O modelo de fila M/M/n+G pode ser usado para descrever o comportamento de uma Central de Atendimento. Nesse modelo as chegadas são Poisson com taxa lambda, o atendimento é exponencialmente distribuído com taxa mi, há n atendentes e os tempos de paciência dos clientes têm distribuição geral. A espera do usuário em fila não pode ultrapassar um tempo (paciência) que tem distribuição G e, se isto ocorrer, ele abandona o sistema. Mandelbaum e Zeltyn [2004] mostraram que existe uma relação linear entre o tempo médio de permanência na fila e a probabilidade de abandono nesses modelos quando a paciência é exponencialmente distribuída. No presente trabalho, estudamos essa relação no caso de distribuiçãao de paciência do tipo mista (com partes discreta e contínua), em que buscamos representar a reação dos usuários às mensagens gravadas reproduzidas periodicamente para aqueles que estão esperando atendimento. Utilizamos duas distribuições de paciência: Exponencial Mista e Uniforme Mista e percebemos que não há uma relação linear entre o tempo médio de espera na fila e a probabilidade de abandono. Observamos que para uma mesma taxa de chegada, o tempo médio de espera na fila é menor para a distribuição de paciência mista quando comparada com a Exponencial ou Uniforme de mesmos parâmetros. Analisamos o que ocorre com essa relação quando alteramos a distribuição do atendimento e percebemos que ela é mais afetada pela média e pelo coeficiente de variação do que pela particular distribuição escolhida para o tempo de serviço. / The M/M/n+G queueing model can be used to describe the behavior of a Call Center. This model has Poisson arrivals with rate lambda, service times are exponentially distributed with rate mi, n agents and the client´s patience time has general distribution. The waiting in line could not exceed a time (patience) which has distribution G, and if it occurs, the client leaves the system. In this models, Mandelbaum and Zeltyn [2004] showed that there is a linear relationship between average waiting time in queue and the probability of abandonment if the distribution of patience is Exponencial. In this work, we study this relationship in the case of patience with mixed distribution (which has discret and continuous parts). Through mixed distributions we try to represent the user´s reaction to recorded messages reproduced periodically when they are waiting for service. We have used Mixed Exponencial and Mixed Uniform distributions and, in both of them, there is not a linear relationship between average waiting time in queue and the probability of abandonment. We observe that for the same arrival rate, the average waiting time in line for mixed distribution is smaller than Exponencial or Uniform distributions with the same parameters. Also, we study the effect on waiting time and abandonment of different distributions of service and we observe that it is more affected by the coeficient of variation and average that by the particular distribution chosen for service.

<p>Lengthy waiting times have been a problem in Swedish health services for many years. In 1992, Sweden implemented a national maximum waiting-time guarantee (MWG) through an agreement between the Swedish Government and the Federation of Swedish County Councils. The “guarantee” assured patients that the waiting time between the decision-to-treat and the treatment itself would not exceed three months. The national MWG covered twelve different treatments/interventions and remained in force for five years. This dissertation describes the genesis of the MWG, its implementation, and its effects.</p><p>Four papers serve as a foundation for the dissertation. Paper I describes how the guarantee was implemented during the first two years. Paper II studies the impact that the MWG had on cataract surgery. Paper III uses the results of two questionnaire surveys of department heads to explain why the MWG, although successfully launched, became increasingly difficult to maintain. Paper IV analyses data from the national cataract register to determine how production and waiting times in cataract surgery were affected by termination of the MWG.</p><p>This dissertation confirms that waiting time for health care is a complex phenomenon resulting from multiple causes. “Guarantees” are of particular interest because they define what constitutes too long in reference to waiting times. Beyond that, they are only a framework for developing a plan of action. The positive effects of the MWG were transient and based on rationalisation, introduction of new technology, and stricter prioritisation. The MWG contributed towards empowering patients and slowing the expansion of treatment indications, but it was unsuccessful in levelling out the wide regional variations in surgical rates.</p>

