Mostafa H. Ammar, Stanley B. Gershwin. / "August 1980." Caption title. / Bibliography: leaf 6. / National Science Foundation Grant DAR 78-17826

M.Ing. / Previous research have entailed developing various network traffic models which describe network traffic behaviour, but no model describes differential traffic treatment to such an extent to be able to relate the impact different rates have on the various traffic classes. The main reason for this being the amount of parameters that needs to be taken into consideration. Previous research performed in this field, analysed certain schedulers according to fixed parameters, thus having a very limited results base. No detailed comparison of these schedulers behaviour in a Differentiated Services (DiffServ) environment is available since the parameters under which their analysis were performed are different. A first objective entailed performing a thorough literature survey concerning DiffSery to summarize the research material that is available. This gives us as well as the reader a foundation to start any future research and the means to make good use of this information. Secondly, a DiffSery module was ported from an old version of Ns-2 which was developed for an older Linux kernel and GCC version; to the newest available. Ns-2 was also limited in respects to traffic generation. We developed a traffic generator that generates traffic according to a certain statistical distribution. This generation is performed according to packet size since distributions according to arrival time was partially implemented already. Our aim is to provide an in depth study regarding the performance of the various schedulers in the network and the effect various network parameters have on them. Since no real-network trace data is available, we resort to computer simulations. With Ns-2, we implement four different standardized perhop-behaviours (PHBs), namely expedited forwarding (EF), assured forwarding (AF1, AF2) and besteffort (BE). The evaluation focuses mainly on the EF PHB in regards to the other PHBs. The priority queuing (PQ), start-time fair queuing (SFQ), self-clocked fair queuing (SCFQ), weighted fair queuing (WFQ), worst-case weighted fair queuing plus (WF2Q+) and low latency queuing (LLQ) scheduling mechanisms are analysed to find their performance in relation to EF traffic and BE traffic. The QoS metrics that are focused on are: one-way delay (OWD), inter-packet delay variation (IPDV) and packet loss. We used Analysis of Variance (ANOVA) to analyse the impact of the various DiffSery node configuration parameters such as rates, packets sizes, schedulers and queue weights have on the output QoS metrics mentioned previously. Regression is then used to explain the relationship between several of these factors and metrics.

The simplest and most widely used queueing model in call centres is the M/M/k system, sometimes referred to as Erlang-C. For many applications the model is an over-simplification. Erlang-C model ignores among other things busy signals, customer impatience and services that span multiple visits. Although the Erlang-C formula is easily implemented, it is not easy to obtain insight from its answers (for example, to find an approximate answer to questions such as "how many additional agents do I need if the arrival rate doubles?"). An approximation of the Erlang-C formula that gives structural insight into this type of question would be of use to better understand economies of scale in call centre operations. Erlang-C based predictions can also turn out highly inaccurate because of violations of underlying assumptions and these violations are not straightforward to model. For example, non-exponential service times lead one to the M/G/k queue which, in stark contrast to the M/M/k system, is difficult to analyse. This thesis deals mainly with the general M/GI/k model with abandonment. The arrival process conforms to a Poisson process, service durations are independent and identically distributed with a general distribution, there are k servers, and independent and identically distributed customer abandoning times with a general distribution. This thesis will endeavour to analyse call centres using M/GI/k model with abandonment and the data to be used will be simulated using EZSIM-software. The paper by Brown et al. [3] entitled "Statistical Analysis of a Telephone Call Centre: A Queueing-Science Perspective," will be the basis upon which this thesis is built.

