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This paper analyzes a finite-buffer queueing system, where customers arrive in batches and the accepted customers are served in batches by a single server. The service is assumed to be dependent on the batch-size and follows a general bulk service rule. The inter-arrival times of batches are assumed to be correlated and they are represented through the batch Markovian arrival process (BMAP). Computation procedure of the queue-length distributions at the post-batch-service completion, an arbitrary, and the pre-batch-arrival epochs are discussed. Various performance measures along with the consecutive customer loss probabilities are studied considering batch-size-dependent renewal service time distributions. Further, the above finite-buffer bulk-service queueing model is also investigated considering correlated batch-service times which are presented through the Markovian service process (MSP). The phase-dependent consecutive loss probabilities for the correlated batch-service times are determined. In the form of tables and graphs, a variety of numerical results for different batch-service time distributions are presented in this paper.

Statistical learning is an innate function in the brain and considered to be essential for producing and comprehending structured information such as music. Within the framework of statistical learning the brain has an ability to calculate the transitional probabilities of sequences such as speech and music, and to predict a future state using learned statistics. This paper computationally examines whether and how statistical learning and knowledge partially contributes to musical representation in jazz improvisation. The results represent the time-course variations in a musician&rsquo, s statistical knowledge. Furthermore, the findings show that improvisational musical representation might be susceptible to higher- but not lower-order statistical knowledge (i.e., knowledge of higher-order transitional probability). The evidence also demonstrates the individuality of improvisation for each improviser, which in part depends on statistical knowledge. Thus, this study suggests that statistical properties in jazz improvisation underline individuality of musical representation.

This study is supported in part by TUBITAK grant 119C028, and in part by Turkcell Technology within the framework of 5G and Beyond Joint Graduate Support Programme coordinated by Information and Communication Technologies Authority. A communication receiver that wants to pull data from a remote sensor by exploiting wireless energy transfer is considered. The receiver has a long-term average energy budget for this operation, and its goal is to keep the time average of a general age penalty function as small as possible. The channel from the source to the receiver is a two-state (ON/OFF) communication link whose state is IID or Markovian, and known instantaneously by the receiver. Modeling the problem as a constrained Markov decision problem, we obtain a randomized threshold-based decision policy that achieves the minimum possible average age penalty. We determine the optimal time average Age of Information and age violation probabilities by exploiting the optimality of the derived policy. IEEE Control Systems Society Information Theory Society Communication Systems Technical Committee (Performance of Communication Systems Working Group) Publisher's Version WOS:000766966900006

Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain tractability. One of the more popular of such memoryless models are Continuous Time Bayesian Networks (CTBNs). In this work, we lift its restriction to exponential survival times to arbitrary distributions. Current extensions achieve this via auxiliary states, which hinder tractability. To avoid that, we introduce a set of node-wise clocks to construct a collection of graph-coupled semi-Markov chains. We provide algorithms for parameter and structure inference, which make use of local dependencies and conduct experiments on synthetic data and a data-set generated through a benchmark tool for gene regulatory networks. In doing so, we point out advantages compared to current CTBN extensions., Comment: 10 main pages, 7 pages appendix, 3 figures, proceedings of ICML2020

International audience; WLANs (Wireless Local Area Networks) based on the IEEE 802.11 standard have become ubiquitous in our daily lives. We typically augment the number of APs (Access Points) within a WLAN to extend its coverage and transmission capacity. This leads to network densification, which in turn demands some form of coordination between APs so as to avoid potential misconfigurations. In this paper, we describe a performance modeling method that can provide guidance for configuring WLANs and be used as a decision-support tool by a network architect or as an algorithm embedded within a WLAN controller. The proposed approach estimates the attained throughput of each AP, as a function of the WLAN's conflict graph, the AP loads, the frame sizes, and the link transmission rates. Our modeling approach employs a Divide-and-Conquer strategy which breaks down the original problem into multiple sub-problems, whose solutions are then combined to provide the solution to the original problem. We conducted extensive simulation experiments using the ns-3 simulator that show the model's accuracy is generally good with relative errors typically less than 10%. We then explore two issues of WLAN configuration: choosing a channel allocation for the APs and enabling frame aggregation on APs.

