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Tesis sobre el tema "Queuing theory"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 9 de junio de 2025

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1

Wu, Kan. "New results in factory physics." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31650.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.<br>Committee Chair: Leon McGinnis; Committee Co-Chair: Bert Zwart; Committee Member: Antonius Dieker; Committee Member: Craig Tovey; Committee Member: Hayriye Ayhan; Committee Member: Mark Ferguson. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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2

Leontas, Angela Zoi. "Modeling queueing systems." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3101.

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The thesis introduces the theory of queueing systems and demonstrates its applicability to real life problems. It discusses (1) Markovian property and measures of effectiveness with exponential interarrival and service times; (2) Erlang service times, and a single server; (3) different goodness-of-fit tests that can be used to determine whether the exponential distribution is appropriate for a given set of data. A single server queueing system with exponential interarrival times and Erlang service times is simulated using Visual Basic for Applications (VBA).

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3

Coyle, Andrew James. "Some problems in queueing theory." Title page, contents and summary only, 1989. http://web4.library.adelaide.edu.au/theses/09PH/09phc8812.pdf.

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4

Rumsewicz, Michael P. "Some contributions to the fields of insensitivity and queueing theory." Title page, contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phr938.pdf.

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5

Kumaran, Jayesh Liefvoort Appie van de. "Approximation models and approaches for computing performance measures that arise in single server queueing systems." Diss., UMK access, 2006.

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Thesis (Ph. D.)--School of Computing and Engineering. University of Missouri--Kansas City, 2006.<br>"A dissertation in telecommunications networking and computer networking." Advisor: Appie van de Liefvoort. Typescript. Vita. Title from "catalog record" of the print edition Description based on contents viewed Jan. 29, 2007. Includes bibliographical references (leaves 108-116). Online version of the print edition.

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6

Sabo, David Warren. "Closure methods for the single-server retrial queue." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26528.

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This work focuses on the development and evaluation of so-called "closure methods" for solving the equations governing the time-dependent behaviour of single-server retrial queues. These methods involve assuming that particular known algebraic relationships between various characteristics of the corresponding steady-state queue also apply approximately when the queue is not at steady-state. The objective is to replace a problem requiring the solution of dozens or hundreds of simultaneous linear differential equations with a system of a few differential equations that has a solution that approximates those queue characteristics of immediate interest. The viability of such closure methods is assessed by examining the results of a series of test calculations. The methods described in this thesis apply to a retrial queue in which inter-arrival times for new customers, inter-retrial times, and service times are all assumed to be exponentially distributed. The steady-state solution for such a queue is described in some detail. A survey of the literature indicates that the description of this steady-state retrial queue has become quite sophisticated, whereas only very tentative steps have been taken in the study of the time-dependent behaviour of such queues. On the other hand, the time-dependent behaviour of the simple M/M/s queues have been studied to a much greater extent. The apparent value of closure methods in computing approximations to various basic time-dependent M/M/s queue characteristics motivated this examination of the extension of such methods to the single-server retrial queue. After discussing the basic approach to be used in devising and testing prospective closure methods for the single-server retrial queue, a variety of such methods is presented, with each being tested in considerable detail. It is found that three of the methods devised give results of comparable or better accuracy than those closure methods for the simple M/M/s queues which motivated this study. All recommended closure methods developed here involve systems of either two or three differential equations and permit the calculation of good approximations to four of the characteristics of greatest interest for non-stationary queues: the probability that the server is idle, the mean queue length, the variance of the queue length, and the conditional mean number of customers in the system given that the server is idle. Each of the methods presented is tested for queues with constant mean arrival, retrial and service rates, as well as for queues in which arrival and retrial rates vary sinusoidally with time.<br>Science, Faculty of<br>Mathematics, Department of<br>Graduate

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7

Chang, Woojin. "Asymptotics of k-limited polling models." Thesis, Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/25507.

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8

程瑋琪 and Wai-ki Ching. "Construction of preconditioners for queueing networks." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B3121132X.

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9

Srinivasan, Rengarajan Carleton University Dissertation Mathematics. "Topics in state dependent queues and queueing networks." Ottawa, 1988.

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10

Ching, Wai-ki. "Construction of preconditioners for queueing networks /." [Hong Kong] : University of Hong Kong, 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1378707X.

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11

Yunus, Muhammad Naim. "Blocking in teletraffic systems under nonstationary arrival and service conditions /." Title page, contents and summary only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phy95.pdf.

