Queues with Customer Induced Interruption

In this thesis we have introduced and studied the notion of self interruption of service by customers. Service interruption in queueing systems have been extensively discussed in literature (see, Krishnamoorthy, Pramod and Chakravarthy [38]) for the most recent survey. So far all work reported deal with cases in which service interruptions are generated by sources other than customers. However, there are situations where interruptions are due to the customers rather than the system. Such situations are especially arise at doctors clinic, banks, reservation counter etc. Our attempt is to quantify a few of such problems. Systematically we have proceed from single server queue (in Chapter 2) to multi-server queues (Chapter 3). In Chapte 4, we have studied a very general multiserver queueing model with service interruption and protection of service phases. We also introduced customer interruption in a retrial setup (in Chapter 5). All models (from Chapter 2 to Chapter 4) that were analyzed involve 'non-preemptive priority' for interrupted customers where as in the model discussed in Chapter 5 interruption of service by customers is not encouraged. So the interrupted customers cannot access the server as long as there are primary customers in the system. In Chapter 5 we have obtained an explicit expression for the stability condition of the system. In all models analyzed in this thesis, we have assumed that no more than one interruption is allowed for a customer while in service. Since the models are not analytically tractable, a large number of numerical illustrations were given in each chapter it illustrate the working of the systems. We can extend the models discussed in this thesis to several directions. For example some of the models can be analyzed with both server induced and customer induced interruptions the results for which are not available till date. Another possible extension of work is to the case where there is no bound on the number of interruptions a customer is permitted to have before service completion. More complex is the case where a customer is permitted to have a nite number (K ≥ 2) of We can extend the models discussed in this thesis to several directions.

A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.

ALGORITHM FOR PROBABILISTIC ANALYSIS of DISTRIBUTION SYSTEMS WITH DISTRIBUTED GENERATION

In this paper an efficient algorithm for probabilistic analysis of unbalanced three-phase weakly-meshed distribution systems is presented. This algorithm uses the technique of Two-Point Estimate Method for calculating the probabilistic behavior of the system random variables. Additionally, the deterministic analysis of the state variables is performed by means of a Compensation-Based Radial Load Flow (CBRLF). Such load flow efficiently exploits the topological characteristics of the network. To deal with distributed generation, a strategy to incorporate a simplified model of a generator in the CBRLF is proposed. Thus, depending on the type of control and generator operation conditions, the node with distributed generation can be modeled either as a PV or PQ node. To validate the efficiency of the proposed algorithm, the IEEE 37 bus test system is used. The probabilistic results are compared with those obtained using the Monte Carlo method.

Distribution Transformer Modeling for Application in Three-Phase Power Flow Algorithm

In this paper, it is presented a methodology for three-phase distribution transformer modeling, considering several types of transformer configuration, to be used in algorithms of power flow in three-phase radial distribution networks. The paper provides a detailed discussion about the models and the results from an implementation of the power flow algorithm. The results, taken from three different networks, are presented for several transformer configurations and for voltage regulators as well.

First-passage time distribution and non-Markovian diffusion dynamics of protein folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a Levy-type distribution with power-law tails, indicating a nonself-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (Levy) distribution of the relaxation time of the underlined protein energy landscape is observed.

