Wireless networks promise ubiquitous communication, and thus facilitate an array of applications that positively impact human life. At a fundamental level, these networks deal with compression and transmission of sources over channels. Thus, accomplishing this task efficiently is the primary challenge shared by these applications. In practice, sources include data and video while channels include interference and relay networks. Hence, effective source and channel aware resource allocation for these scenarios would result in a comprehensive solution applicable to real-world networks. This dissertation studies the problem of source and channel aware resource allocation in certain scenarios. A framework for network resource allocation that stems from rate-distortion theory is presented. Then, an optimal decomposition into an application-layer compression control, a transport-layer congestion control and a network-layer scheduling is obtained. After deducing insights into compression and congestion control, the scheduling problem is explored in two cross-layer scenarios. First, appropriate queue architecture for cooperative relay networks is presented, and throughput-optimality of network algorithms that do not assume channel-fading and input-queue distributions are established. Second, decentralized algorithms that perform rate allocation, which achieve the same overall throughput region as optimal centralized algorithms, are derived. In network optimization, an underlying throughput region is assumed. Hence, improving this throughput region is the next logical step. This dissertation addresses this problem in the context of three significant classes of interference networks. First, degraded networks that capture highly correlated channels are explored, and the exact sum capacity of these networks is established. Next, multiple antenna networks in the presence of channel uncertainty are considered. For these networks, robust optimization problems that result from linear precoding are investigated, and efficient iterative algorithms are derived. Last, multi-cell time-division-duplex systems are studied in the context of corrupted channel estimates, and an efficient linear precoding to manage interference is developed. / text

Baigiamojo darbo tikslas – sukurti masinio aptarnavimo sistemų modeliavimo programinę įrangą ir sumodeliuoti bei ištirti įvairias masinio aptarnavimo kompiuterines sistemas. Modeliavimo programinė įranga buvo parašyta C# programavimo kalba. Programos branduolys – Delsi 2.0 masinio aptarnavimo sistemų modeliavimo biblioteka. Sukurta programa buvo sumodeliuota ir ištirta keletas masinio aptarnavimo sistemų: sistemos su apribotu paraiškų eilės ilgiu, sistemos su apribotu paraiškų laukimo eilėje laiku, mišrios sistemos, vieno ir daugelio aptarnavimo kanalų sistemos. Taip pat buvo sumodeliuotas vidutinio dydžio kompiuterių tinklo komutatoriaus darbas ir ištirtos jo pagrindinės charakteristikos. Nustatyta optimali komutatoriaus paketų aptarnavimo sparta ir optimalus paketų buferio dydis. Darbo apimtis – 51 p. teksto be priedų, 14 iliustracijų, 6 lentelės, 16 bibliografinių šaltinių. / Master thesis objective – to create universal modeling software for queueing systems and with its help to conduct simulation experiments, investigating several various queueing systems. The software was written with the help of C# programming language. The core of the created software is Delsi. 2.0 simulation library. Using created software several different queueing systems were modeled and investigated: systems with the restricted queue length, systems with the restricted transaction waiting time in a queue, combined systems, semi- and multichannel systems. Also there was modeled the operation of a middle-sized computer network switch and its main characteristics were investigated. The optimal packet serving rate and packet buffer size of the switch were found. Thesis consists of: 51 p. of text without extras, 14 illustrations, 6 tables, 16 bibliographical entries.