A general method to discover and embed variable orders of dependencies in a network representation., To ensure the correctness of network analysis methods, the network (as the input) has to be a sufficiently accurate representation of the underlying data. However, when representing sequential data from complex systems, such as global shipping traffic or Web clickstream traffic as networks, conventional network representations that implicitly assume the Markov property (first-order dependency) can quickly become limiting. This assumption holds that, when movements are simulated on the network, the next movement depends only on the current node, discounting the fact that the movement may depend on several previous steps. However, we show that data derived from many complex systems can show up to fifth-order dependencies. In these cases, the oversimplifying assumption of the first-order network representation can lead to inaccurate network analysis results. To address this problem, we propose the higher-order network (HON) representation that can discover and embed variable orders of dependencies in a network representation. Through a comprehensive empirical evaluation and analysis, we establish several desirable characteristics of HON, including accuracy, scalability, and direct compatibility with the existing suite of network analysis methods. We illustrate how HON can be applied to a broad variety of tasks, such as random walking, clustering, and ranking, and we demonstrate that, by using it as input, HON yields more accurate results without any modification to these tasks.

A Markovian single server queue in a varying environment with gate mechanism is studied. Exact expressions for the duration of the nth batch and the number served are obtained by exploiting the connection between queues, branching processes and continued fractions. Numerical illustrations are presented.

In recent years fluid approaches to the analysis of Markov populations models have been demonstrated to have great pragmatic value. Initially developed to estimate the behaviour of the system in terms of the expected values of population counts, the fluid approach has subsequently been extended to more sophisticated interrogations of models through its embedding within model checking procedures. In this paper we extend recent work on checking CSL properties of individual agents within a Markovian population model, to consider the checking of properties which incorporate rewards., Comment: In Proceedings QAPL 2015, arXiv:1509.08169

We introduce a new class of processes aiming at modelling random fluctuations of an asset value more efficiently than traditional Lévy processes. In this study, we consider that the object value C is a real discrete random process (N → R), whose increments are subject to the present state of a "market", described by a Markovian process M : as the successive market states are not pairwise independent, C's fluctuations are not independent either, so C cannot be assimilated as a Lévy process. We call this structure a C-process : we present methods to analyze it, mainly extending the notion of Lundberg's parameter of a diffusion Lévy process, to take M into account during the computations. Once done, we aim more specifically at controlling C's default time T0 = min ({t ∈ N|C(t), Nous introduisons une nouvelle classe de processus dont l'objet est de modéliser les fluctuations de la valeur d'un actif plus efficacement que le font les processus habituels Lévy. Dans cette étude, nous considérons que la valeur objet C est un processus aléatoire discret réel (N → R), dont les incréments sont soumis à l'état courant d'un "marché" décrit par un processus Markovien M : les états successifs du marché n'étant pas indépendants deux à deux, les fluctuations de C ne le sont pas non plus, donc C ne peut pas être assimilé à un processus de Lévy. Nous nommons cette structure un C-processus : nous présentons des méthodes pour l'analyser, notamment en étendant la notion d'exposant de Lundberg d'un processus de diffusion de Lévy, en tenant compte de M durant les calculs. Par la suite, nous nous intéresserons plus précisément au contrôle du temps de faillite de C, T0 = min ({t ∈ N|C(t)

AimWhile early warning scores (EWS) have the potential to identify physiological deterioration in an acute care setting, the implementation of EWS in clinical practice has yet to be fully realized. The primary aim of this study is to identify optimal patient-centered rapid response team (RRT) activation rules using electronic medical records (EMR)-derived Markovian models.MethodsThe setting for the observational cohort study included 38,356 adult general floor patients hospitalized in 2011. The national early warning score (NEWS) was used to measure the patient health condition. Chi-square and Kruskal Wallis tests were used to identify statistically significant subpopulations as a function of the admission type (medical or surgical), frailty as measured by the Braden skin score, and history of prior clinical deterioration (RRT, cardiopulmonary arrest, or unscheduled ICU transfer).ResultsStatistical tests identified 12 statistically significant subpopulations which differed clinically, as measured by length of stay and time to re-admission (P