Lengthy waiting times have been a problem in Swedish health services for many years. In 1992, Sweden implemented a national maximum waiting-time guarantee (MWG) through an agreement between the Swedish Government and the Federation of Swedish County Councils. The “guarantee” assured patients that the waiting time between the decision-to-treat and the treatment itself would not exceed three months. The national MWG covered twelve different treatments/interventions and remained in force for five years. This dissertation describes the genesis of the MWG, its implementation, and its effects. Four papers serve as a foundation for the dissertation. Paper I describes how the guarantee was implemented during the first two years. Paper II studies the impact that the MWG had on cataract surgery. Paper III uses the results of two questionnaire surveys of department heads to explain why the MWG, although successfully launched, became increasingly difficult to maintain. Paper IV analyses data from the national cataract register to determine how production and waiting times in cataract surgery were affected by termination of the MWG. This dissertation confirms that waiting time for health care is a complex phenomenon resulting from multiple causes. “Guarantees” are of particular interest because they define what constitutes too long in reference to waiting times. Beyond that, they are only a framework for developing a plan of action. The positive effects of the MWG were transient and based on rationalisation, introduction of new technology, and stricter prioritisation. The MWG contributed towards empowering patients and slowing the expansion of treatment indications, but it was unsuccessful in levelling out the wide regional variations in surgical rates.

La tesi descriu dos algorismes relatius al transport públic que actuen en sèrie. El primer genera una xarxa d'autobusos urbans entesa com a un conjunt de línies o be en modifica una de ja existent de forma que minimitzi el temps total de viatge en una ciutat. Es tracta d'un algorisme iteratiu que tracta les línies d'una en una i aquestes al seu torn de nus en nus. El segon algorisme dit d'assignació un cop coneguda la xarxa i la flota d'autobusos minimitza el temps total de viatge per mitja de l'assignació d'autobusos a les línies.

We propose a situation in which a single employee is responsible for processing incoming claims to an insurance company that can be classified as being one of two possible types. More specifically, we consider a priority-based system having separate buffers to store high priority and low priority incoming claims. We construct a mathematical model and perform queueing analysis to evaluate the performance of this priority-based system, which incorporates the possibility of claims being redistributed, lost, or prematurely processed.

We propose a situation in which a single employee is responsible for processing incoming claims to an insurance company that can be classified as being one of two possible types. More specifically, we consider a priority-based system having separate buffers to store high priority and low priority incoming claims. We construct a mathematical model and perform queueing analysis to evaluate the performance of this priority-based system, which incorporates the possibility of claims being redistributed, lost, or prematurely processed.

Different applications of communication networks have different requirements that depend on the type of application. We consider the problem of differentiating between delay-sensitive applications based on their average delay requirements, as may be of interest in signalling networks. We consider packets of different classes that are to be transmitted on the same link with different average delay requirements, to reside in separate queues with the arrival statistics for the queues being specified. This statistical multiplexer has to schedule packets from different queues in so that the average delays of the queues approach the specified target delays as quickly as possible. For simplicity, we initially consider a discrete-time model with two queues and a single work-conserving server, with independent Bernoulli packet arrivals and unit packet service times. With arrival rates specified, achieving mean queue lengths in a ratio which corresponds to the ratio of target mean delays is a means of achieving individual target mean delays. We formulate the problem in the framework of Markov decision theory. We study two scheduling policies called Queue Length Balancing and Delay Balancing respectively, and show through numerical computation that the expectation of magnitude of relative error in θ (1/m) and θ (1/√m) respectively, and that the expectation of the magnitude of relative error in weighted average delays decays as θ (1/√m) and θ (1/m) respectively, where m is the averaging interval length. We then consider the model for an arbitrary number of queues each with i.i.d. batch arrivals, and analyse the errors in the average delays of individual queues. We assume that the fifth moment of busy period is finite for this model. We show that the expectation of the absolute value of error in average queue length for at least one of the queues decays at least as slowly as θ (1/√m), and that the mean squared error in queue length for at least one of the queues decays at least as slowly as θ (1/m). We show that the expectation of the absolute value of error in approximating Little’s law for finite horizon is 0 (1/m). Hence, we show that the mean squared error in delay for at least one of the queues decays at least slowly as θ (1/m). We also show that if the variance of error in delay decays for each queue, then the expectation of the absolute value of error in delay for at least one of the queues decays at least as slowly as θ (1/√m).

