We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed proportions. When one of the stations becomes empty, the total service capacity is given to the non-empty station. Moreover, arrival rates depend on the state of the network. The system is described by a Markov modulated random walk in the quarter plane representing the number of jobs in the two stations and the state of the network. By applying the generating function approach, we first apply the power series approximation method to obtain power series expansions of the generating function of the stationary queue lengths for both network states. Then, we also provide a way to derive the generating function of the stationary queue lengths for both network states in terms of the solution of a Riemann-Hilbert boundary value problem. Numerical results are obtained to show insights in the system performance.
A tandem queue with two coupled processors was analyzed in @cite_27 , while later computational issues, as well as asymptotic results were discussed and presented in @cite_15 @cite_25 , respectively. There, it was shown that the problem of finding the bivariate generating function of the stationary joint queue length distribution is reduced to a Riemann-Hilbert boundary value problem.
@cite_27 @cite_25 @cite_15
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We consider a tandem queue with coupled processors and analyze the two-dimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this two-dimensional process is derived and solved through the theory of Riemann-Hilbert boundary value problems. In Resing and Ormeci [16] it is shown that the two-stage tandem queue with coupled processors can be solved using the theory of boundary value problems. In this paper we consider the issues that arise when calculating performance measures like the mean queue length and the fraction of time a station is empty. It is assumed that jobs arrive at the first station according to a Poisson process and require service at both stations before leaving the system. The amount of work that a job requires at each of the stations is an independent, exponentially distributed random variable. When both stations are nonempty, the total service capacity is shared among the stations according to fixed proportions. When one of the stations becomes empty, the total service capacity is given to the nonempty station. We study the two-dimensional Markov process representing the numbers of jobs at the two stations. The problem of finding the generating function of the stationary distribution can be reduced to two different Riemann-Hilbert boundary value problems, where both problems yield a complete analytical solution. We discuss the similarities and differences between the two problems, and relate them to the computational aspects of obtaining performance measures. This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis. We provide power series approximations for a structured batch arrival single server retrial system with two infinite capacity weighted fair orbit queues, i.e., the re-transmission rate of an orbit depends on the state of the other orbit queue. We consider both exponential and arbitrary distributed service times. In both cases we obtain power series expansions of the generating functions of the stationary joint orbit queue-length distributions, and provide a recursive approach to calculate their coefficients. We also show how to obtain the generating function of the stationary joint orbit queue-length distribution with the aid of a Riemann boundary value problem. Power series approximations are also provided for the model with two independent Poisson streams of jobs with single arrivals. Numerical illustrations are performed and show the accuracy of our approach. We derive in this paper closed formulae for the joint probability generating function of the number of customers in the two FIFO queues of a generalized processor-sharing (GPS) system with two classes of customers arriving according to Poisson processes and requiring exponential service times. In contrast to previous studies published on the GPS system, we show that it is possible to establish explicit expressions for the generating functions of the number of customers in each queue without calling for the formulation of a Riemann-Hilbert problem. We specifically prove that the problem of determining the unknown functions due to the reflecting conditions on the boundaries of the positive quarter plane can be reduced to a Poisson equation. The explicit formulae are then used to derive some characteristics of the GPS system (in particular the tails of the probability distributions of the numbers of customers in each queue). We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability β, and a customer of queue 2 is served with probability 1?β. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z 1,z 2) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z 1,z 2) in β. The first coefficient of this power series corresponds to the priority case β=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Pade approximation. Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i = 1,2) finds the server busy, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. This creates a system with three dependent queues. Such a queueing system serves as a model for two competing job streams in a carrier sensing multiple access system. We study the queueing system using multi-dimensional probability generating functions, and derive its necessary and sufficient stability conditions while solving a Riemann- Hilbert boundary value problem. Various performance measures are calculated and numerical results are presented. In particular, numerical results demonstrate that the proposed multiple access system with two types of jobs and constant retrial rates provides incentives for the users to respect their contracts. The Laplace transform of the probability distribution of the end-to-end delay in tandem networks is obtained where the first and or second queue are G-queues, i.e. they have negative arrivals. For the most general case the method is based on the solution of a boundary value problem on a closed contour in the complex plane, which itself reduces to the solution of a Fredholm integral equation of the second kind. We also consider the dependence or independence of the sojourn times at each queue in the two special cases where only one of the queues is a G-queue, the other having no negative arrivals. In this work, we consider an adaptive two-user random access scheme with multipacket reception (MPR) capabilities. A user adapts its transmission characteristics based on the status of the other user. The users have external random traffic stored in their queues. We derive the stable throughput region of the system and the convexity conditions of this region. We derive analytically the queueing delay by formulating and solving a Riemann- Hilbert boundary value problem. Finally, we evaluate numerically the presented theoretical results. We are studying the semiclassical limit of the 1+1 dimensional integrable nonlinear Schrodinger equation with defocusing cubic nonlinearity on the half line. Our analysis relies on the recent theory of , which reduces boundary value problems for soliton equations to Riemann–Hilbert factorization problems. We employ the method of nonlinear steepest descent to asymptotically deform the given Riemann–Hilbert problem to an explicilty solvable one. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. Most existing discussions regarding the time-dependent distribution of queue length was undertaken in the context of isolated intersections. However, computing queue length distributions for a signalized network with generic topology is very challenging because such process involves convolution and nonlinear transformation of random variables, which is analytically intractable. To address such issue, this study proposes a stochastic queue model considering the strong interdependence relations between adjacent intersections using the probability generating function as a mathematical tool. Various traffic flow phenomena, including queue formation and dissipation, platoon dispersion, flow merging and diverging, queue spillover, and downstream blockage, are formulated as stochastic events, and their distributions are iteratively computed through a stochastic network loading procedure. Both theoretical derivation and numerical investigations are presented to demonstrate the effectiveness of the proposed approach in analyzing the delay and queues of signalized networks under different congestion levels. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. In this paper, we consider a two-user and a three-user slotted ALOHA network with multi-packet reception (MPR) capabilities and a queue-aware transmission control. In this setting, the nodes can adapt their transmission probabilities and their transmission parameters based on the status of the other nodes. Each user has external bursty arrivals that are stored in their infinite capacity queues. We focus on the fundamental problem of characterizing the stable throughput region, as well as of investigating the queueing delay. For the two- and the three-user cases, we obtain the exact stability region, whereas in the former case, we also provide the conditions under which the stability region is a convex set. We perform a detailed mathematical analysis to study the queueing delay in the two-user case by formulating two boundary value problems, the solution of which provides the generating function of the joint stationary probability distribution of the queue size at user nodes. Furthermore, for the two-user symmetric case with MPR, we obtain a lower and an upper bound for the average delay without the need of solving a boundary value problem. In addition, we provide a closed form expression for the gap between the lower and the upper bound. The bounds as it is seen in the numerical results appear to be tight. Explicit expressions for the average delay are obtained for the symmetrical model with capture effect. We also provide a closed form expression for the optimal transmission probability that minimizes the average delay in the symmetric capture case. Finally, we evaluate numerically the presented theoretical results. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . Abstract In this work, we investigate a slotted-time relay assisted cooperative random access wireless network with multipacket (MPR) reception capabilities. MPR refers to the capability of a wireless node to successfully receive packets from more than two other modes that transmit simultaneously at the same slot. We consider a network of N saturated sources that transmit packets to a common destination node with the cooperation of two infinite capacity relay nodes. The relays assist the sources by forwarding the packets that failed to reach the destination. Moreover, the relays have also packets of their own to transmit to the destination. We further assume that the relays employ a state-dependent retransmission control mechanism. In particular, a relay node accordingly adapts its transmission probability based on the status of the other relay. Such a protocol is towards self-aware networks and leads to substantial performance gains in terms of delay. We investigate the stability region and the throughput performance for the full MPR model. Moreover, for the asymmetric two-sources, two-relay case we derive the generating function of the stationary joint queue-length distribution with the aid of the theory of boundary value problems. For the symmetric case, we obtain explicit expressions for the average queueing delay in a relay node without solving a boundary value problem. Extensive numerical examples are presented and provide insights on the system performance.