"Livelihood systems that depend on mobile resources must constantly adapt to change. For people living in permanent settlements, environmental changes that affect the distribution of a migratory species may reduce the availability of a primary food source, with the potential to destabilize the regional social-ecological system. Food security for Arctic indigenous peoples harvesting barren ground caribou (Rangifer tarandus granti) depends on movement patterns of migratory herds. Quantitative assessments of physical, ecological, and social effects on caribou distribution have proven difficult because of the significant interannual variability in seasonal caribou movement patterns. We developed and evaluated a modeling approach for simulating the distribution of a migratory herd throughout its annual cycle over a multiyear period. Beginning with spatial and temporal scales developed in previous studies of the Porcupine Caribou Herd of Canada and Alaska, we used satellite collar locations to compute and analyze season-by-season probabilities of movement of animals between habitat zones under two alternative weather conditions for each season. We then built a set of transition matrices from these movement probabilities, and simulated the sequence of movements across the landscape as a Markov process driven by externally imposed seasonal weather states. Statistical tests showed that the predicted distributions of caribou were consistent with observed distributions, and significantly correlated with subsistence harvest levels for three user communities. Our approach could be applied to other caribou herds and could be adapted for simulating the distribution of other ungulates and species with similarly large interannual variability in the use of their range."

A Pyro-electric Infrared (FIR) sensor based flame detection system is proposed using a Markovian decision algorithm. A differential PIR sensor is only sensitive to sudden temperature variations within its viewing range and it produces a time-varying signal. The wavelet transform of the FIR sensor signal is used for feature extraction from sensor signal and wavelet parameters are fed to a set of Markov models corresponding to the flame flicker process of an uncontrolled fire, ordinary activity of human beings and other objects. The final decision is reached based on the model yielding the highest probability among others. Comparative results show that the system can be used for fire detection in large rooms. (c) 2012 Elsevier Ltd. All rights reserved.