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12

Coombs-Reyes, Jerome D. "Customer allocation policies in a two server network stability and exact asymptotics /." Diss., Available online, Georgia Institute of Technology, 2004:, 2003. http://etd.gatech.edu/theses/available/etd-03292004-141826/unrestricted/coombs-reyes%5Fjerome%5Fd%5F200312%5Fphd.pdf.

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13

Park, Young Wook. "Large deviation theory for queueing systems." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39858.

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14

Molloy, Charles T. Whitham G. B. "Contributions to the kinetic theory of traffic flow with queuing /." Diss., Pasadena, Calif. : California Institute of Technology, 1985. http://resolver.caltech.edu/CaltechETD:etd-03262008-101545.

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15

Jalali-Nadoushan, A. (Ahmad). "Approximate analysis of a polling system with limited service." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63323.

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16

Yeung, Wing-wah. "Queuing model simulating Kwai Chung Terminal's utilization." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B2250557X.

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17

Roughan, Matthew. "An application of martingales to queueing theory /." Title page, table of contents and summary only, 1993. http://web4.library.adelaide.edu.au/theses/09PH/09phr856.pdf.

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18

May, Meredith Augusta. "Applications of Queuing Theory for Open-Pit Truck/Shovel Haulage Systems." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/19218.

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Surface mining is the most common mining method worldwide, and open pit mining accounts for more than 60% of all surface output. Haulage costs account for as much as 60% of the total operating cost for these types of mines, so it is desirable to maintain an efficient haulage system. As the size of the haulage fleet being used increases, shovel productivity increases and truck productivity decreases, so an effective fleet size must be chosen that will effectively utilize all pieces of equipment. One method of fleet selection involves the application of queuing theory to the haul cycle. Queuing theory was developed to model systems that provide service for randomly arising demands and predict the behavior of such systems. A queuing system is one in which customers arrive for service, wait for service if it is not immediately available, and move on to the next server or exit the system once they have been serviced. Most mining haul routes consist of four main components: loading, loaded hauling, dumping, and unloaded hauling to return to the loader. These components can be modeled together as servers in one cyclic queuing network, or independently as individual service channels. Data from a large open pit gold mine are analyzed and applied to a multichannel queuing model representative of the loading process of the haul cycle. The outputs of the model are compared against the actual truck data to evaluate the validity of the queuing model developed.<br>Master of Science

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19

Fountanas, Leonidas. "Active queue management mechanisms for real-time traffic in MANETs /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2001. http://handle.dtic.mil/100.2/ADA401102.

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Thesis (Electrical Engineer and M.S. in Electrical Engineering) Naval Postgraduate School, Dec. 2001.<br>"December 2001." Thesis advisor(s): Tummala, Murali ; Ives, Robert W. ; Parker, Robert E. Includes bibliographical references (p. 101-104). Also available online.

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20

Rouskas, George N. "Single-hop lightwave WDM networks and applications to distributed computing." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/8257.

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21

Hasenbein, John Jay. "Stability, capacity, and scheduling of multiclass queueing networks." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/24836.

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22

Huang, Wenzong. "Spatial queueing systems and reversible markov processes." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/24871.

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23

Chin, Ke-Tsai Edward. "Networks of queues with state-dependent flows." Diss., Georgia Institute of Technology, 1986. http://hdl.handle.net/1853/25419.

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24

Chang, Kuo-Hwa. "Extreme queues and stationarity of heavy-traffic service systems." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/25441.

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25

Dai, Wanyang. "Brownian approximations for queueing networks with finite buffers : modeling, heavy traffic analysis and numerical implementations." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/29335.

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26

Litko, Joseph R. "An application of the Laguerre transform to the GI/G/1 queue /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487260531957808.

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27

Lacek, Steven. "Non-preemptive shunting in M/M/1 and dynamic service queuing systems." [Huntington, WV : Marshall University Libraries], 2008. http://www.marshall.edu/etd/descript.asp?ref=874.

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28

Sitaraman, Hariharakrishnan. "Approximation of a class of Markov-modulated Poisson processes with a large state-space." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184828.

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Many queueing systems have an arrival process that can be modeled by a Markov-modulated Poisson process. The Markov-modulated Poisson process (MMPP) is a doubly stochastic Poisson process in which the arrival rate varies according to a finite state irreducible Markov process. In many applications of MMPPs, the point process is constructed by superpositions or similar constructions, which lead to modulating Markov processes with a large state space. Since this limits the feasibility of numerical computations, a useful problem is to approximate an MMPP represented by a large Markov process by one with fewer states. We focus our attention in particular, to approximating a simple but useful special case of the MMPP, namely the Birth and Death Modulated Poisson process. In the validation stage, the quality of the approximation is examined in relation to the MMPP/G/1 queue.

