Design and management decisions require an accurate prediction of the performance of the network. Network performance estimation techniques require accurate network traffic models. In this thesis we are concerned with the modelling of network traffic for the wireless mesh network (WMN) environment. Queueing theory has been used in the past to model the WMN environment and we found in this study that queueing theory was used in two main methods to model WMNs. The first method is to consider each node in the network in terms of the number of hops it is away from the gateway. Each node is then considered as a queueing station and the parameters for the station is derived from the number of hops each node is away from the gateway. These topologies can be very limiting in terms of the number of physical topologies they can model due to the fact that their parameters are only dependent on the number of hop-counts each node is away from the gateway. The second method is to consider a fixed topology with no gateways. This method simplifies analysis but once again is very limiting. In this dissertation we propose a queueing based network traffic model that uses a connection matrix to define the topology of the network. We then derive the parameters for our model from the connection matrix. The connection matrix allows us to model a wider variety of topologies without modifying our model. We verify our model by comparing results from our model to results from a discrete event simulator and we validate our model by comparing results from our model to results from models previously proposed by other authors. By comparing results from our model to results of other models we show that our model is indeed capable of modelling a wider variety of topologies. / Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013.

Design and management decisions require an accurate prediction of the performance of the network. Network performance estimation techniques require accurate network traffic models. In this thesis we are concerned with the modelling of network traffic for the wireless mesh network (WMN) environment. Queueing theory has been used in the past to model the WMN environment and we found in this study that queueing theory was used in two main methods to model WMNs. The first method is to consider each node in the network in terms of the number of hops it is away from the gateway. Each node is then considered as a queueing station and the parameters for the station is derived from the number of hops each node is away from the gateway. These topologies can be very limiting in terms of the number of physical topologies they can model due to the fact that their parameters are only dependent on the number of hop-counts each node is away from the gateway. The second method is to consider a fixed topology with no gateways. This method simplifies analysis but once again is very limiting. In this dissertation we propose a queueing based network traffic model that uses a connection matrix to define the topology of the network. We then derive the parameters for our model from the connection matrix. The connection matrix allows us to model a wider variety of topologies without modifying our model. We verify our model by comparing results from our model to results from a discrete event simulator and we validate our model by comparing results from our model to results from models previously proposed by other authors. By comparing results from our model to results of other models we show that our model is indeed capable of modelling a wider variety of topologies. / Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013.