In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper., {"references":["Y. C. Cheng and T. Robertazzi, Critical connectivity phenomena in\nmultihop radio models. IEEE Trans. on Commun., 37(1989) 770-777.","F. Chung, S. Handjani and D. Jungreis, Generalizations of Polya-s urn\nproblem. Annals of Combinatorics, 7(2003) 141-153.","S. Cs┬¿org╦Øo and W.-B. Wu, On the clustering of independent uniform\nrandom variables. Random Structures and Algorithms, 25(2004) 396-420.","J. D'─▒az, D. Mitsche and X. P'erez-Gim'enez, On the connectivity of\ndynamic random geometric graphs. Proc. of the 19th Annual ACM-SIAM\nSymposium on Discrete Algorithms, San Francisco, 2008, 601-610.","O. Dousse, P. Thiran and M. Hasler, Connectivity in ad hoc and hybrid\nnetworks. Proc. of IEEE Infocom, New York, 2002, 1079-1088.","E. Godehardt and J. Jaworski, On the conncetivity of a random interval\ngraph. Random Structures and Algorithms, 9 (1996) 137-161.","B. Gupta, S. K. Iyer and D. Manjunath, Topological properties of the one\ndimensional exponential random geometric graph. Random Structures and\nAlgorithms, 32(2008) 181-204.","S. K. Iyer and D. Manjunath, Topological properties of random wireless\nnetworks. S┬»adhan┬»a, 31(2006) 117-139.","K. K. Jose and R. N. Pillai, Geometric infinite divisiblility and its\napplications in autoregressive time series modeling. In: V. Thankaraj\n(Ed.)Stochastic Process and its Applications, Wiley Eastern, New Delhi,\n1995.\n[10] N. Karamchandani, D. Manjunath and S. K. Iyer, On the clustering\nproperties of exponential random networks. IEEE Proc. of 6th WoWMoM,\n2005, 177-182.\n[11] N. Karamchandani, D. Manjunath, D. Yogeshwaran and S. K. Iyer,\nEvolving random geometric graph models for mobile wireless networks.\nIEEE Proc. of the 4th WiOpt, Boston, 2006, 1-7.\n[12] V. Kurlin, L. Mihaylova and S. Maskell, How many randomly distributed\nwireless sensors are enough to make a 1-dimensional network connected\nwith a given probability? Technical Report, arXiv:0710.1001v1[cs.IT].\n[13] A. J. Lawrance and P. A. W. Lewis, A new autoregressive time\nseries model in exponential variables (NEAR(1)). Advances in Applied\nProbability, 13(1981) 826-845.\n[14] D. Miorandi and E. Altman, Connectivity in one-dimensional ad hoc\nnetworks: A queueing theoretical approach. Wireless Networks, 12(2006)\n573-587.\n[15] S. Muthukrishnan and G. Pandurangan, The bin-covering technique for\nthresholding random geometric graph properties. Proc. of 16th Annual\nACM-SIAM Symposium on Discrete Algorithms, Vancouver, 2005, 989-\n998.\n[16] M. D. Penrose, Random Geometric Graphs, Oxford University Press,\n2003.\n[17] S. M. Ross, Introduction to Probability Models. Academic Press, 2006.\n[18] V. Seetha Lekshmi and K. K. Jose, Autoregressive processes with Pakes\nand geometric Pakes generalized Linnik marginals. Statist. Probab. Lett.,\n76(2006) 318-326.\n[19] E. Seneta, Non-negative Matrices and Markov Chains. Springer-Verlag,\n1981.\n[20] Y. Shang, Exponential random geometric graph process models for\nmobile wireless networks. International Conference on Cyber-Enabled\nDistributed Computing and Knowledge Discovery, Zhangjiajie, 2009, 56-\n61.\n[21] Y. Shang, Connectivity in a random interval graph with access points.\nInformation Processing Letters, 109(2009), 446-449.\n[22] Y. Shang, On the degree sequence of random geometric digraphs.\nApplied Mathematical Sciences, 4(2010) 2001-2012.\n[23] Y. Shang, Laws of large numbers of subgraphs in directed random\ngeometric networks. International Electronic Journal of Pure and Applied\nMathematics, 2(2010) 69-79."]}

Darbe bus nagrinėjama mišraus tipo masinė aptarnavimo sistema, kurią gali sudaryti n paraiškų šaltinių, su atitinkamais paprasčiausių srautų intensyvumais, o paraiškos gali būti paskirstomos į m aptarnavimo įrenginių su fiksuotomis prioritetinėmis paraiškų eilėmis, kur paraiškos aptarnavimo laikas S yra pasiskirstęs pagal apibendrintą tikimybinio skirstinio funkciją G(t). Darbo tikslas – sukurti programinę įrangą, kuri pagal pateiktą sistemos funkcionavimo aprašymą schematine struktūra apskaičiuoja sistemos stacionariąsias tikimybes ir tikimybines charakteristikas. This paper analyses the underlying multi-server and multi-class queuing system which is receiving applications of corresponding intensities distributed by Poisson process and can be spread among multi-class servers with fixed waiting positions, where service time S of a application has a general probability distribution function G(t). The object of this paper is to create the software which enables to compute stationary probabilities and to estimate stochastic characteristics of the system which is defined in schematic structure.