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29

Yeung, Wing-wah, and 揚永華. "Queuing model simulating Kwai Chung Terminal's utilization." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31225470.

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30

Pemmaraju, Sriram V. "Exploring the powers of stacks and queues via graph layouts." Diss., This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-06062008-170556/.

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31

Kussard, Michael. "Performance analysis of a controlled database unit with single queue configuration subject to control delays with decision errors." Diss., Online access via UMI:, 2006.

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32

Toro-Ramos, Zulma R. "Network of queues and decomposition methods for modeling manufacturing systems." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/25107.

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33

Thomas, Nigel Anthony. "Performance and reliability in distributed systems." Thesis, University of Newcastle Upon Tyne, 1997. http://hdl.handle.net/10443/1996.

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This thesis is devoted to the construction and analysis of models which can be used to evaluate the performance and reliability of distributed systems. The general object of the research therefore is to extend the types of queueing models with breakdowns which have been solved, with a particular interest in networking structures. The systems that are studied involve various collections of servers and their associated queues. These range from isolated nodes, though parallel nodes coupled by the effect of breakdowns on arrivals, to pipelines of such parallel stages and more general networks. The issues that are explored include the influence of breakdowns and repairs on delays, job losses and optimal routeing. Obtaining performance measures for interacting queues is difficult, however a degree of abstraction has been used here which allows long run averages to be calculated (exactly in many cases) for quite complex systems. A variety of different techniques are used in order to obtain solutions to these models, including exact equations, exact numerical and approximate numerical techniques.

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34

Brahimi, Mammar. "Approximating multi-server queues with inhomgeneous arrival rates and continuous service time distributions." Thesis, Lancaster University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.254028.

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35

Choi, Sin-man, and 蔡倩雯. "Game theory and stochastic queueing networks with applications to service systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44907035.

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36

Jennings, Otis Brian. "Multiclass queueing networks with setup delays : stability analysis and heavy traffic approximation." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/25190.

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37

Reed, Joshua E. "Queueing Models for Large Scale Call Centers." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16332.

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In the first half of this thesis, we extend the results of Halfin and Whitt to generally distributed service times. This is accomplished by first writing the system equations for the G/GI/N queue in a manner similar to the system equations for G/GI/Infinity queue. We next identify a key relationship between these two queues. This relationship allows us to leverage several existing results for the G/GI/Infinity queue in order to prove our main result. Our main result in the first part of this thesis is to show that the diffusion scaled queue length process for the G/GI/N queue in the Halfin-Whitt regime converges to a limiting stochastic process which is driven by a Gaussian process and satisfies a stochastic convolution equation. We also show that a similar result holds true for the fluid scaled queue length process under general initial conditions. Customer abandonment is also a common feature of many call centers. Some researchers have even gone so far as to suggest that the level of customer abandonment is the single most important metric with regards to a call center's performance. In the second half of this thesis, we improve upon a result of Ward and Glynn's concerning the GI/GI/1+GI queue in heavy traffic. Whereas Ward and Glynn obtain a diffusion limit result for the GI/GI/1+GI queue in heavy traffic which incorporates only the density the abandonment distribution at the origin, our result incorporate the entire abandonment distribution. This is accomplished by a scaling the hazard rate function of the abandonment distribution as the system moves into heavy traffic. Our main results are to obtain diffusion limits for the properly scaled workload and queue length processes in the GI/GI/1+GI queue. The limiting diffusions we obtain are reflected at the origin with a negative drift which is dependent upon the hazard rate of the abandonment distribution. Because these diffusions have an analytically tractable steady-state distribution, they can be used to provide a closed-form approximation for the steady-state distribution of the queue length and workload processes in a GI/GI/1+GI queue. We demonstrate the accuracy of these approximations through simulation.

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38

Brown, Adam J. "A STUDY OF QUEUING THEORY IN LOW TO HIGH REWORK ENVIRONMENTS WITH PROCESS AVAILABILITY." UKnowledge, 2012. http://uknowledge.uky.edu/ms_etds/2.