济阳-昌潍坳陷火成岩油气藏体系形成机理和分布规律研究

Jiyang & Changwei depressions are two neighboring depressions in Bahai Bay Basin, the famous oil rich basin in East China. The exploration activities in the past 40 years has proved that, within the basins, there exists not only plentiful sandstone hydrocarbon reservoirs (conventional), but also abundant special reservoirs as igneous rock, mudstone and conglomerate ones which have been knowing as the unconventional in the past, and with the prospecting activity is getting more and more detailed, the unconventional reservoirs are also getting more and more important for further resources, among which, the igneous lithological reservoir be of significance as a new research and exploration area. The purpose of this paper is, with the historical researches and data as base, the System Theory, Practice Theory and Modern Comprehensive Petroleum Geology Theory as guide, the theoretical and practice break through as the goal, and the existing problems in the past as the break through direction, to explore and establish a valid reservoir formation and distribution models for igneous strata in the profile of the eastern faulted basins. After investigating the distribution of the igneous rocks and review the history of the igneous rocks reservoirs in basins, the author focused on the following issues and correspondingly the following progresses have been made: 1.Come to a new basin evolution and structure model named "Combined-Basin-bodies Model" for Jiyang even Eastern faulted basins based on the study on the origin and evolution of Jiyang & Changwei basins, depending on this model, every faulted basin in the Bo-hai Bay Basin is consisted of three Basin-Bodies including the Lower (Mesozoic), Middle (Early Tertiary) and the Upper (Late Tertiary) Bodies, each evolved in different geo-stress setting and with different basin trend, shape and igneous-sedimentary buildings system, and from this one to next one, the basin experienced a kind of process named "shape changing" and "Style changing". 2. Supposed a serious of new realizations as follows (1) There were "multi-level magma sources" including Upper mantel and the Lower, Middle and even the Upper Shell magma Chambers in the historical Magma Processes in the basins; (2) There were "multi-magma accessing or pass" from the first level (Mantel faults) to the second, third and fourth levels (that is the different levels of fault in the basin sediment strata) worked in the geo-historical and magma processes; (3) Three tectonic magma cycles and more periods have been recognized those are matched with the "Basin -body-Model" and (4)The geo-historical magma processes were non-homogeneous in time and space scale and so the magma rocks distributed in "zones" or "belts". 3. The study of magma process's effect on basin petroleum conditions have been made and the following new conclusions were reached: (1) the eruptive rocks were tend to be matched with the "caped source rock", and the magma process were favorable to the maturing of the source rocks. (2) The magma process were fruitful to the accumulation of the non-hydrocarbon reservoirs however a over magma process may damage the grade of resource rock; (3) Eruptive activity provided a fruitful environment for the formation of such new reservoir rocks as "co-eruptive turbidity sandstones" and "thermal water carbonate rocks" and the intrusive process can lead to the origin of "metamorphism rock reservoir"; (4) even if the intrusive process may cause the cap rock broken, the late Tertiary intrusive rocks may indeed provide the lateral seal and act as the cap rock locally even regionally. All above progresses are valuable for reconstructing the magma-sedimentary process history and enriching the theory system of modem petroleum geology. 4. A systematic classification system has been provided and the dominating factors for the origin and distribution of igneous rock reservoirs have been worked out based on the systematic case studies, which are as follows: (1) The classification is given based on multi-factors as the origin type, litho-phase, type of reservoir pore, reservoir ability etc., (2) Each type of reservoir was characterized in a detailed way; (3) There are 7 factors dominated the intrusive reservoir's characteristics including depth of intrusion, litho-facies of surrounding rocks, thickness of intrusive rock, intrusive facies, frequency and size of the working faults, shape and tectonic deformation of rock, erosion strength of the rock and the time of the intrusion ect., in the contrast, 4 factors are for eruptive rocks as volcanic facies, frequency and size of the working faults, strength of erosion and the thermal water processing. 5. Several new concept including "reservoir litho-facies", "composite-volcanic facies" and "reservoir system" ect. Were suggested, based on which the following models were established: (1) A seven reservoir belts model for a intrusive unit profile and further more, (2) a three layers cubic model consisted of three layer as "metamorphic roe layer", "marginal layer" and "the core"; (3) A five zones vertical reservoir sequence model consisted of five litho-facies named A, B, C, D and E for a original lava unit and furthermore three models respectively for a erosion, subsidence and faulted lava unit; (4) A composite volcanic face model for a lava cone or a composite cone that is consisted of three facies as "crater and nearby face", "middle slope" and "far slope", among which, the middle slope face is the most potential reservoir area and producible for oil & gas. 6. The concept of "igneous reservoir" was redefined as the igneous, and then a new concept of "igneous reservoir system" was supposed which means the reservoir system consisted of igneous and associated non-igneous reservoirs, with non-hydrocarbon reservoir included. 7. The origin and distribution of igneous reservoir system were probed and generalized for the exploration applications, and origin models of the main reservoir sub-systems have been established including those of igneous, related non-igneous and non-hydrocarbon. For intrusive rocks, two reservoir formation models have been suggested, one is called "Original or Primary Model", and the another one is "Secondary Model"; Similarly, the eruptive rock reservoirs were divided in three types including "Highly Produced", "Moderately Produced" and "Lowly Produced" and accordingly their formation models were given off; the related non-igneous reservoir system was considered combination of eight reservoirs, among which some ones like the Above Anticline Trap are highly produced; Also, the non-hydrocarbon. Trap system including five kinds of traps was discussed. 8. The concept models for four reservoir systems were suggested, which include the intrusive system consisted of 7 kinds of traps, the land eruptive system with 6 traps, the under water eruptive system including 6 kinds of traps and the non-hydrocarbon system combined by 5 kinds of traps. In this part, the techniques for exploration of igneous reservoir system were also generalized and probed, and based on which and the geological progresses of this paper, the potential resources and distributions of every reservoir system was evaluated and about 186 millions of reserves and eight most potential non-hydrocarbon areas were predicted and outlined. The author believe that the igneous reservoir system is a very important exploration area and its study is only in its early stage, the framework of this paper should be filled with more detailed studies, and only along way, the exploration of igneous reservoir system can go into it's really effective stage.

