Stochastic analyses arising from a new approach for closed queueing networks

Analyses are addressed for a number of problems in queueing systems and stochastic modeling that arose due to an investigation into techniques that could be used to approximate general closed networks. In Chapter II, a method is presented to calculate the system size distribution at an arbitrary point in time and at departures for a (n)/G/1/N queue. The analysis is carried out using an embedded Markov chain approach. An algorithm is also developed that combines our analysis with the recursive method of Gupta and Rao. This algorithm compares favorably with that of Gupta and Rao and will solve some situations when Gupta and Rao's method fails or becomes intractable. In Chapter III, an approach is developed for generating exact solutions of the time-dependent conditional joint probability distributions for a phase-type renewal process. Closed-form expressions are derived when a class of Coxian distributions are used for the inter-renewal distribution. The class of Coxian distributions was chosen so that solutions could be obtained for any mean and variance desired in the inter-renewal times. In Chapter IV, an algorithm is developed to generate numerical solutions for the steady-state system size probabilities and waiting time distribution functions of the SM/PH/1/N queue by using the matrix-analytic method. Closed form results are also obtained for particular situations of the preceding queue. In addition, it is demonstrated that the SM/PH/1/N model can be implemented to the analysis of a sequential two-queue system. This is an extension to the work by Neuts and Chakravarthy. In Chapter V, principal results developed in the preceding chapters are employed for approximate analysis of the closed network of queues with arbitrary service times. Specifically, the (n)/G/1/N queue is applied to closed networks of a general topology, and a sequential two-queue model consisting of the (n)/G/1/N and SM/PH/1/N queues is proposed for tandem queueing networks

Performance evaluation of warehouses with automated storage and retrieval technologies.

In this dissertation, we study the performance evaluation of two automated warehouse material handling (MH) technologies - automated storage/retrieval system (AS/RS) and autonomous vehicle storage/retrieval system (AVS/RS). AS/RS is a traditional automated warehouse MH technology and has been used for more than five decades. AVS/RS is a relatively new automated warehouse MH technology and an alternative to AS/RS. There are two possible configurations of AVS/RS: AVS/RS with tier-captive vehicles and AVS/RS with tier-to-tier vehicles. We model the AS/RS and both configurations of the AVS/RS as queueing networks. We analyze and develop approximate algorithms for these network models and use them to estimate performance of the two automated warehouse MH technologies. Chapter 2 contains two parts. The first part is a brief review of existing papers about AS/RS and AVS/RS. The second part is a methodological review of queueing network theory, which serves as a building block for our study. In Chapter 3, we model AS/RSs and AVS/RSs with tier-captive vehicles as open queueing networks (OQNs). We show how to analyze OQNs and estimate related performance measures. We then apply an existing OQN analyzer to compare the two MH technologies and answer various design questions. In Chapter 4 and Chapter 5, we present some efficient algorithms to solve SOQN. We show how to model AVS/RSs with tier-to-tier vehicles as SOQNs and evaluate performance of these designs in Chapter 6. AVS/RS is a relatively new automated warehouse design technology. Hence, there are few efficient analytical tools to evaluate performance measures of this technology. We developed some efficient algorithms based on SOQN to quickly and effectively evaluate performance of AVS/RS. Additionally, we present a tool that helps a warehouse designer during the concepting stage to determine the type of MH technology to use, analyze numerous alternate warehouse configurations and select one of these for final implementation

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Generalised analytic queueing network models. The need, creation, development and validation of mathematical and computational tools for the construction of analytic queueing network models capturing more critical system behaviour.

Modelling is an important technique in the comprehension and management of complex systems. Queueing network models capture most relevant information from computer system and network behaviour. The construction and resolution of these models is constrained by many factors. Approximations contain detail lost for exact solution and/or provide results at lower cost than simulation. Information at the resource and interactive command level is gathered with monitors under ULTRIX'. Validation studies indicate central processor service times are highly variable on the system. More pessimistic predictions assuming this variability are in part verified by observation. The utility of the Generalised Exponential (GE) as a distribution parameterised by mean and variance is explored. Small networks of GE service centres can be solved exactly using methods proposed for Generalised Stochastic Petri Nets. For two centre. systems of GE type a new technique simplifying the balance equations is developed. A very efficient "building bglloocbka"l. is presented for exactly solving two centre systems with service or transfer blocking, Bernoulli feedback and load dependent rate, multiple GE servers. In the tandem finite buffer algorithm the building block illustrates problems encountered modelling high variability in blocking networks. ': . _. A parametric validation study is made of approximations for single class closed networks of First-Come-First-Served (FCFS) centres with general service times. The multiserver extension using the building block is validated. Finally the Maximum Entropy approximation is extended to FCFS centres with multiple chains and implemented with computationally efficient convolution