This thesis explores the queueing performance of a wireless communication system that transmits packets over a correlated erasure channel using the IEEE 802.11 protocol suit. The channel states and the queue length together form a Markov chain. Exploiting this mathematical structure, the probability of the queue exceeding a certain threshold can be obtained. Most previous contributions in this area treat code-rate selection, channel erasure probability and network congestion separately. In this thesis, a simple integrated approach, which jointly considers these factors, is introduced. This approach becomes especially valuable for capturing the performance of delay-sensitive communication systems over time-varying channels. This thesis starts with a review of related work about correlated bit-erasure wireless channel models. A numerical study is then conducted to demonstrate the importance of optimizing overall system performance, and how this process impacts error-control coding at the physical layer. Following this exercise, a packet-erasure channel model with a Poisson arrival process is analyzed. The Baum-Welch algorithm is subsequently presented as a means to estimate the parameters of wireless communication systems. Furthermore, a matrix geometric method for obtaining the stationary distribution of the ensuing Markov chain is discussed. This offers a new perspective on wireless communication in the context of delay-sensitive applications. To complement the analysis platform put forth in this work, illustrative numerical results are contained in the last section of the thesis. From these results, design guidelines for improving the performance of delay-sensitive wireless communication systems are established. Although these results are obtained under simplifying assumptions, the overall methodology applies to more general situations, especially for wide-band delay-sensitive wireless communication applications.

Wireless communication systems continue to face the challenge of time varying quality of the underlying communication channel. When a slow fading channel goes into a deep fade, the corresponding communication system might face successive decoding failures at the destination, and for delay-sensitive communication systems, this amounts to delays that are not desired. In such situations, it becomes a priority to get out of the deep fades. Many techniques and approaches are already available in the literature to counteract fading effects. This work is motivated by recent advances in fast reconfigurable antennas, which provide new means to change the statistical profile of fading channels, and hence reduce the probability of prolonged fades. Fast reconfigurable antennas are poised to improve overall performance, especially for delay-sensitive traffic in slow-fading environments. This potential enhanced performance motivates this study of the queueing behavior of point-to-point communication systems with reconfigurable antennas. We focus on finite-state channels with memory, and we analyze the queueing behavior of the wireless communication system over erasure channels, for a traditional system versus a reconfigurable antenna implementation. We provide numerical results for situations where using reconfigurable antennas yield substantial performance gains in terms of throughput, delay and buffer overflow.

Decomposition methods based on the hierarchical partitioning of the state space of queueing network models offer powerful evaluation tools for the performance analysis of computer systems and communication networks. These methods being conventionally implemented capture the exact solution of separable queueing network models but their credibility differs when applied to general queueing networks. This thesis provides a universal information theoretic framework for the implementation of hierarchical decomposition schemes, based on the principle of minimum relative entropy given fully decomposable subset and aggregate utilization, mean queue length and flow-balance constraints. This principle is used, in conjuction with asymptotic connections to infinite capacity queues, to derive new closed form approximations for the conditional and marginal state probabilities of general queueing network models. The minimum relative entropy solutions are implemented iteratively at each decomposition level involving the generalized exponential (GE) distributional model in approximating the general service and asymptotic flow processes in the network. It is shown that the minimum relative entropy joint state probability, subject to mean queue length and flow-balance constraints, is identical to the exact product-form solution obtained as if the network was separable. An investigation into the effect of different couplings of the resource units on the relative accuracy of the approximation is carried out, based on an extensive experimentation. The credibility of the method is demonstrated with some illustrative examples involving first-come-first-served general queueing networks with single and multiple servers and favourable comparisons against exact solutions and other approximations are made.

Priority based scheduling disciplines are widely used by existing computer operating systems. However, the mathematical analysis and modelling of these systems present great difficulties since priority schedulling is not compatible with exact product form solutions of queueing network models (QNM's). It is therefore, necessary to employ credible approximate techniques for solving QNM's with priority classes. The principle of maximum entropy (ME) is a method of inference for estimating a probability distribution given prior information in the form of expected values. This principle is applied, based on marginal utilisation, mean queue length and idle state probability constraints, to characterise new product-form approximations for general open and closed QNM's with priority (preemptive-resume, non-preemtive head-of-line) and non-priority (first-come-first-served, processor-sharing, last-come-first-served with, or without preemtion) servers. The ME solutions are interpreted in terms of a decomposition of the original network into individual stable GIG11 queueing stations with assumed renewal arrival processes. These solutions are implemented by making use of the generalised exponential (GE) distributional model to approximate the interarrival-time and service-time distributions in the network. As a consequence the ME queue length distribution of the stable GE/GEzl priority queue, subject to mean value constraints obtained via classical queueing theory on bulk queues, is used as a 'building block' together with corresponding universal approximate flow formulae for the analysis of general QNM's with priorities. The credibility of the ME method is demonstrated with illustrative numerical examples and favourable comparisons against exact, simulation and other approximate methods are made.

