Analysis of new schemes aimed at improving congestion in communications systems is vital for todays service providers. Many techniques are used to evaluate such schemes be it precisely via mathematics or approximately using simulation. This thesis introduces a new scheme, the multi priority dual queue (MPDQ). The MPDQ is the combination of two concepts, the dual queue introduced by [Hayes et. al., 1999] and prioritised traffic. The MPDQ is a system with finite waiting room with two queues where traffic upon arrival if finding the first queue full wait in the second queue if there is room. When a space becomes vacant in the first queue, a customer at the front of the second queue enters the back of the first, which is the queue that has the service centre at the front of it. The traffic can be of two or more classes. The analysis of such a system is complex, both analytically using queueing theory and approximately using simulation analysis. Both approaches are taken in this thesis. To begin, the new algorithmic approach used for the MPDQ is applied for the single buffer model. The steady state and waiting time distributions are obtained and later compared to the MPDQ. Next the performance characteristics are obtained by solving the steady state and waiting time distributions of a two class MPDQ. Preemptive and non-preemptive service disciplines are investigated. Maple is also used to solve the algorithm. To broaden the application of the MPDQ scheme, computer simulations using Arena are undertaken to extend the application of the scheme (and existing finite queueing models) to situations with more than two priorities, something that is extremely difficult to solve analytically. Using simulation, comparisons are undertaken for the single and dual queue schemes for more than two priorities with a variety of queueing disciplines used including First In First Out (FIFO), Last In First Out (LIFO), High Class First (HCF), and Low Class First (LCF). Network scenarios are also modelled to determine the performance of the MPDQ in this environment.

Thesis (Ph.D.)-- University of Adelaide, Dept. of Computing Science, 1982. / Typescript (photocopy).

This thesis includes three essays exploring some economic implications of queueing. A preliminary chapter introducing useful results from the literature which help contextualize the original research in the thesis is presented first. This introductory chapter starts by surveying queueing results from probability theory and operations research. Then it covers a few seminal papers on strategic queueing, mostly but not exclusively from the economics literature. These cover issues of individual and social welfare in the context of First Come First Served (FCFS) and Equitable Processor Sharing (EPS) queues, with one or multiple servers, as well as a discussion of strategic interactions surrounding queue cutting. Then an overview of some important papers on the impact of queueing on competitive behaviour, mostly Industrial Organization economists, is presented. The first original chapter presents a model for the endogenous determination of the number of queues in an M/M/2 system. Customers arriving at a system where two customers are being served play a game, choosing between two parallel queues or one single queue. Subgame perfect equilibria are obtained, varying with customer characteristics and game specifications. With risk neutrality and when jockeying is not permitted, a single queue is an equilibrium, as is two queues. With risk neutrality and jockeying allowed, there is a unique two queue equilibrium. With risk aversion and no jockeying, there is a unique single queue equilibrium, and with risk aversion and jockeying, the equilibrium depends on the magnitude of risk aversion. The second chapter analyses the individual decisions taken by consumers when deciding whether to join an M/M/1 queue where a subset of customers who interact repeatedly can both cut the queue and be overtaken once they join, by-passing occasional users. This is shown to be an equilibrium in repeated games for sufficiently patient customers. The expected sojourn time for customers under this discipline is described as a solution of a system of difference equations, and this is then used to obtain a threshold joining strategy for arrivals, which is independent of the number of regular customers in the queue, as regulars form a sub-queue under the LCFS discipline. Numerical methods are then employed to contrast sojourn times and thresholds with the equilibrium for a strict First Come First Served queueing discipline, and with the socially optimal joining rule. Finally, the third chapter describes a duopoly market for healthcare where one of the two providers is publicly owned and charges a price of zero, while the other sets a price so as to maximize its profit. Both providers are subject to congestion in the form of an M/M/1 queue, and they serve patient-customers with randomly distributed unit costs of time. Consumer demand (as market share) for both providers is obtained and described with its full complement of comparative statics. The private provider’s pricing decision is explored, and equilibrium existence is proven. Social welfare functions are described and the welfare maximizing condition obtained. Numerical simulations with uniform and Kumaraswamy distributions are performed for several parameter values, showcasing the pricing provider’s decision and its relationship with social welfare.

The bulk of this thesis considers how biological rhythms (oscillators) can be made to synchronize their rhythms by virtue of coupling to an external signal. Such externally controlled synchronization, known as entrainment, is explored using a synthetic biology approach in E.~coli, where I have used rationally designed gene circuits as an experimental model. Two novel modes of entrainment are explored: entrainment by competition between components for degradation, and entrainment by a noisy (aperiodic) stimulus. Both of these modes of entrainment can be shown to strongly synchronize ensembles of synthetic gene oscillators, and thus, these modes of entrainment may be important to understand the appearance of synchrony in natural systems. In addition to the study of entrainment, this thesis contains a general background of relevant material, contributions to the biophysics of multisite proteases, and updated protocols for experimental procedures in microfluidics and microscopy. / Ph. D.