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-12-10T14:45:42Z No. of bitstreams: 2 Dissertação - Murilo Antonio de Oliveira - 2015.pdf: 1647647 bytes, checksum: 5b2f01764dbbc90bb9c3b4c20c2a32f7 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-12-11T09:25:38Z (GMT) No. of bitstreams: 2 Dissertação - Murilo Antonio de Oliveira - 2015.pdf: 1647647 bytes, checksum: 5b2f01764dbbc90bb9c3b4c20c2a32f7 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2015-12-11T09:25:38Z (GMT). No. of bitstreams: 2 Dissertação - Murilo Antonio de Oliveira - 2015.pdf: 1647647 bytes, checksum: 5b2f01764dbbc90bb9c3b4c20c2a32f7 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2015-08-27 / Waiting lines are boldly present in our society following us since the beginnings of civilization. Sometimes they occur in a traditional way with a well-seen aspect and thus look like similar to the model we already have in mind, but also there are times in which waiting lines occur in di erent formats becoming unperceivable to the common observer not yet introduced to the Queuing Theory. The present study aims in demonstrating the applicability of Mathematics. Statistics and the Queuing Theory to real tasks such as the waiting line of a bank cashier in the City of Jataí-Goiás. In this regard we present a short history of the Queuing Theory embracing its advent, the rst task to be dealt with, the de nitions and the adopted terminology looking forward to subsidize a theoretical base in an introductory level. As our object of observation is a waiting line of a bank cashier we additionally present a short history of the National Financial System in which comprehends every bank, and also the municipal law that rules the maximum waiting time in a line. After the choice of a bank agency in the City of Jataí-Goiás we succeeded to get access to the detailing tape of the cashiers under managers authorization. The tape has all the data about daily transactions. The time of analysis refers to the month of November 2014. After appropriate organization and data cataloging, they were processed according to the Queuing Theory illustrating its applicability. Results allowed us to work a few mathematical concepts, specially the idea of average. However, more detailed results and analysis were not dealt with in this work due to its complexity but will be considered in future studies that might take the present work as a starting point. / As las tem presença marcante em nossa sociedade e nos acompanham desde o início da civilização. Algumas vezes manifestam-se de forma tradicional e apresentam caráter bastante visual assemelhando-se assim ao modelo que temos em nossas mentes, mas às vezes manifestam-se de formas variadas e tornam-se imperceptíveis ao olhar não familiarizado com a Teoria das Filas. O presente texto teve como propósito mostrar a aplicabilidade da matemática, estatística e Teoria das Filas a problemas reais tal como a la de guichê de caixa de uma agência bancária da cidade de Jataí-Go. Para isso apresentamos um breve histórico da Teoria das Filas, contemplando o seu surgimento, o primeiro problema estudado, as de nições e os termos empregados visando subsidiar um embasamento teórico em nível básico. Por ter se pautado na análise da la do caixa de uma agência bancária complementarmente apresentamos um breve histórico do Sistema Financeiro Nacional - SFN no qual todos os bancos encontram-se inseridos e a lei municipal que normatiza o tempo máximo de espera em la. Após escolhido uma agência bancária na cidade de Jataí-Go conseguimos com a autorização do gerente a ta detalhe dos caixas, a qual nos apresenta os dados referentes a movimentação diária. O período de análise refere-se ao mês de novembro do ano de 2014. Após a devida organização e catalogação os dados foram tratados sob o olhar da Teoria das Filas ilustrando a aplicabilidade desta teoria. Os resultados possibilitaram trabalhar alguns conceitos básicos da matemática, em especí co o conceito de média. Contudo, resultados e análises mais elaboradas deixaram de ser tratadas no presente texto, devido a sua complexidade, mas serão analisados em textos futuros que poderão ter este como ponto de partida.