Capacity pooling in production systems, in the form of production capacity or inventory pooling, has been extensively studied in the literature. While production capacity pooling has been proven to be beneficial, the impact of inventory pooling has been less significant. These results cannot be easily extended to repairable systems due to fundamental differences between repairable and production systems. For one thing, in repairable systems, the demand rate is a function of the number of operational machines, whereas it is exogenous and constant in production systems. In this Thesis, to serve different fleets of machines possibly at different locations, we study whether repair shop pooling is more cost effective than having dedicated on-site repair shops for each fleet. In the first model, we consider transportation delays and related costs, which have been traditionally ignored in the literature. We include on-site spare-part inventories that operate according to a continuous-review base-stock policy. Our numerical findings indicate that when transportation costs are reasonable, repair shop pooling is a better alternative. Next, we model a pooled repair shop that fixes failed components from different k-out-of-n:G systems. We permit a shared spare parts inventory serving all systems and/or reserved spare parts inventories for each system; we call this a hybrid model. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our findings show that both hybrid policies are more cost effective than having separate repair shops and inventories for each system. We propose implementing the multilevel rationing (MR) policy in systems with shared inventory. The MR policy prioritizes classes, and stops serving a class from inventory if the inventory level is below the inventory threshold identified for that class. When there is no inventory, the repaired component is sent to the highest priority class among those with down machines. To approximate the cost of the MR policy, we study an M/G/1//N queueing system serving multiple classes of customers with an unreliable server. Our numerical findings indicate that the MR policy performs as well as the epsilon-optimal policy and outperforms the hybrid policies.

Capacity pooling in production systems, in the form of production capacity or inventory pooling, has been extensively studied in the literature. While production capacity pooling has been proven to be beneficial, the impact of inventory pooling has been less significant. These results cannot be easily extended to repairable systems due to fundamental differences between repairable and production systems. For one thing, in repairable systems, the demand rate is a function of the number of operational machines, whereas it is exogenous and constant in production systems. In this Thesis, to serve different fleets of machines possibly at different locations, we study whether repair shop pooling is more cost effective than having dedicated on-site repair shops for each fleet. In the first model, we consider transportation delays and related costs, which have been traditionally ignored in the literature. We include on-site spare-part inventories that operate according to a continuous-review base-stock policy. Our numerical findings indicate that when transportation costs are reasonable, repair shop pooling is a better alternative. Next, we model a pooled repair shop that fixes failed components from different k-out-of-n:G systems. We permit a shared spare parts inventory serving all systems and/or reserved spare parts inventories for each system; we call this a hybrid model. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our findings show that both hybrid policies are more cost effective than having separate repair shops and inventories for each system. We propose implementing the multilevel rationing (MR) policy in systems with shared inventory. The MR policy prioritizes classes, and stops serving a class from inventory if the inventory level is below the inventory threshold identified for that class. When there is no inventory, the repaired component is sent to the highest priority class among those with down machines. To approximate the cost of the MR policy, we study an M/G/1//N queueing system serving multiple classes of customers with an unreliable server. Our numerical findings indicate that the MR policy performs as well as the epsilon-optimal policy and outperforms the hybrid policies.