孔隙介质中油气二次运移动力学机制研究

Study of dynamical mechanism of hydrocarbon secondary migration is the key research project of China Petroleum and Chemical Corporation in the ninth "Five-Year Plan", and this research is the hot and difficult spot and frontline in the domain of reservoir forming study in recent years. It is a common recognition that the dynamical mechanism of hydrocarbon's secondary migration is the important factor to control the reservoir type, distribution and oil/gas abundance. Therefore, to study this mechanism and establish the modes of hydrocarbon's migration and accumulation in different reservoirs under different conditions are of great theoretical meaningfulness and practical value on both developing the theory and method of hydrocarbon migration/accumulation dynamics in terrestrial rift-subsidence lacustrine basins and guiding the exploration and production. A laboratory for physical simulation of hydrocarbon's secondary migration/accumulation mechanism has been build up. 12 types of physical simulation tests to determine the volume of oil/gas migration and accumulation within these 3 series of plentiful hydrocarbon sources, different hydrocarbon abundance and pore level have been carried out under the guide of multidisciplinary theories, applying various methods and techniques, and 24 migration/accumulation modes have been established. The innovative results and recognition are as follows: 1, The oil/gas migration and accumulation modes for sandstones of moderate, fine grain size and silt in these six paleo depositional environments of shallow lake, fluvial, lacustrine, fluvial-deltaic, turbidite-delta, and salty-semi salty lake have been established. A new view has been put forward that the oil/gas volumetric increment during their migration and accumulation in different porous media of different rocks has similar features and evolution history. 2. During oil/gas migration and accumulation in different grain-sized porous media or different reservoirs, all the volumetric increment had experienced three period of rapid increasing, balanced and slower increasing and limited increasing. The dynamical process of oil/gas secondary migration and accumulation has been expounded. 3 The two new concepts of "source supply abundance" and "source supply intensity" have been proposed for the first time, and the physical simulation for hydrocarbon's migration, accumulation and forming a reservoir has been realized. 4, Source supply abundance is the important factor to control the accumulated volume of oil phase in the porous media. It is impossible to accumulate large amount of hydrocarbon volume in an open boundary system when the source supply abundance is low, i.e. impossible to form reservoirs of high productivity. 5 The above 12 types of physical simulation tests indicated that enough energy (pressure) of the oil sources is the decisive factor to ensure hydrocarbon's entering, flowing and accumulating through porous media, and both oil and gas phase will accumulate into the favorable places nearest to the oil sources. 6 The theory, method and related techniques for physical simulation of hydrocarbon's secondary migration/accumulation mechanism have been formed and applied to the E&P of Shengtuo rollover anticline and Niuzhuang turbidite lithological reservoirs. 7 This study developed the theory and method of hydrocarbon migration/accumulation dynamics in terrestrial rift-subsidence lacustrine basins, and the benefits and social effect are remarkable.

Modelling Patient Duration of Stay to Facilitate Resource Management of Geriatric Hospitals

A fundamental aspect of health care management is the effective allocation of resources. This is of particular importance in geriatric hospitals where elderly patients tend to have more complex needs. Hospital managers would benefit immensely if they had advance knowledge of patient duration of stay in hospital. Managers could assess the costs of patient care and make allowances for these in their budget. In this paper, we tackle this important problem via a model which predicts the duration of stay distribution of patients in hospital. The approach uses phase-type distributions conditioned on a Bayesian belief network.

