative case in the context of scholarly literature to date, showing how psychological expertise has been (and can be) used in a legal setting. The cases include petty and serious crime, from illegal gambling, infringed trademarks and risqué courtship behaviour, to honour killing and death on the climbing wall. The authors' findings and recommendations apply to legal systems worldwide. There is no other English-language textbook covering a similarly wide range of offences, and this volume will fill a gap in the existing literature and demonstrate how psychological expertise can be used in a much larger area than is often realised.Psychologisch onderzoek is voor de rechter niet altijd gemakkelijk toe te passen binnen de context van een strafrechtelijk of civiel geding. Inzichten in de werking van het geheugen, het gedrag, logisch denkvermogen en het nemen van beslissingen kunnen uitkomst bieden als er sprake is van valse voorwendselen, fraude, diefstal of zelfs moord, maar vaak is daar wel de toelichting van een deskundige voor nodig. Op onderhoudende en toegankelijke wijze beschrijven rechtspsychologen Willem Albert Wagenaar en Hans Crombag tot in detail vijftien representatieve zaken uit de Nederlandse rechtspraak, hun rol daarin als deskundige, en hoe het afliep. Naast de betrouwbaarheid van ooggetuigenverklaringen en bekentenissen is er aandacht voor de psychologische aspecten van minder gangbare onderwerpen zoals illegaal gokken, verwarrende consumentenvoorlichting en seksuele intimidatie. The Popular Policeman and Other Cases vult een belangrijke lacune in de bestaande literatuur over de psychologie in de rechtszaal. Niet eerder werd er buiten de Verenigde Staten in één boek zo uitgebreid en gedetailleerd aandacht besteed aan zoveel uiteenlopende zaken. Het boek is in eerste instantie geschreven voor het hoger onderwijs, maar ook buiten de collegezaal zal dit boek op de nodige belangstelling kunnen rekenen
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