Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2007. / Jiangang Dai, Committee Co-Chair ; Amy Ward, Committee Co-Chair ; Anton Kleywegt, Committee Member ; Ron Billings, Committee Member ; Mor Armony, Committee Member.

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.

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.

We examine the problem of staffing refreshment stations at a long distance road race. A race is modeled as a mixed queueing network in which the required number of servers at each service station has to be estimated. Two models to represent the progress of runners along a long distance road race course are developed. One model is a single-class model that allows a road race manager to staff service stations assuming the runners are identical to those in some historical dataset. Another model is a multi-class simulation model that allows a road race manager to simulate a race of any number of runners, classified based on their running pace into different runner classes. Both the single-class model and the multi-class model include estimates for the rates at which the runners arrive at specified locations along the course. The arrival rates, combined with assumed service rates, allow us to base staffing decisions on the Erlang loss formula or a lesser known staffing rule that gives a lower bound for the required number of servers. We develop a staffing strategy that we call the Peak Arrival Staffing Bound (PASB), which is based on this staffing bound. The PASB and the Erlang loss formula are implemented in the single-class model and the multi-class simulation model. By way of numerical experiments, we find that the PASB is numerically stable and can be used to get staffing results regardless of the traffic intensity. This finding is in contrast to the Erlang loss formula, which is known to become numerically unstable and overflows when the traffic intensity exceeds 171. We compare numerical results of the PASB and the Erlang loss formula with a blocking probability level of 5% and find that when iii the traffic intensity is high, staffing results based on the PASB are more conservative than staffing results based on the Erlang loss formula. As the traffic intensity gets lower, we find that staffing results based on the PASB are similar to staffing results based on the Erlang loss formula. These findings suggest that the PASB can be a valuable tool to aid race directors in making staffing decisions for races of all traffic intensities

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.

In this paper we analyze the relationships between the flows of customers in a queueing network whose queue length process is a Markov process. A flow is a stochastic process formed by embedding the queue length process at transitions corresponding to: customers arriving to the network at a node; customers departing the network from a node; customers moving from one node to another node; all customers entering a node; all customers leaving a node; superpositions and decompositions of the flows described above. We show that flow processes in queueing networks are Markov renewal processes. In fact, we construct two Markov renewal processes corresponding to a flow. One Markov renewal process is formed by embedding the queue length process just before transitions of interest. The other Markov renewal process is formed by embedding the queue length process just after the transitions of interest. If a queueing network is a Jackson network and if the queue length process is reversible then the Markov renewal process formed by embedding the queue length process just before inputs to a node is the reverse process of the Markov renewal process formed by embedding the queue length process just after outputs from the node. Similar results hold for other flows in the network. We extend the above results to networks of symmetric queues where the service times are restricted to the Erlang distributed. To do this we need to introduce the concept of the quasi-reversed process of a Markov renewal process. A closed queueing network is constructed where the queue length process is not reversible yet the input process is the reverse process of the output process at each node. Another closed network is constructed where the queue length process is not reversible and the input process is not the reverse process of the output process at a node. From these two examples we conclude that reversibility is not a necessary condition for the input process to be the reverse process of the output process at a node and that the input process is not always the reverse process of the output process. Some implications of these results when applied to the decomposition or recomposition of stochastic processes are discussed. / Ph. D.

This thesis develops a stochastic model for satellite packet switching networks, using results from queueing theory that have been previously explored in modeling communication networks. This thesis also analyzes message queueing delay when users of the network are generating data at moderate to high rates. Average packet delay and average number of packets in the system are formulated. The model developed herein is applied to two cases. In the first case packet transmission and back off times are deterministic. In the second case packet transmission and back off times are exponentially distributed. The input parameters to this model are packet arrival rate, average packet transmission time, average back off time and probability of packet collision. The model yields average packet delay and average number of packets in the system. Methods to compute the probability of collision are presented. / Master of Science

Materials requirements planning (MRP) is a widely used method for production planning and scheduling. Planned lead-time (PLT) and lot size are two of the input parameters for MRP systems, which determine planned order release dates. Presently, planned lead-time and lot size are estimated using independent methodologies. No existing PLT estimation methods consider factors such as machine breakdown, scrap-rate, etc. Moreover, they do not consider the capacity of a shop, which changes dynamically, because the available capacity at any given time is determined by the loading of the shop at that time. The absence of such factors in calculations leads to a huge lead-time difference between the actual lead-time and PLT, i.e., lead-time error. Altering the size of a lot will have an effect not only on the lead-time of that lot but also on that of other lots. The estimation of lot size and lead-time using independent methodologies currently does not completely capture the inter-dependent nature of lead-time and lot size. In this research, a lot-sizing model is modified in such a way that it minimizes the combination of setup cost, holding cost and work-in-process cost. This proposed approach embeds an optimization routine, which is based on dynamic programming on a manufacturing system model, which is based on open queuing network theory. Then, it optimizes lot size by using realistic estimates of WIP and the lead-time of different lots simultaneously for single-product, single-level bills of material. Experiments are conducted to compare the performance of the production plans generated by applying both conventional and the proposed methods. The results show that the proposed method has great potential and it can save up to 38% of total cost and minimize lead-time error up to 72%. / Master of Science