Assessing length of stay and associated characteristics of geriatric patients in Northern Ireland

The effective provision of care for the elderly is becoming increasingly more difficult. This is due to the rising proportion of elderly in the population, increasing demands placed on the health services and the financial strain placed on an already stretched economy. The research presented in this paper uses three different models to represent the length of stay distribution of geriatric patients admitted to one of the six key acute hospitals in Northern Ireland and various patient characteristics associated with their respective length of stay. The accurate modelling of bed usage within wards would enable hospital managers to prepare patient discharge packages and rehabilitation services in advance. The models presented within the paper include a Cox proportional hazards model, a Bayesian network with a discrete variable to represent length of stay and a special conditional phase-type model (C-Ph) with a connecting outcome node. This research demonstrates the new efficient fitting algorithm employed for Coxian phase-type distributions while updating C-Ph models for recent elderly patient data.

Nakagami-m Phase Model: Further Results and Validation

This paper contributes to and expands on the Nakagami-m phase model. It derives exact, closed-form expressions for both the phase cumulative distribution function and its inverse. In addition, empirical first- and second-order statistics obtained from measurements conducted in a body-area network scenario were used to fit the phase probability density function, the phase cumulative distribution function, and the phase crossing rate expressions. Remarkably, the unlikely shapes of the phase statistics, as predicted by the theoretical formulations, are actually encountered in practice.

On Queues with Interruptions and Repeat or Resumption of Service

This thesis entitled' On Queues with Interruptions and Repeat or Resumption of Service' introduces several new concepts into queues with service interruption. It is divided into Seven chapters including an introductory chapter. The following are keywords that we use in this thesis: Phase type (PH) distribution, Markovian Arrival Process (MAP), Geometric Distribution, Service Interruption, First in First out (FIFO), threshold random variable and Super threshold random variable. In the second chapter we introduce a new concept called the 'threshold random variable' which competes with interruption time to decide whether to repeat or resume the interrupted service after removal of interruptions. This notion generalizes the work reported so far in queues with service interruptions. In chapter 3 we introduce the concept of what is called 'Super threshold clock' (a random variable) which keeps track of the total interruption time of a customer during his service except when it is realized before completion of interruption in some cases to be discussed in this thesis and in other cases it exactly measures the duration of all interruptions put together. The Super threshold clock is OIl whenever the service is interrupted and is deactivated when service is rendered. Throughout this thesis the first in first out service discipline is followed except for priority queues.

Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.

CLASSICAL DISTRIBUTION-FUNCTIONS DERIVED FROM WIGNER DISTRIBUTION-FUNCTIONS

A mapping which relates the Wigner phase-space distribution function associated with a given stationary quantum-mechanical wavefunction to a specific solution of the time-independent Liouville transport equation is obtained. Two examples are studied.

Mapping Wigner distribution functions into semiclassical distribution functions

A mapping that relates the Wigner phase-space distribution function of a given stationary quantum mechani-cal wave function, a solution of the Schrödinger equation, to a specific solution of the Liouville equation, both subject to the same potential, is studied. By making this mapping, bound states are described by semiclassical distribution functions still depending on Planck's constant, whereas for elastic scattering of a particle by a potential they do not depend on it, the classical limit being reached in this case. Following this method, the mapped distributions of a particle bound in the Pöschl-Teller potential and also in a modified oscillator potential are obtained.

Distribution of radiolarians from ODP Leg 128 holes

The analysis of radiolarians from Japan Sea subsurface sediments recovered during Leg 128 of the Ocean Drilling Program reveals that a warm-water assemblage similar to that of the North Pacific was replaced by unique post-middle Miocene faunas probably as a result of the restriction of Oceanographic circulation. The modern fauna was gradually established only in the Pleistocene. No attempt was made to establish the radiolarian zonation because of low species diversity and the absence of generally recognized index forms in the North Pacific. In the diagenetically altered quartz section, however, a radiolarian assemblage correlative to the middle Miocene Cyrtocapsella tetrapera Zone of western Honshu was identified from Hole 799B.