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In manufacturing systems subject to machine and operator resource constraints the effects of rework can be profound. High levels of rework burden the resources unnecessarily and as the utilization of these resources increases the expected queuing time of work in process increases exponentially. Queuing models can help managers to understand and control the effects of rework, but often this tool is overlooked in part because of concerns over accuracy in complex environments and/or the need for limiting assumptions. One aim of this work is to increase understanding of system variables on the accuracy of simple queuing models. A queuing model is proposed that combines G/G/1 modeling techniques for rework with effective processing time techniques for machine availability and the accuracy of this model is tested under varying levels of rework, external arrival variability, and machine availability. Results show that the model performs best under exponential arrival patterns and can perform well even under high rework conditions. Generalizations are made with regards to the use of this tool for allocation of jobs to specific workers and/or machines based on known rework rates with the ultimate aim of queue time minimization.

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39

Chu, Qiao M. Eng Massachusetts Institute of Technology, and Nisha Palvia. "Enhancing the customer service experience in call centers using preemptive solutions and queuing theory." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112874.

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Thesis: M. Eng. in Supply Chain Management, Massachusetts Institute of Technology, Supply Chain Management Program, 2017.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (page 79).<br>The security alarms services market in the United States delivers hardware equipment and services to homeowners and businesses to help monitor and enhance personal property protection. Customer satisfaction via wait time reduction, first call resolution, and cost minimization are key drivers of success to players in this market. Most companies invest heavily in customer service systems including call centers. Our client, AlarmCo, a top provider of property protection, manages an inbound call center that supports a range of questions from customers who call within thirty days from the alarm installation date. Often, security companies fail to utilize strategic solutions when managing inbound customer call traffic and default to reactive measures which unnecessarily increase customer wait times. The key question the team aims to address in this thesis is: "How can we improve the customer service experience for customers of a major security service provider in the United States?" For this thesis, MIT partnered with OnProcess Technology, a managed services provider specializing in complex, global service supply chain operations, to develop a robust framework to preemptively reduce the number of inbound customer calls, and thereby improve customer service. Using ABC segmentation, the team categorized customers by reason code and demographics. To simulate the client's call center queue, the team calculated the key inputs for the queuing model including average wait time, interarrival rates and number of servers. The team then chose and developed the M/M/n stochastic queuing model for the simulation. The M/M/n queue reflects a simple system with parallel servers, arrivals with a Poisson distribution and service times that are exponentially distributed. Next, the customer segmentation was used to develop targeted preemptive solutions. Taking into account feasibility ratings, the team assigned success rates to each solution and adjusted the inbound call data accordingly. By analyzing the outputs of the simulation before and after adjusting the dataset, the team quantified the impact of preemptive solutions on the call center queue. Ultimately, narrowing to twelve strategic preemptive solutions led to the enhancement of the as-is queuing model by reducing average wait time by up to 35%.<br>by Qiao Chu and Nisha Palvia.<br>M. Eng. in Supply Chain Management

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40

Muthuvelu, Sethumadhavan. "Simultaneous Lot sizing and Lead-time Setting (SLLS)Via Queuing Theory and Heuristic search." Thesis, Virginia Tech, 2003. http://hdl.handle.net/10919/9692.

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Materials requirements planning (MRP) is a widely used method for production planning and scheduling. Planned lead-time (PLT) and lot size are two of the input parameters for MRP systems, which determine planned order release dates. Presently, planned lead-time and lot size are estimated using independent methodologies. No existing PLT estimation methods consider factors such as machine breakdown, scrap-rate, etc. Moreover, they do not consider the capacity of a shop, which changes dynamically, because the available capacity at any given time is determined by the loading of the shop at that time. The absence of such factors in calculations leads to a huge lead-time difference between the actual lead-time and PLT, i.e., lead-time error. Altering the size of a lot will have an effect not only on the lead-time of that lot but also on that of other lots. The estimation of lot size and lead-time using independent methodologies currently does not completely capture the inter-dependent nature of lead-time and lot size. In this research, a lot-sizing model is modified in such a way that it minimizes the combination of setup cost, holding cost and work-in-process cost. This proposed approach embeds an optimization routine, which is based on dynamic programming on a manufacturing system model, which is based on open queuing network theory. Then, it optimizes lot size by using realistic estimates of WIP and the lead-time of different lots simultaneously for single-product, single-level bills of material. Experiments are conducted to compare the performance of the production plans generated by applying both conventional and the proposed methods. The results show that the proposed method has great potential and it can save up to 38% of total cost and minimize lead-time error up to 72%.<br>Master of Science

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41

Ko, Sung-Seok. "Behavior of fork-join networks, and effect of variability in service systems." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/24376.

