A tandem queue with server slow-down and blocking

We consider two variants of a two-station tandem network with blocking. In both variants the first server ceases to work when the queue length at the second station hits a `blocking threshold'. In addition, in variant $2$ the first server decreases its service rate when the second queue exceeds a `slow-down threshold', which is smaller than the blocking level. In both variants the arrival process is Poisson and the service times at both stations are exponentially distributed. Note, however, that in case of slow-downs, server $1$ works at a high rate, a slow rate, or not at all, depending on whether the second queue is below or above the slow-down threshold or at the blocking threshold, respectively. For variant $1$, i.e., only blocking, we concentrate on the geometric decay rate of the number of jobs in the first buffer and prove that for increasing blocking thresholds the sequence of decay rates decreases monotonically and at least geometrically fast to $\max\{\rho_1,\rho_2\}$, where $\rho_i$ is the load at server $i$. The methods used in the proof also allow us to clarify the asymptotic queue length distribution at the second station. Then we generalize the analysis to variant $2$, i.e., slow-down and blocking, and establish analogous results. \u

A Stochastic Model for Car-Sharing Systems

Vehicle-sharing systems are becoming important for urban transportation. In these systems, users arrive at a station, pick up a vehicle, use it for a while and then return it to another station of their choice. Depending on the type of system, there might be a possibility to book vehicles before picking-up and/or a parking space at the chosen arrival station. Each station has a finite capacity and cannot host more vehicles and reserved parking spaces than its capacity. We propose a stochastic model for an homogeneous car-sharing system with possibility to reserve a parking space at the arrival station when picking-up a car. We compute the performance of the system and the optimal fleet size according to a specific metric. It differs from a similar model for bike-sharing systems because of reservation that induces complexity, especially when traffic increases

Modeling and analysis to improve the quality of healthcare services

For many healthcare services or medical procedures, patients have extensive risk of complication or face death when treatment is delayed. When a queue is formed in such a situation, it is very important to assess the suffering and risk faced by patients in queue and plan sufficient medical capabilities in advance to address the concerns. As the diversity of care settings increases, congestion in facilities causes many patients to unnecessarily spend extra days in intensive care facilities. Performance evaluation of current healthcare service systems using queueing theory gains more and more importance because of patient flows and systems complexity. Queueing models have been used in handsome number of healthcare studies, but the incorporation of blocking is still limited. In this research work, we study an efficient two-stage multi-class queueing network system with blocking and phase-type service time distribution to analyze such congestion processes. We also consider parallel servers at each station and first-come-first-serve non-preemptive service discipline are used to improve the performance of healthcare service systems

Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation

We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient importance sampling algorithms with provable performance guarantees. For linear stochastic fluid networks without modulation, we prove that the number of runs needed (so as to obtain an estimate with a given precision) increases polynomially (whereas the probability under consideration decays essentially exponentially); for networks operating in the slow modulation regime, our algorithm is asymptotically efficient. Our techniques are in the tradition of the rare-event simulation procedures that were developed for the sample-mean of i.i.d. one-dimensional light-tailed random variables, and intensively use the idea of exponential twisting. In passing, we also point out how to set up a recursion to evaluate the (transient and stationary) moments of the joint storage level in Markov-modulated linear stochastic fluid networks

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"

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

Detecting Markov Chain Instability: A Monte Carlo Approach

We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of deciding whether the set has a subset of positive Lebesgue measure for which the Markov chain is unstable. The approach is based on a variant of simulated annealing, and consequently only mild assumptions are needed to obtain performance guarantees. The theoretical underpinnings of our algorithm are based on a result stating that the stability of a set of parameters can be phrased in terms of the stability of a single Markov chain that searches the set for unstable parameters. Our framework leads to a procedure that is capable of performing statistically rigorous tests for instability, which has been extensively tested using several examples of standard and non-standard queueing networks