This dissertation focuses on the performance analysis of multiclass open queueing networks using semi-martingale reflecting Brownian motion (SRBM) approximation. It consists of four parts. In the first part, we derive a strong approximation for a multiclass feedforward queueing network, where jobs after service completion can only move to a downstream service station. Job classes are partitioned into groups. Within a group, jobs are served in the order of arrival; that is, a first-in-first-out (FIFO) discipline is in force, and among groups, jobs are served under a pre-assigned preemptive priority discipline. We obtain an SRBM as the result of strong approximation for the network, through an inductive approach. Based on the strong approximation, some procedures are proposed to approximate the stationary distribution of various performance measures of the queueing network. Our work extends and complements the previous work done on the feedforward queueing network. The numeric examples show that the strong approximation provides a better approximation than that suggested by a straightforward interpretation of the heavy traffic limit theorem. In the second part, we develop a Brownian approximation for a general multiclass queueing network with a set of single-server stations that operate under a combination of FIFO (first-in-first-out) and priority service disciplines and are subject to random breakdowns. Our intention here is to illustrate how to approximate a queueing network by an SRBM, not to justify such approximation. We illustrate through numerical examples in comparison against simulation that the SRBM model, while not always supported by a heavy traffic limit theorem, possesses good accuracy in most cases, even when the systems are moderately loaded. Through analyzing special networks, we also discuss the existence of the SRBM approximation in relation to the stability and the heavy traffic limits of the networks. In most queueing network applications, the stationary distributions of queueing networks are of great interest. It becomes natural to approximate these stationary distributions by the stationary distributions of the approximating SRBMs. Although we are able to characterize the stationary distribution of an SRBM, except in few limited cases, it is extremely difficult to obtain the stationary distribution analytically. In the third part of the dissertation, we propose a numerical algorithm, referred to as BNA/FM (Brownian network analyzer with finite element method), for computing the stationary distribution of an SRBM in a hypercube. SRBM in a hypercube serves as an approximate model of queueing networks with finite buffers. Our BNA/FM algorithm is based on finite element method and an extension of a generic algorithm developed in the previous work. It uses piecewise polynomials to form an approximate subspace of an infinite dimensional functional space. The BNA/FM algorithm is shown to produce good estimates for stationary probabilities, in addition to stationary moments. This is in contrast to the BNA/SM (Brownian network analyzer with spectral method) developed in the previous work, where global polynomials are used to form the approximate subspace and they sometime fail to produce meaningful estimates of these stationary probabilities. We also report extensive computational experiences from our implementation that will be useful for future numerical research on SRBMs. A three-station tandem network with finite buffers is presented to illustrate the effectiveness of the Brownian approximation model and our BNA/FM algorithm. In the last part of the dissertation, we extend the BNA/FM algorithm to calculate the stationary distribution of an SRBM in an orthant. This type of SRBM arises as a Brownian approximation model for queueing networks with infinite buffers. We prove the convergence theorems which justify the extension. A three-machine job shop example is presented to illustrate the accuracy of our extended BNA/FM algorithm. In fact, this extended algorithm is also used in the first two parts of this dissertation to analyze the performance of several queueing network examples and it gives fairly good performance estimates in most cases. / Business, Sauder School of / Graduate

In post-industrial economies, modern service systems are dramatically changing the daily lives of many people. Such systems are often complicated by uncertainty: service providers usually cannot predict when a customer will arrive and how long the service will be. Fortunately, useful guidance can often be provided by exploiting stochastic models such as queueing networks. In iterating the design of service systems, decision makers usually favor analytical analysis of the models over simulation methods, due to the prohibitive computation time required to obtain optimal solutions for service operation problems involving multidimensional stochastic networks. However, queueing networks that can be solved analytically require strong assumptions that are rarely satisfied, whereas realistic models that exhibit complicated dependence structure are prohibitively hard to analyze exactly. In this thesis, we continue the effort to develop useful analytical performance approximations for the single-class open queueing network with Markovian routing, unlimited waiting space and the first-come first-served service discipline. We focus on open queueing networks where the external arrival processes are not Poisson and the service times are not exponential. We develop a new non-parametric robust queueing algorithm for the performance approximation in single-server queues. With robust optimization techniques, the underlying stochastic processes are replaced by samples from suitably defined uncertainty sets and the worst-case scenario is analyzed. We show that this worst-case characterization of the performance measure is asymptotically exact for approximating the mean steady-state workload in G/G/1 models in both the light-traffic and heavy-traffic limits, under mild regularity conditions. In our non-parametric Robust Queueing formulation, we focus on the customer flows, defined as the continuous-time processes counting customers in or out of the network, or flowing from one queue to another. Each flow is partially characterized by a continuous function that measures the change of stochastic variability over time. This function is called the index of dispersion for counts. The Robust Queueing algorithm converts the index of dispersion for counts into approximations of the performance measures. We show the advantage of using index of dispersion for counts in queueing approximation by a renewal process characterization theorem and the ordering of the mean steady-state workload in GI/M/1 models. To develop generalized algorithm for open queueing networks, we first establish the heavy-traffic limit theorem for the stationary departure flows from a GI/GI/1 model. We show that the index of dispersion for counts function of the stationary departure flow can be approximately characterized as the convex combination of the arrival index of dispersion for counts and service index of dispersion for counts with a time-dependent weight function, revealing the non-trivial impact of the traffic intensity on the departure processes. This heavy-traffic limit theorem is further generalized into a joint heavy-traffic limit for the stationary customer flows in generalized Jackson networks, where the external arrival are characterized by independent renewal processes and the service times are independent and identically distributed random variables, independent of the external arrival processes. We show how these limiting theorems can be exploited to establish a set of linear equations, whose solution serves as approximations of the index of dispersion for counts of the flows in an open queueing network. We prove that this set of equations is asymptotically exact in approximating the index of dispersion for counts of the stationary flows. With the index of dispersion for counts available, the network is decomposed into single-server queues and the Robust Queueing algorithm can be applied to obtain performance approximation. This algorithm is referred to as the Robust Queueing Network Analyzer. We perform extensive simulation study to validate the effectiveness of our algorithm. We show that our algorithm can be applied not only to models with non-exponential distirbutions but also to models with more complex arrival processes than renewal processes, including those with Markovian arrival processes.

