<p>Queueing models have been used extensively in the design of call centres. In particular, a queueing model will be used to describe a help desk which is a form of a call centre. The design of the queueing model involves modelling the arrival an service processes of the system.</p><p>Conventionally, the arrival process is assumed to be Poisson and service times are assumed to be exponentially distributed. But it has been proposed that practically these are seldom the case. Past research reveals that the log-normal distribution can be used to model the service times in call centres. Also, services may involve stages/tasks before completion. This motivates the use of a phase-type distribution to model the underlying stages of service.</p><p>This research work focuses on developing statistical models for the overall service times and the service times by job types in a particular help desk. The assumption of exponential service times was investigated and a log-normal distribution was fitted to service times of this help desk. Each stage of the service in this help desk was modelled as a phase in the phase-type distribution.</p><p>Results from the analysis carried out in this work confirmed the irrelevance of the assumption of exponential service times to this help desk and it was apparent that log-normal distributions provided a reasonable fit to the service times. A phase-type distribution with three phases fitted the overall service times and the service times of administrative and miscellaneous jobs very well. For the service times of e-mail and network jobs, a phase-type distribution with two phases served as a good model.</p><p>Finally, log-normal models of service times in this help desk were approximated using an order three phase-type distribution.</p>

<p>Queueing models have been used extensively in the design of call centres. In particular, a queueing model will be used to describe a help desk which is a form of a call centre. The design of the queueing model involves modelling the arrival an service processes of the system.</p><p>Conventionally, the arrival process is assumed to be Poisson and service times are assumed to be exponentially distributed. But it has been proposed that practically these are seldom the case. Past research reveals that the log-normal distribution can be used to model the service times in call centres. Also, services may involve stages/tasks before completion. This motivates the use of a phase-type distribution to model the underlying stages of service.</p><p>This research work focuses on developing statistical models for the overall service times and the service times by job types in a particular help desk. The assumption of exponential service times was investigated and a log-normal distribution was fitted to service times of this help desk. Each stage of the service in this help desk was modelled as a phase in the phase-type distribution.</p><p>Results from the analysis carried out in this work confirmed the irrelevance of the assumption of exponential service times to this help desk and it was apparent that log-normal distributions provided a reasonable fit to the service times. A phase-type distribution with three phases fitted the overall service times and the service times of administrative and miscellaneous jobs very well. For the service times of e-mail and network jobs, a phase-type distribution with two phases served as a good model.</p><p>Finally, log-normal models of service times in this help desk were approximated using an order three phase-type distribution.</p>

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal.

In order to make statistical inference, that is drawing conclusions from a sample to describe a population, it is crucial to know the correct distribution of the data. This paper focused on censored data from the normal distribution. The purpose of this paper was to answer whether we can test if data comes from a censored normal distribution. This by using normality tests and tests designed for censored data and investigate if we got correct size of these tests. This has been carried out with simulations in the program R for left censored data. The results indicated that with increasing censoring normality tests failed to accept normality in a sample. On the other hand the censoring tests met the requirements with increasing censoring level, which was the most important conclusion in this paper.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

This thesis analyzes the end-user quality of service (QoS) in cellular mobile networks using device-side measurements. Quality of service in a wireless network is a significant factor in determining a user's satisfaction. Customers' perception of poor QoS is one of the core sources of customer churn for telecommunications companies. A core focus of this work is on assessing how user density impacts QoS within cellular networks. Kernel density estimation is used to produce user density estimates for high, medium, and low density areas. The QoS distributions are then compared across these areas. The k-sample Anderson-Darling test is used to determine the degree to which user densities vary over time. In general, it is shown that users in higher density areas tend to experience overall lower QoS levels than those in lower density areas, even though these higher density areas service more subscribers. The conducted analyses highlight the value of mobile device-side QoS measurements in augmenting traditional network-side QoS measurements. / Graduate

When data is collected sample size and precision in measurements are often limited. In what sense this impacts the size, unadjusted and adjusted power of different normality tests is a relatively unexplored field. Therefore this paper is dedicated to perform a simulation study where these three properties of the normality tests Anderson-Darling, Jarque-Bera and Shapiro-Wilk are examined. The study is based on different combinations of sample sizes and roundings where repeated samples are drawn from both normally and asymmetrically distributed populations. The results from the study indicate that coarser roundings results in increased size and unadjusted power of Anderson-Darling and Shapiro-Wilk, while Jarque-Bera is seemingly unaffected by roundnings. The three tests have in common that a larger sample size leads to an increase in the size, unadjusted and adjusted power of the tests and that roundings have no substantial impact on adjusted power. / När data samlas in är ofta stickprovsstorlek och precision i mätningarna begränsad i olika grad. Vilken betydelse detta får för sannolikheten för typ I-fel, ojusterad samt justerad styrka hos olika normalitetstest är ett förhållandevis outforskat område. Därför dedikeras denna uppsats till att genomföra en simuleringsstudie där dessa tre egenskaper hos normalitetstesten Anderson-Darling, Jarque-Bera samt Shapiro-Wilk undersöks. Studien baseras på olika kombinationer av stickprovsstorlekar samt avrundningar där upprepade stickprov dras från både normalfördelade och asymmetriskt fördelade populationer. Resultaten från studien indikerar att grövre avrundningar leder till ökad sannolikhet för typ I-fel och ojusterad styrka hos Anderson-Darling och Shapiro-Wilk, medan Jarque-Bera inte påverkas nämnvärt av avrundningar. Gemensamt för samtliga test är att en större stickprovsstorlek leder till ökad sannolikhet för typ I-fel, ojusterad styrka och justerad styrka samt att avrundningar inte nämnvärt påverkar justerad styrka.

This paper presents a stability analysis of the sensor data which is collected by QTAGG from alarge ocean going ship and using the stability results, introduces some information about howthe measurements that come from the sensors can be improved and how reliable they are. In thetheoretical part, some background information is given mainly based on British Standard(BS)ISO 19030 which was published in November, 2016. This source basically includes someinformation about the measurement of changes in hull and propeller performance of a vessel.Using the theoretical information, in the implementation part, the necessary methods areimplemented in python programming language on a real life data set of a vessel which is givenfrom QTAGG company. To measure the stability of the parameters in the data, we loosenthe filters of the parameters and observe how they respond to the technical changes. In orderto understand how loosen the filters can be made, a reference speed-power curve is createdby using a curve fitting method, and after creating a performance indicator by utilizing thereference curve, Anderson-Darling and Shapiro-Wilk tests are used to measure the stability ofthe performance indicator. Besides these numerical tests, some visual methods such as Q-Qplot and histogram plot are also used in this process. Finally, we could provide stability resultsby using both our theoretical knowledge and the practical implementation.

To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test.

To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test.