The advances of high-throughput technologies, such as next-generation sequencing and microarrays, have rapidly improved the accessibility of molecular profiles in tumor samples. However, due to the immaturity of relevant theories, analyzing these data and systematically understanding the underlying mechanisms causing diseases, which are essential in the development of therapeutic applications, remain challenging. This dissertation attempts to clarify the effects of DNA copy number alterations (CNAs), which are known to be common mutations in genetic diseases, on steady- state gene expression values, time-course expression activities, and the effectiveness of targeted therapy. Assuming DNA copies operate as independent subsystems producing gene transcripts, queueing theory is applied to model the stochastic processes representing the arrival of transcription factors (TFs) and the departure of mRNA. The copy-number-gene-expression relationships are shown to be generally nonlinear. Based on the mRNA production rates of two transcription models, one corresponding to an unlimited state with prolific production and one corresponding to a restrictive state with limited production, the dynamic effects of CNAs on gene expression are analyzed. Simulations reveal that CNAs can alter the amplitudes of transcriptional bursting and transcriptional oscillation, suggesting the capability of CNAs to interfere with the regulatory signaling mechanism. With this finding, a string-structured Bayesian network that models a signaling pathway and incorporates the interference due to CNAs is proposed. Using mathematical induction, the upstream and downstream CNAs are found to have equal influence on drug effectiveness. Scoring functions for the detection of unfavorable CNAs in targeted therapy are consequently proposed. Rigorous experiments are keys to unraveling the etiology of genetic diseases such as cancer, and the proposed models can be applied to provide theory-supporting hypotheses for experimental design.

Although healthcare operations management has been an active and popular research direction over the past few years, there is a lack of formal quantitative models to analyze the ambulance o oad delay problem. O oad delays occur when an ambulance arriving at a hospital Emergency Department (ED) is forced to remain in front of the ED until a bed is available for the patient. Thus, the ambulance and the paramedic team are responsible to care for the patient until a bed becomes available inside the ED. But it is not as simple as waiting for a bed, as EDs also admit patients based on acuity levels. While the main cause of this problem is the lack of capacity to treat patients inside the EDs, Emergency Medical Services (EMS) coverage and availability are signi cantly a ected. In this thesis, we develop three network queueing models to analyze the o oad delay problem. In order to capture the main cause of those delays, we construct queueing network models that include both EMS and EDs. In addition, we consider patients arriving to the EDs by themselves (walk-in patients) since they consume ED capacity as well. In the rst model, ED capacity is modeled as the combination of bed, nurse, and doctor. If a patient with higher acuity level arrives to the ED, the current patient's service is interrupted. Thus, the service discipline at the EDs is preemptive resume. We also assume that the time the ambulance needs to reach the patient, upload him into the ambulance, and transfer him to the ED (transit time) is negligible. We develop e cient algorithms to construct the model Markov chain and solve for its steady state probability distribution using Matrix Analytic Methods. Moreover, we derive di erent performance measures to evaluate the system performance under di erent settings in terms of the number of beds at each ED, Length Of Stay (LOS) of patients at an ED, and the number of ambulances available to serve a region. Although capacity limitations and increasing demand are the main drivers for this problem, our computational analysis show that ambulance dispatching decisions have a substantial impact on the total o oad delays incurred. In the second model, the number of beds at each ED is used to model the service capacity. As a result of this modeling approach, the service discipline of patients is assumed to be nonpreemptive priority. We also assume that transit times of ambulances are negligible. To analyze the queueing network, we develop a novel algorithm to construct the system Markov chain by de ning a layer for each ED in a region. We combine the Markov chain layers based on the fact that regional EDs are only connected by the number of available ambulances to serve the region. Using Matrix Analytic Methods, we nd the limiting probabilities and use the results to derive di erent system performance measures. Since each ED's patients are included in the model simultaneously, we solve only for small instances with our current computational resources. In the third model, we decompose the regional network into multiple single EDs. We also assume that patients arriving by ambulances have higher nonpreemptive priority discipline over walk-in patients. Unlike the rst two models, we assume that transit times of ambulances are exponentially distributed. To analyze the decomposed queueing network performance, we construct a Markov chain and solve for its limiting probabilities using Matrix Analytic Methods. While the main objective for the rst two models is performance evaluation, in this model we optimize the steady state dispatching decisions for ambulance patients. To achieve this goal, we develop an approximation scheme for the expected o oad delays and expected waiting times of patients. Computational analysis conducted suggest that larger EDs should be loaded more heavily in order to keep the total o oad delays at minimal levels.