In recent years, increasing availability of data and advances in predictive analytics present new opportunities and challenges to healthcare management. Predictive models are developed to evaluate various aspects of healthcare systems, such as patient demand, patient pathways, and patient outcomes. While these predictions potentially provide valuable information to improve healthcare delivery, there are still many open questions considering how to integrate these forecasts into operational decisions. In this context, this dissertation develops methodologies to combine predictive analytics with the design of healthcare delivery systems. The first part of dissertation considers how to schedule proactive care in the presence of patient deterioration. Healthcare systems are typically limited resource environments where scarce capacity is reserved for the most urgent patients. However, there has been a growing interest in the use of proactive care when a less urgent patient is predicted to become urgent while waiting. On one hand, providing care for patients when they are less critical could mean that fewer resources are needed to fulfill their treatment requirement. On the other hand, due to prediction errors, the moderate patients who are predicted to deteriorate in the future may self cure on their own and never need the treatment. Hence, allocating limited resource for these patients takes the capacity away from other more urgent ones who need it now. To understand this tension, we propose a multi-server queueing model with two patient classes: moderate and urgent. We allow patients to transition classes while waiting. In this setting, we characterize how moderate and urgent patients should be prioritized for treatment when proactive care for moderate patients is an option. The second part of the dissertation focuses on the nurse staffing decisions in the emergency departments (ED). Optimizing ED nurse staffing decisions to balance the quality of service and staffing cost can be extremely challenging, especially when there is a high level of uncertainty in patient demand. Increasing data availability and continuing advancements in predictive analytics provide an opportunity to mitigate demand uncertainty by utilizing demand forecasts. In the second part of the dissertation, we study a two-stage prediction-driven staffing framework where the prediction models are integrated with the base (made weeks in advance) and surge (made nearly real-time) staffing decisions in the ED. We quantify the benefit of having the ability to use the more expensive surge staffing. We also propose a near-optimal two-stage staffing policy that is straightforward to interpret and implement. Lastly, we develop a unified framework that combines parameter estimation, real-time demand forecasts, and capacity sizing in the ED. High-fidelity simulation experiments for the ED demonstrate that the proposed framework can reduce annual staffing costs by 11%-16% ($2 M-$3 M) while guaranteeing timely access to care.