Conditional dynamics of non-Markovian, infinite-server queues

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (p. 75-79).We study the transient dynamics of a partially observed, infinite server queue fed with a Poisson arrival process whose controlled rate is changed at discrete points in time. More specifically, we define a state that incorporates partial information from the history of the process and write analytical formula for the dynamics of the system (state transition probabilities). Moreover, we develop an approximation method that makes the state finite-dimensional, and introduce techniques to further reduce the dimension of the state. This method could thus enable the formulation of tractable DPs in the future.by Theophane Weber.S.M

Queueing Networks With Blocking.

The area of classical (product form) queueing networks is briefly discussed. The principal results for classical queueing networks are summarized. The transfer, service and rejection blocking policies are defined, and their use in queueing network models are presented. An overview of the literature in the area of queueing networks with blocking is given, and the relations between the three blocking policies is discussed in general. Duality theorems for open and closed queueing networks with rejection blocking and a single job class are proved. Using a duality theorem, an exact solution is found for closed blocking networks which contain so many jobs that if one station is empty all other stations are full. Algorithms to compute performance measures, in particular throughputs, follow from the way the solution is obtained. It is then proved that for open, mixed and closed networks with rejection blocking, multiple job classes, general service time distributions and reversible routing the equilibrium state probabilities have product form. The reversed process for these networks is examined, and it is proved that it represents a network of the same type. Formulas for throughputs are derived, and algorithms to compute performance measures are outlined. Finally, closed central server models with state-dependent routing, multiple job classes and rejection blocking are investigated. The equilibrium state probabilities have a modified product form, and the reversed process is a network of the same type. Formulas for performance measures are derived for this model and algorithms to compute them are outlined

フレキシブル生産セルの性能解析に関する研究

本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである京都大学0048新制・課程博士博士(工学)甲第5117号工博第1238号新制||工||869(附属図書館)UT51-92-J164京都大学大学院工学研究科数理工学専攻(主査)教授 長谷川 利治, 教授 茨木 俊秀, 教授 片山 徹学位規則第4条第1項該当Doctor of EngineeringKyoto UniversityDFA

Entropy Maximisation and Queues With or Without Balking. An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks.

An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks Keywords: Queues, Balking, Maximum Entropy (ME) Principle, Global Balance (GB), Queue Length Distribution (QLD), Generalised Geometric (GGeo), Generalised Exponential (GE), Generalised Discrete Half Normal (GdHN), Congestion Management, Packet Dropping Policy (PDP) Generalisations to links between discrete least biased (i.e. maximum entropy (ME)) distribution inferences and Markov chains are conjectured towards the performance modelling, analysis and prediction of general, single server queues with or without arrival balking. New ME solutions, namely the generalised discrete Half Normal (GdHN) and truncated GdHN (GdHNT) distributions are characterised, subject to appropriate mean value constraints, for inferences of stationary discrete state probability distributions. Moreover, a closed form global balance (GB) solution is derived for the queue length distribution (QLD) of the M/GE/1/K queue subject to extended Morse balking, characterised by a Poisson prospective arrival process, i.i.d. generalised exponential (GE) service times and finite capacity, K. In this context, based on comprehensive numerical experimentation, the latter GB solution is conjectured to be a special case of the GdHNT ME distribution. ii Owing to the appropriate operational properties of the M/GE/1/K queue subject to extended Morse balking, this queueing system is applied as an ME performance model of Internet Protocol (IP)-based communication network nodes featuring static or dynamic packet dropping congestion management schemes. A performance evaluation study in terms of the model’s delay is carried out. Subsequently, the QLD’s of the GE/GE/1/K censored queue subject to extended Morse balking under three different composite batch balking and batch blocking policies are solved via the technique of GB. Following comprehensive numerical experimentation, the latter QLD’s are also conjectured to be special cases of the GdHNT. Limitations of this work and open problems which have arisen are included after the conclusion