Scheduling policies adopted for statistical multiplexing should provide delay differentiation between different traffic classes, where each class represents an aggregate traffic of individual applications having same target-queueing-delay requirements. We propose scheduling to optimally balance weighted mean instanteneous queue lengths and later weighted mean cumulative queue lengths as an approach to delay differentiation, where the class weights are set inversely proportional to the respective products of target delays and packet arrival rates. In particular, we assume a discrete-time, two-class, single-server queueing model with unit service time per packet and provide mathematical frame-work throughout our work. For iid Bernoulli packet arrivals, using a step-wise cost-dominance analytical approach using instantaneous queue lengths alone, for a class of one-stage cost functions not necessarily convex, we find the structure of the total-cost optimal policies for a part of the state space. We then consider two particular one-stage cost functions for finding two scheduling policies that are total-cost optimal for the whole state-space. The policy for the absolute weighted difference cost function minimizes the stationary mean, and the policy for the weighted sum-of-square cost function minimizes the stationary second-order moment, of the absolute value of the weighted difference of queue lengths. For the case of weighted sum-of-square cost function, the ‘iid Bernoulli arrivals’ assumption can be relaxed to either ‘iid arrivals with general batch sizes’ or to ‘Markovian zero-one arrivals’ for all of the state space, but for the linear switching curve. We then show that the average cost, starting from any initial state, exists, and is finite for every stationary work-conserving policy for our choices of the one-stage cost-function. This is shown for arbitrary number of class queues and for any i.i.d. batch arrival processes with finite appropriate moments. We then use cumulative queue lengths information in the one-step cost function of the optimization formulation and obtain an optimal myopic policy with 3 stages to go for iid arrivals with general batch sizes. We show analytically that this policy achieves the given target delay ratio in the long run under finite buffer assumption, given that feasibility conditions are satisfied. We take recourse to numerical value iteration to show the existence of average-cost for this policy. Simulations with varied class-weights for Bernoulli arrivals and batch arrivals with Poisson batch sizes show that this policy achieves mean queueing delays closer to the respective target delays than the policy obtained earlier. We also note that the coefficients of variation of the queueing delays of both the classes using cumulative queue lengths are of the same order as those using instantaneous queue lengths. Moreover, the short-term behaviour of the optimal myopic policy using cumulative queue lengths is superior to the existing standard policy reported by Coffman and Mitrani by a factor in the range of 3 to 8. Though our policy performs marginally poorer compared to the value-iterated, sampled, and then stationarily employed policy, the later lacks any closed-form structure. We then modify the definition of the third state variable and look to directly balance weighted mean delays. We come up with another optimal myopic policy with 3 stages to go, following which the error in the ratio of mean delays decreases as the window-size, as opposed to the policy mentioned in the last paragraph, wherein the error decreases as the square-root of the window-size. We perform numerical value-iteration to show the existence of average-cost and study the performance by simulation. Performance of our policy is comparable with the value-iterated, sampled, and then stationarily employed policy, reported by Mallesh. We have then studied general inter-arrival time processes and obtained the optimal myopic policy for the Pareto inter-arrival process, in particular. We have supported with simulation that our policy fares similarly to the PAD policy, reported by Dovrolis et. al., which is primarily heuristic in nature. We then model the possible packet errors in the multiplexed channel by either a Bernoulli process, or a Markov modulated Bernoulli process with two possible channel states. We also consider two possible round-trip-time values for control information, namely zero and one-slot. The policies that are next-stage optimal (for zero round-trip-time), and two-stage optimal (for one-slot round-trip-time) are obtained. Simulations with varied class-weights for Bernoulli arrivals and batch arrivals with Poisson batch sizes show that these policies indeed achieve mean queueing delays very close to the respective target delays. We also obtain the structure for optimal policies with N = 2 + ⌈rtt⌉ stages-to-go for generic values of rtt, and which need not be multiple of time-slots.

Thousands of call centers operate in the United States employing millions of people. Since personnel costs represent as much as 80% of the total operating expense of these centers, it is important for call center managers to determine an appropriate staffing level required to maintain the desired operating performance. Historically, queueing models serve an important role in this regard. The one most commonly used is the Erlang-C model. The Erlang-C model has several assumptions, however, which are required for the predicted performance measures to be valid. One assumption that has received significant attention from researchers is that callers have infinite patience and will not terminate a call until the service is complete regardless of the wait time. Since this assumption is not likely to occur in reality, researchers have suggested using Erlang-A instead. Erlang-A does consider caller patience and allows for calls to be abandoned prior to receiving service. However, the use of Erlang-A still requires an assumption that is very unlikely to occur in practice - the assumption that all agents provide service at the same rate. Discrete event simulation is used to examine the effects of agent heterogeneity on the operating performance of a call center compared to the theoretical performance measures obtained from Erlang-A. Based on the simulation results, it is concluded that variability in agent service rate does not materially affect call center performance except to the extent that the variability changes the average handle time of the call center weighted by the number of calls handled and not weighted by agent. This is true regardless of call center size, the degree of agent heterogeneity, and the distribution shape of agent variability. The implication for researchers is that it is unnecessary to search for an analytic solution to relax the Erlang-A assumption that agents provide service at the same rate. Several implications for managers are discussed including the reliability of using Erlang-A to determine staffing levels, the importance of considering the service rates of the agents rather than the average handle time, and the unintended consequence of call routing schemes which route calls to faster rather than slower agents.