Students’ learning processes can be affected negatively by long waiting times to get assistance on lesson- and lab-sessions. Studies show that digital queuing systems decrease the waiting time. Thus, the purpose of this report is to investigate how to design a web-based queuing application to achieve a high perceived usability for students and tutors. Especially based on navigability and design which in accordance with research in the area has a direct impact on the usability. To achieve a high perceived usability the application was developed iteratively. In the first version the implemented functionality was built upon the result from the feasibility study combined with research in the area. After a set of user evaluations, changes from the first version were implemented to further improve the perceived usability. Lastly, another set of evaluations were performed to confirm the improvement in the final version. The results showed that the first version of the system was perceived as 84 out of 100 on the System Usability Scale (SUS) and the final version as 88 out of 100, an improvement by four units. Uniform design, no irrelevant functionality, placing buttons in conspicuous positions and having double checks to “dangerous actions” all seem to be factors contributing to the navigability, desirability and thus the usability on a queuing-application. / Studenters lärandeprocess kan påverkas negativt av långa väntetider för att få hjälp under lektions- och laborationspass. Studier visar att digitala kösystem reducerar väntetiden. Följaktligen är syftet med arbetet att undersöka hur en webb-baserad köapplikation kan designas för att uppnå en hög upplevd användbarhet hos studenter och handledare. Speciellt med avseende på navigerbarhet och design vilket enligt tidigare forskning har en direkt påverkan på användbarheten. För att uppnå en hög upplevd användbarhet utvecklades applikationen iterativt. I den första versionen implementerades funktionalitet som byggde på resultatet från förstudien i kombination med tidigare forskning. Efter användartester implementerades ändringar från den första versionen för att ytterlige förbättra användbarheten. Slutligen genomfördes ytterligare användartester för att bekräfta förbättringen i den slutgiltiga versionen. Resultatet visade att den första versionen av systemet uppfattades som 84 av 100 på systemanvändbarhetsskalan SUS och den slutgiltiga som 88 av 100, en förbättring med fyra enheter. Enhetlig design, ingen irrelevant funktionalitet, placering av knappar i iögonfallande positioner och att ha kontroller vid “farliga klick” verkar alla vara faktorer som bidrar till navigerbarheten, åtråvärdheten och där med användbarheten för en kö-applikation.

Recently, wireless access has become an essential part of modern society. Consequently, the demand for new wireless applications and services, as well as the number of wireless users, are gradually increasing. Given that this amount of expansion is eventually controlled by the available radio frequency spectrum, government regulatory agencies have recently adopted a strict approach to the licensing of limited amounts of spectrum to different entities (e.g., public safety, military, service providers, unlicensed devices, and TV). All of them possess exclusive transmissions to their assigned frequency channels. A new study on spectrum efficiency revealed big geographic and temporal variations in spectrum utilisation, ranging from 15-85% in the bands below 3GHz. These variations were less at frequencies above this figure. Recently, the Cognitive Radio (CR) has risen as an encouraging piece of technology to improve spectrum efficiency and to solve the problem of spectrum scarcity. This is because CR allows the secondary (unlicensed) users to occupy unused licensed spectrum bands temporarily, given that the interference of the primary (licensed) users is prohibited or minimised. In this thesis, various spectrum handoff management schemes have been proposed in order to improve the performance evaluation for CR networks. The proposed spectrum handoff schemes use the Opportunistic Spectrum Access (OSA) concept to utilise available spectrum bands. The handoff Secondary Users (SUs) have a higher priority to occupy available spectrum channels in the licensed and unlicensed spectrum bands without interfering with the legacy spectrum owner, i.e. primary users (PUs). However, existing spectrum handoff management schemes in CR networks do not provide high transmission opportunities for handoff secondary users to utilise the available radio spectrum resources. The first part of this thesis addresses the issue of spectrum handoff management in a licensed spectrum band environment. In this case, both reactive and proactive spectrum handoff schemes are proposed. Queuing theory or/and simulation experiments have been used to evaluate the performance of the proposed schemes and compare them with other existing schemes. Handoff delay has mainly been used to investigate the impact of successive handoff operations on the performance of the proposed CR networks. Implemented models have shown an improvement in the adopted performance measures. According to the achieved results, the improvement of the proposed, prioritised handoff schemes in some cases is approximately 75% when compared with existing schemes. On the other hand, the second part of this research proposed a prioritised spectrum handoff scheme in a heterogeneous spectrum environment, which is composed of a pool of licensed and unlicensed spectrum channels. In general, the availability of substantial numbers of the licensed spectrum channels is the key benefit of using this type of radio spectrum channel. Whereas, accessing with equal rights for all types of users is the main advantage of using unlicensed spectrum channels. In this respect, no transmission interruptions occur once a user obtains a channel. In addition, the proposed schemes use only the unlicensed spectrum channels as their backup channels. This enables the user to resume interrupted transmission in the case of the spectrum handoff operation (mainly; due to the appearance of the primary users), and thus facilitates a SUs communication. The proposed principle is investigated using a retrial queuing theory as well as extensive simulation experiments, and is compared with another non-prioritised scheme which do not give any preference to handoff SUs over new SUs. The results indicate that the proposed model has improved on current average handoff delay. This thesis contributes to knowledge by further enhancing the efficient utilisation of available radio spectrum resources and therefore subsequently provides an improvement in the spectrum capacity for wireless cognitive radio networks.

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