Wireless scheduling is a fundamental problem in wireless networks that involves scheduling transmissions of multiple users in order to support data flows with as high rates as possible. This problem was first addressed by Tassuilas and Ephremides, resulting in the celebrated Back-Pressure network scheduling algorithm. This algorithm schedules network links to maximize throughput in an opportunistic fashion using instantaneous network state information (NSI), i.e., queue and channel state knowledge across the entire network. However, the Back-Pressure (BP) algorithm suffers from various drawbacks - (a) it requires knowledge of instantaneous NSI from the whole network, i.e. feedback about time-varying channel and queue states from all links of the network, (b) the algorithm requires solving a global optimization problem at each time to determine the schedule, making it highly centralized. Further, Back-pressure algorithm was originally designed for wireless networks where interference is modeled using protocol interference model. As recent break-throughs in full-duplex communications and interference cancelation techniques provide greatly increased capacity and scheduling flexibility, it is not clear how BP algorithm can be modified to improve the data rates and reduce the delay. In this thesis, we address the drawbacks of Back-Pressure algorithm to some extent. In particular, our first work provides a new scheduling algorithm (similar to BP) that allows users to make individual decisions (distributed) based on heterogeneously delayed network state information (NSI). Regarding the complexity issue, in our second work, we analyze the performance of the greedy version of BP algorithm, known as Greedy Maximal Scheduling (GMS) and understand the effect of channel variations on the performance of GMS. In particular, we characterize the efficiency ratio of GMS in wireless networks with fading. In our third and fourth work, we propose and analyze new scheduling algorithms that can benefit from new advancements in interference cancelation techniques. / text

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Network coding allows each node in a network to perform some coding operations on the data packets and improve the overall throughput of communication. However, network coding cannot be done unless there are enough packets to be coded so at times it may be advantageous to wait for packets to arrive. We consider a scenario in which two wireless nodes each with its own buffer communicate via a single access point using network coding. The access point first pairs each data packet being sent from each node and then performs the network coding operation. Packets arriving at the access point that are unable to be paired are instead loaded into one of the two buffers at the access point. In the case where one of the buffers is empty and the other is not network coding is not possible. When this happens the access point must either wait for a network coding opportunity, or transmit the unpaired packet without coding. Delaying packet transmission is associated with an increased waiting cost but also allows for an increase in the overall efficiency of wireless spectrum usage, thus a decrease in packet transmission cost. Conversely, sending packets un-coded is associated with a decrease in waiting cost but also a decrease in the overall efficiency of the wireless spectrum usage. Hence, there is a trade-off between decreasing packet delay time, and increasing the efficiency of the wireless spectrum usage. We show that the optimal waiting policy for this system with respect to total cost, under phase-type packet arrivals, is to have a separate threshold for the buffer size that is dependent on the current phase of each arrival. We then show that the solution to this optimization problem can be obtained by treating it as a double ended push-out queueing theory problem. We develop a new technique to keep track of the packet waiting time and the number of packets waiting in the two ended push-out queue. We use the resulting queueing model to resolve the optimal threshold policy and then analyze the performance of the system using numerical approach. / October 2016

無 / We derive the MacLaurin series for the moments of the idle time with respect to the parameters in the service time and interarrival time distributions for a GI/G/I queue. The light traffic derivatives are obtained to investigate the quality of a well-known MacLaurin series. The coefficients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The result for the idle period is easily taken as input to the calculation of other performance measures of the system, e.g., interdeparture time distributions. Numerical examples are given to illustrate these results.

Databases form the common component of many software systems, including mission critical transaction processing systems and multi-tier Internet applications. There is a large body of research in the performance of database management system components, while studies of overall database system performance have been limited. Moreover, performance models specifically targeted at the database design have not been extensively studied. This thesis attempts to address this concern by proposing a performance evaluation method for database designs based on queueing network models. The method is targeted at designs of large databases in which I/O is the dominant cost factor. The database design queueing network performance model is suitable in providing what if comparisons of database designs before database system implementation. A formal specification that captures the essential database design features while keeping the performance model sufficiently simple is presented. Furthermore, the simplicity of the modelling algorithms permits the direct mapping between database design entities and queueing network models. This affords for a more applicable performance model that provides relevant feedback to database designers and can be straightforwardly integrated into early database design development phases. The accuracy of the modelling technique is validated by modelling an open source implementation of the TPC-C benchmark. The contribution of this thesis is considered to be significant in that the majority of performance evaluation models for database systems target capacity planning or overall system properties, with limited work in detailed database transaction processing and behaviour. In addition, this work is deemed to be an improvement over previous methodologies in that the transaction is modelled at a finer granularity, and that the database design queueing network model provides for the explicit representation of active database rules and referential integrity constraints. / Iqra Foundation

Databases form the common component of many software systems, including mission critical transaction processing systems and multi-tier Internet applications. There is a large body of research in the performance of database management system components, while studies of overall database system performance have been limited. Moreover, performance models specifically targeted at the database design have not been extensively studied. This thesis attempts to address this concern by proposing a performance evaluation method for database designs based on queueing network models. The method is targeted at designs of large databases in which I/O is the dominant cost factor. The database design queueing network performance model is suitable in providing what if comparisons of database designs before database system implementation. A formal specification that captures the essential database design features while keeping the performance model sufficiently simple is presented. Furthermore, the simplicity of the modelling algorithms permits the direct mapping between database design entities and queueing network models. This affords for a more applicable performance model that provides relevant feedback to database designers and can be straightforwardly integrated into early database design development phases. The accuracy of the modelling technique is validated by modelling an open source implementation of the TPC-C benchmark. The contribution of this thesis is considered to be significant in that the majority of performance evaluation models for database systems target capacity planning or overall system properties, with limited work in detailed database transaction processing and behaviour. In addition, this work is deemed to be an improvement over previous methodologies in that the transaction is modelled at a finer granularity, and that the database design queueing network model provides for the explicit representation of active database rules and referential integrity constraints. / Iqra Foundation