The advancement of wireless technology has led to an increase in the employment of wireless sensor networks (WSNs). Traditionally, WSNs are powered by batteries. However, the high power consump- tion and the need to change the batteries regularly has made these networks costly to maintain. The nodes in the WSNs are increasingly strained as power consumption increases and the batteries are depleted faster. This has consequently decreased the overall lifetime of the WSNs. Although many energy-conserving techniques exist, for example energy-efficient medium access control and energy-efficient routing protocols, energy consumption remains one of the significant constraints in the development of WSNs. A natural solution to this constraint is harvesting energy from the environment. However, unlike conventional energy, energy harvested from the environment is random in nature, making it challenging to realise energy-harvesting transmission schemes. Although energy harvesting might be considered a solution to many problems, it brings about new challenges with regard to the usage and management of the energy harvested. Some of these challenges include uneven consumption of power in the network, resulting in dead nodes in some portion of the network and the batteries used in the network are being affected negatively by the energy usage; they may consequently sustain the nodes for long or short periods. To analyse the usage and consumption of energy, a number of techniques have been proposed, namely; information theory, game theory and queueing theory. By this time, the performance of the sensor nodes in WSNs has been analysed making use of a queueing-theoretic model for each sensor. The aforementioned model inadequately expresses the physical constraints, namely, the energy drawing process and the finite battery capacity. This research focuses on developing a model that captures the harvesting, accumulation and dissipation of energy, utilising queueing theory. A rechargeable battery with a finite storage capacity will be used. To ensure that the battery does not lose its capability to store charge after being recharged repeatedly, the leaky bucket model is proposed to check the network data flow as the harvested energy in the WSN is analysed. To capture real-world WSNs with energy harvesting in which there is energy leakage, the energy- harvesting sensor node performance is analysed with two assumptions: data transmission and energy leakage occurring and the token buffer being subjected to a threshold. The system had finite buffers for the data and energy. To make it possible to have some influence over the system performance measures a threshold is imposed on the token buffer. Four models are developed: a basic model, a basic model with leakage incorporated, a basic model with leakage and priority incorporated and a basic model with leakage, priority and threshold incorporated. The developed models are simulated and results for the performance measures are obtained. / Dissertation (MEng (Computer Engineering))--University of Pretoria, 2021. / BWMC, NRF / Electrical, Electronic and Computer Engineering / MEng (Computer Engineering) / Unrestricted

With the increase in wireless technology devices and mobile users, wireless radio spectrum is coming under strain. Networks are becoming more and more congested and free usable spectrum is running out. This creates a resource allocation problem. The resource, wireless spectrum, needs to be allocated to users in a manner such that it is utilised efficiently and fairly. The objective of this research is to find a solution to the resource allocation problem in radio networks, i.e to increase the efficiency of spectrum utilisation by making maximum use of the spectrum that is currently available through taking advantage of co-existence and exploiting interference limits. The solution proposed entails adding more secondary users (SU) on a cognitive radio network (CRN) and having them transmit simultaneously with the primary user. A typical network layout was defined for the scenario. The interference temperature limit (ITL) was exploited to allow multiple SUs to share capacity. Weighting was applied to the SUs and was based on allowable transmission power under the ITL. Thus a more highly weighted SU will be allowed to transmit at more power. The weighting can be determined by some network-defined rule. Specific models that define the behaviour of the network were then developed using queuing theory, specifically weighted processor sharing techniques. Optimisation was finally applied to the models to maximize system performance. Convex optimization was deployed to minimize the length of the queue through the power allocation ratio. The system was simulated and results for the system performance obtained. Firstly, the performance of the proposed models under the processor-sharing techniques was determined and discussed, with explanations given. Then optimisation was applied to the processor-sharing results and the performance was measured. In addition, the system performance was compared to other existing solutions that were deemed closest to the proposed models. / Dissertation (MEng)--University of Pretoria, 2017. / Electrical, Electronic and Computer Engineering / MEng / Unrestricted

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