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42

Menich, Ronald Paul. "Resource allocation in parallel processing systems." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28049.

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43

Uribe, Jaime Trevino. "Design procedures for "pull" production systems." Diss., Georgia Institute of Technology, 1986. http://hdl.handle.net/1853/31063.

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44

Shalmon, Michael S. "Queues and packet multiplexing networks." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=71999.

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This thesis has to do with certain fundamental queues that are well established as models for delay in simple packet-switching concentrators and networks. We first revisit the single server queue with Poisson arrivals and general independent service times. We then work out a complete delay analysis for a traffic concentrating tandem network of queues with deterministic service and batch Poisson sources connected to every node; this is the most comprehensive analysis available for a network which is not of Jackson type. We also show how to (partially) extend the analysis to a concentrating tree network, and to an arrival process somewhat more general that batch Poisson.<br>The two parts of the thesis have a close methodological relationship. Our contribution in both cases is to rederive certain known results, and to produce a variety of new ones, using techniques that are essentially qualitative. Our particular view of the stochastic processes in question is guided by a very special queue discipline, namely Last Come First Served preemptive resume; by identifying certain structural features of the sample paths, one can read, almost without calculation, a host of statistics of common interest. The LCFS preemptive resume discipline also enables us: (i) to strengthen the connection between the single server queue with general independent service times and interarrival times, and the fluctuation theory of random walks; (ii) to strengthen the connection between the queue with Poisson arrivals and branching processes.

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45

Pan, Menghai. "Feasibility Study on Smart Cloud Commuting with Shared Autonomous Vehicles." Digital WPI, 2018. https://digitalcommons.wpi.edu/etd-theses/1220.

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Emergence of autonomous vehicles (AVs) offers the potential to fundamentally transform the way how urban transport systems be designed and deployed, and alter the way we view private car ownership. In this thesis we advocate a forward-looking, ambitious and disruptive smart cloud commuting system (SCCS) for future smart cities based on shared AVs. Employing giant pools of AVs of varying sizes, SCCS seeks to supplant and integrate various modes of transport -- most of personal vehicles, low ridership public buses, and taxis used in today€™s private and public transport systems -- in a unified, on-demand fashion, and provides passengers with a fast, convenient, and low cost transport service for their daily commuting needs. To explore feasibility and efficiency gains of the proposed SCCS, we model SCCS as a queueing system with passengers' trip demands (as jobs) being served by the AVs (as servers). Using a 1-year real trip dataset from Shenzhen China, we quantify (i) how design choices, such as the numbers of depots and AVs, affect the passenger waiting time and vehicle utilization; and (ii) how much efficiency gains (i.e., reducing the number of service vehicles, and improving the vehicle utilization) can be obtained by SCCS comparing to the current taxi system. Our results demonstrate that the proposed SCCS system can serve the trip demands with 22% fewer vehicles and 37% more vehicle utilization, which shed lights on the design feasibility of future smart transportation systems.

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46

de, Carvalho Jose Manuel Vasconcelos Valerio. "A finite population queueing system with a supporting inventory of spare parts-analysis and design." Thesis, Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/94452.

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In this thesis, a model is developed for a finite population queueing system deployed to meet a constant demand for the situation where failed units require a single spare part to initiate repair action. A supporting inventory of spare parts is included in the model operating under a one-for-one ordering policy. The system was modeled as a Markov process, and an algorithm is presented that numerically evaluates the steady state probabilities. Cost was chosen as the measure of effectiveness of the system. Total system cost consists of shortage costs for not being able to meet the demand for units, population and repair facility annual equivalent costs, holding costs for keeping spare parts in inventory, and procurement and spare part costs related to procurement and purchase activities. A computer program in BASIC, designed for a microcomputer, enables the decision maker to interactively find the design that optimizes the effectiveness measure of the system. The decision variables considered are the number of units in the population, the number of repair channels, and the maximum level of spare parts. One specific design problem is presented.<br>M.S.

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47

Lee, Howoo. "A diffusion approximation for multi-server finite-capacity bulk queues /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487265143146895.

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48

Patuwo, Butje Eddy. "The effect of the dependency in the Markov renewal arrival process on the various performance measures of an exponential server queue." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54258.

