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.

The central thesis of this dissertation is that insight from queueing analysis can effectively guide standard (combinatorial) scheduling algorithms in dynamic environments. Scheduling is generally concerned with complex combinatorial decisions for static problems, whereas queueing theory simplifies the combinatorics and focuses on dynamic systems. We examine a queueing network with flexible servers under queueing and scheduling techniques. Based on the strengths of queueing analysis and scheduling, we develop a hybrid model that guides scheduling with results from the queueing model. In order to include setup times, we create a logic-based Benders decomposition model for a static representation of the queueing network. Our model is able to find optimal schedules up to 5 orders of magnitude faster than the only other model in the literature. A hybrid model is then developed for the dynamic problem and shown to achieve the best mean flow time while also guaranteeing maximal capacity.

The central thesis of this dissertation is that insight from queueing analysis can effectively guide standard (combinatorial) scheduling algorithms in dynamic environments. Scheduling is generally concerned with complex combinatorial decisions for static problems, whereas queueing theory simplifies the combinatorics and focuses on dynamic systems. We examine a queueing network with flexible servers under queueing and scheduling techniques. Based on the strengths of queueing analysis and scheduling, we develop a hybrid model that guides scheduling with results from the queueing model. In order to include setup times, we create a logic-based Benders decomposition model for a static representation of the queueing network. Our model is able to find optimal schedules up to 5 orders of magnitude faster than the only other model in the literature. A hybrid model is then developed for the dynamic problem and shown to achieve the best mean flow time while also guaranteeing maximal capacity.

We consider the optimal pricing problem in a service facility in order to maximize its long-run average profit per unit time. We model the facility as a queueing process that may have finite or infinite capacity. Customers are admitted into the system if it is not full and if they are willing to pay the price posted by the service provider. Moreover, the congestion level in the facility incurs penalties that greatly influence profit. We model congestion penalties in three different manners: holding costs, balking customers and impatient customers. First, we assume that congestion-dependent holding costs are incurred per unit of time. Second, we consider that each customer might be deterred by the system congestion level and might balk upon arrival. Third, customers are impatient and can leave the system with a full refund before being serviced. We are interested in both static and dynamic pricing for all three types of congestion penalties. In the static case, we demonstrate that there is a unique optimal price that maximizes the long-run average profit per unit time. We also investigate how optimal prices vary as system parameters change. In the dynamic case, we show the existence of an optimal stationary policy in a continuous and unbounded action space that maximizes the long-run average profit per unit time. We provide explicit expressions for this policy under certain conditions. We also analyze the structure of this policy and investigate its relationship with our optimal static price.

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Typescript (photocopy) / xvi 239 leaves : ill., charts ; 31 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Computing Science, 1982

In many branches of the economy, including transportation, lodging, and more recently cloud computing, users can reserve resources in advance. Although advance reservations are gaining popularity, little is known about the strategic behavior of customers facing the decision whether to reserve a resource in advance or not. Making an advance reservation can reduce the waiting time or the probability of not getting service, but it is usually associated with an additional cost. To evaluate this trade-off, we develop a game-theoretic framework, called advance reservation games, that helps in reasoning about the strategic behavior of customers in systems that allow advance reservations. Using this framework, we analyze several advance reservation models, in the context of slotted loss queues and waiting queues. The analysis of the economic equilibria, from the provider perspective, yields several key insights, including: (i) If customers have no a-priori information about the availability of servers, then only customers granted service should be charged a reservation fee; (ii) Informing customers about the exact number of available servers is less profitable than only informing them that servers are available; (iii) In many cases, the reservation fee that leads to the equilibrium with maximum possible profit leads to other equilibria, including one resulting with no profit; (iv) If the game repeats many times and customers update their strategy after observing actions of other customers at previous stage, then the system converges to an equilibrium where no one makes an advance reservation, if such an equilibrium exists. Else, the system cycles and yields positive profit to the provider Finally, we study the impact of information sharing in M/M/1 queues with strategic customers. We analyze the intuitive policy of sharing the queue length with customers when it is small and hiding it when it is large. We prove that, from the provider perspective, such a policy is never optimal. That is, either always sharing the queue length or always hiding it maximizes the average number of customers joining the queue.

A thesis based around saving response time costs as well as respecting electrical costs of a homogenous multi-server system. / In this thesis we consider the impacts of energy costs as they relate to Size Interval Task Assignment Equally--loaded (SITA-E) systems. We find that given systems which have small and large jobs being processed (high variance systems) we could in some cases find savings in terms of energy costs and in terms of lowering the mean response times of the system. How we achieve this is by first working from SITA-E, wherein servers are always on to Electrically Aware SITA-E (EA-SITA-E) by seeing if it is beneficial to make any of our servers rotate between being on and being off as needed. When most beneficial to do so we will turn off some of the servers in question, after this is completed we reallocate some of the jobs that are on the servers that we decide will be cycling to servers that will remain on indefinitely to better use their idle time. This also lowers the mean response time below what we originally saw with SITA-E, by lowering the variance in the sizes of jobs seen by the servers with the longest jobs. These long--job servers are by far the most impacted by the variance of the sizes of the jobs, so it is very desirable to lower this variance. The algorithm contained here can provide benefits in terms of both energy costs and mean response time under some specific conditions. Later we discuss the effect of errors in our assumed knowledge of task sizes. This research contributes methodology that may be used to expand on EA-SITA-E system design and analysis in the future. / Thesis / Master of Science (MSc) / The intention of this research is to be able to improve on existing size interval task-based assignment policies. We try to improve by turning servers off at key times to save energy costs, while not sacrificing too greatly in terms of mean response time of the servers, and in some cases even improving the mean response time through an intelligent re-balancing of the server loads.

Parameter estimation is a long-lasting topic in queueing systems and has attracted considerable attention from both academia and industry. In this thesis, we design a parameter estimation framework for a tandem queueing system that collects end-to-end measurement data and utilizes the finite mixture model for the maximum likelihood (ML) estimation. The likelihood equations produced by ML are then solved by the iterative expectation-maximization (EM) algorithm, a powerful algorithm for parameter estimation in scenarios involving complicated distributions. We carry out a set of experiments with different parameter settings to test the performance of the proposed framework. Experimental results show that our method performs well for tandem queueing systems, in which the constituent nodes' service time follow distributions governed by exponential family. Under this framework, both the Newton-Raphson (NR) algorithm and the EM algorithm could be applied. The EM algorithm, however, is recommended due to its ease of implementation and lower computational overhead. / Graduate / hangli@uvic.ca