Wartezeiten von durchschnittlich mehreren Monaten sind auch nach Inkrafttreten des Psychotherapeutengesetzes in der deutschen Psychotherapieversorgung die Regel. Behandlungsbedürftige Störungen, für die ein Behandlungswunsch besteht, unversorgt zu lassen, ist weder unter ethischen, noch praktischen und therapeutischen Gesichtspunkten vertretbar. Aus diesem Grund schlagen viele Praktiker ihren wartenden Patienten niedrigschwellige Selbsthilfeangebote vor, die von psychoedukativen Informationen über Bibliotherapie bis zu Gruppenangeboten reichen. Die vorliegende Arbeit gibt einen Überblick über verschiedene Möglichkeiten, wartende Psychotherapiepatienten gut auf die bevorstehende Therapie vorzubereiten und während der Wartezeit zugleich sekundäre Prävention zu betreiben. Hierbei muss nach unserer Einschätzung vor allem die Maxime gelten, dass die vorgeschlagenen Maßnahmen mit dem Rational der darauf folgenden Therapie vereinbar sein sollten. / Even after the new psychotherapy law has been implemented, waiting times of several months remain rather common in the German mental health care system. For ethical, practical, and therapeutic reasons, however, patients who are in serious need of treatment should not be left unattended. Many practitioners therefore suggest self-help treatments such as psychoeducational information, bibliotherapy, or supportive groups to their waiting patients. The present study provides an overview on possibilities of preparing waiting psychotherapy patients for their upcoming therapy as well as implementing secondary prevention during the waiting time. As a basic, we suggest that the proposed methods should be in line with the treatment rationale of the subsequent therapy. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

This dissertation is concerned with the tail asymptotics of queueing networks with subexponential service time distributions. Our objective is to investigate the tail characteristics of key performance measures such as cycle times and waiting times on a variety of queueing models which may arise in many applications such as communication and manufacturing systems. First, we focus on a general class of closed feedforward fork and join queueing networks under the assumption that the service time distribution of at least one station is subexponential. Our goal is to derive the tail asymptotics of transient cycle times and waiting times. Furthermore, we argue that under certain conditions the asymptotic tail distributions remain the same for stationary cycle times and waiting times. Finally, we provide numerical experiments in order to understand how fast the convergence of tail probabilities of cycle times and waiting times is to their asymptotic counter parts. Next, we consider closed tandem queues with finite buffers between stations. We assume that at least one station has a subexponential service time distribution. We analyze this system under communication blocking and manufacturing blocking rules. We are interested in the tail asymptotics of transient cycle times and waiting times. Furthermore, we study under which conditions on system parameters a stationary regime exists and the transient results can be generalized to stationary counter parts. Finally, we provide numerical examples to understand the convergence behavior of the tail asymptotics of transient cycle times and waiting times. Finally, we study open tandem queueing networks with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max,+) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times. Finally, we provide numerical examples to investigate the convergence of the tail probabilities of transient response times and waiting times to their asymptotic counter parts.

Submitted by Ronildo Prado (ronisp@ufscar.br) on 2017-08-16T18:49:11Z No. of bitstreams: 1 DissVM.pdf: 10400529 bytes, checksum: 6f3a8dfea497dd3a1543a2b5847ad36e (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-08-16T18:49:21Z (GMT) No. of bitstreams: 1 DissVM.pdf: 10400529 bytes, checksum: 6f3a8dfea497dd3a1543a2b5847ad36e (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-08-16T18:49:27Z (GMT) No. of bitstreams: 1 DissVM.pdf: 10400529 bytes, checksum: 6f3a8dfea497dd3a1543a2b5847ad36e (MD5) / Made available in DSpace on 2017-08-16T18:49:35Z (GMT). No. of bitstreams: 1 DissVM.pdf: 10400529 bytes, checksum: 6f3a8dfea497dd3a1543a2b5847ad36e (MD5) Previous issue date: 2017-04-07 / Não recebi financiamento / Let {Xn} be a sequence of i.i.d. random variables taking values in an enumerable alphabet. Given a finite collection of words, we observe this sequence till the moment T at which one of these words appears as a run. In this work we apply the martingale approach introduced by Li (1980) and Gerber e Li (1981) in order to study the waiting time until one of the words occurs for the first time, the mean of T and the probability of a word to be the first one to appear. / Seja {Xn} uma sequência de variáveis aleatórias i.i.d. assumindo valores num alfabeto enumerável. Dada uma coleção de palavras finita, observamos esta sequência até o momento T em que uma dessas palavras apareça emX1,X2, .... Neste trabalho utilizamos a abordagem de martingais, introduzida por Li (1980) e Gerber e Li ( 981), para estudar o tempo de espera até que uma das palavras ocorra pela primeira vez, o tempo médio de T e a probabilidade de uma palavra ser a primeira a aparecer.