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The thesis of this paper is to investigate how the dependency in the arrival process affects the queueing performance measures. The Markov renewal arrival process (MRAP) was chosen as the arrival process. This choice was made because many of the typical arrival processes can be obtained as special cases of the MRAP. But the main reason behind this choice is that the interarrival times of the MRAP are dependent. We assume that the queue is a single server queue with exponential service time and the investigation was carried out numerically because no analytical solution was available. There are 5 parameters of the arrival process used in this investigation: the traffic intensity (ρ), the squared coefficient of variation (scν), the serial correlation defined by the lag-1 correlation (corr) plus the rate ξ and the coefficient of skewness (𝛾). Here are the performance measures of the MR/M/1 queue we investigate: the expected queue length at arbitrary times (L<sup>𝓽</sup>), the standard deviation (σ) of the queue length at arbitrary times and the caudal characteristic η. The other performance measures such as: the expected queue length at arrival time, the waiting time, the sojourn time, etc. can be easily obtained from L<sup>𝓽</sup>. We compare these performance measures against those of the corresponding GI/M/1 queue. When the lag-1 correlation of the arrival process is negative (this means that the lags of the serial correlation alternate in signs), the L<sup>t</sup> of the MR/M/1 queue is smaller (but not by much) than the L<sup>𝓽</sup> of the GI/M/1 queue. Therefore, we focus our attention to the MR/M/1 queue with positive serial correlation. The results are presented using graphs. We find that the coefficient of skewness of the arrival process (𝛾) plays an important role. The L<sup>𝓽</sup> curve decreases rapidly as 𝛾 increases and after certain values of 𝛾 called the turning region, the L<sup>𝓽</sup> curves Hatten. This important observation indicates that to the left of the turning region, the L<sup>𝓽</sup> is almost insensitive to the dependency in the arrival process. However, to the right of the turning region, the L<sup>𝓽</sup> is sensitive to the positive serial correlation in the arrival process. Highly correlated arrival process (large corr and ξ) can cause the L<sup>𝓽</sup> to be significantly larger than the L<sup>𝓽</sup> for the uncorrelated queue. For the MR/M/1 queue, the magnitude of the standard deviation σ is larger than the corresponding L<sup>𝓽</sup>. However, the shapes of the σ curves are similar to those of the L<sup>𝓽</sup> curves. So, all of the conclusions drawn for the L<sup>𝓽</sup> also apply to the standard deviation σ. For the M/M/1 queue, the caudal characteristic η equals to the traffic intensity ρ (η=ρ). For the uncorrelated Gl/M/1 queue, one would expect that when scν<1.0, η<ρ (i.e., the queue would behave like a H/M/1 queue) and when scν>1.0, η>ρ (i.e., the queue would behave like a H/M/1 queue). Our results indicates that this is not necessarily true. We found again that the coefficient of skewness (𝛾) plays an important role. For the uncorrelated GI/M/1 queue with scν>1.0, η can be smaller than ρ when 𝛾 is large enough. For the correlated MR/M/1 queue, even for scν<1.0, a low 𝛾 value combined with the positive serial correlation can cause η to be larger than ρ. On the other hand, scν>1.0 does not necessarily results in η>ρ. A large value of 𝛾 can cause η to be smaller than ρ, even for the queue with highly correlated interarrival times.<br>Ph. D.

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Garikiparthi, Chaitanya N. Liefvoort Appie van de. "Sample path analysis of stochastic processes busy periods of auto-correlated single server queues /." Diss., UMK access, 2008.

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Thesis (Ph. D.)--School of Computing and Engineering. University of Missouri--Kansas City, 2008.<br>"A dissertation in computing networking and telecommunications networking." Advisor: Appie van de Liefvoort. Typescript. Vita. Title from "catalog record" of the print edition Description based on contents viewed Feb. 6, 2009. Includes bibliographical references (leaves 85-89). Online version of the print edition.

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Qua, John F. "Optimum levels of work in process (WIP) for navy field contracting organizations a decision rule /." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA241831.

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Thesis (M.S. in Management)--Naval Postgraduate School, December 1990.<br>Thesis Advisor: Lamm, David V. Second Reader: Caldwell, William J. "December 1990." Description based on title screen as viewed on April 1, 2010. DTIC Identifier(s): Contract administration, decision making, navy, WIP(work in process), backlogs, regression analysis, small purchase actions, procurement, theses. Author(s) subject terms:Decision rule, contracting, small purchase, backlog. Includes bibliographical references (p. 63-64). Also available in print.

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