We present a \textit{mesoscopic}description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time variable. The main assumption is that the longer a particle survives inside spine, the smaller becomes the transition probability from spine to dendrite. We extend a linear model presented in [PRL, \textbf{101}, 218102 (2008)] and derive the nonlinear Master equations for the average densities of particles inside spines and parent dendrite by eliminating residence time variable. We show that the flux of particles between spines and parent dendrite is not local in time and space. In particular the average flux of particles from a population of spines through spines necks into parent dendrite depends on chemical reactions in spines. This memory effect means that one can not separate the exchange flux of particles and the chemical reactions inside spines. This phenomenon does not exist in the Markovian case. The flux of particles from dendrite to spines is found to depend on the transport process inside dendrite. We show that if the particles inside a dendrite have constant velocity, the mean particle's position $ $ increases as $t^{\mu}$ with $\mu, Comment: 12 pages

The Lamperti transformation of a self-similar process is a stationary process. In particular, the fractional Brownian motion transforms to the second order stationary Gaussian process. This process is represented as a series of independent processes. The terms of this series are Ornstein-Uhlenbeck processes if H1/2. From the representation effective approximations of the process are derived. The corresponding results for the fractional Brownian motion are obtained by applying the inverse Lamperti transformation. Implications for simulating the fractional Brownian motion are discussed. 40 5 1395 1435 Cited By :2

Numeraire invariance is a well-known technique in option pricing and hedging theory. It takes a convenient asset as the numeraire, as if it were the medium of exchange, and expresses all other asset and option prices in units of this numeraire. Since the price of the numeraire relative to itself is identically 1 at all times, this reduces pricing and hedging to a market with zero-interest rates. A somewhat controversial implication is that the modelling focus should be more on the asset price ratios rather than on the asset price processes themselves. The idea of numeraire invariance is already implicit in Merton (1973), and since then many authors have contributed to its development. After a brief survey of its origins, we state and prove the numeraire invariance principle for general semimartingale price processes, following essentially Duffie [3]. We then present its application to unique pricing in arbitrage-free models and discuss nondegeneracy and unique hedging.

Numeraire invariance is a well-known technique in option pricing and hedging theory. It takes a convenient asset as the numeraire, as if it were the medium of exchange, and expresses all other asset and option prices in units of this numeraire. Since the price of the numeraire relative to itself is identically 1 at all times, this reduces pricing and hedging to a market with zero-interest rates. A somewhat controversial implication is that the modelling focus should be more on the asset price ratios rather than on the asset price processes themselves. The idea of numeraire invariance is already implicit in Merton (1973), and since then many authors have contributed to its development. After a brief survey of its origins, we state and prove the numeraire invariance principle for general semimartingale price processes, following essentially Duffie [3]. We then present its application to unique pricing in arbitrage-free models and discuss nondegeneracy and unique hedging.

The contract is described and market examples given. Essential theoretical developments are introduced and cited chronologically. The principles and techniques of hedging and unique pricing are illustrated for the two simplest nontrivial examples: the classical Black-Scholes/Merton/Margrabe exchange option model brought somewhat uptodate from its form three decades ago, and a lesser exponential Poisson analogue to illustrate jumps. Beyond these, a simplified Markovian SDE/PDE line is sketched in an arbitrage-free semimartingale setting. Focus is maintained on construction of a hedge using Itˆo’s formula and on unique pricing, now for general homogenous payoff functions. Clarity is primed as the multivariate log-Gaussian and exponential Poisson cases are worked out. Numeraire invariance is emphasized as the primary means to reduce dimensionality by one to the projective space where the SDE dynamics are specified and the PDEs solved (or expectations explicitly calculated). Predictable representation of a homogenous payoff with deltas (hedge ratios) as partial derivatives or partial differences of the option price function is highlighted. Equivalent martingale measures are utilized to show unique pricing with bounded deltas (and in the nondegenerate case unique hedging) and to exhibit the PDE or closed-form solutions as numeraire-deflated conditional expectations in the usual way. Homogeneity, change of numeraire, and extension to dividends are discussed.

The contract is described and market examples given. Essential theoretical developments are introduced and cited chronologically. The principles and techniques of hedging and unique pricing are illustrated for the two simplest nontrivial examples: the classical Black-Scholes/Merton/Margrabe exchange option model brought somewhat uptodate from its form three decades ago, and a lesser exponential Poisson analogue to illustrate jumps. Beyond these, a simplified Markovian SDE/PDE line is sketched in an arbitrage-free semimartingale setting. Focus is maintained on construction of a hedge using Itˆo’s formula and on unique pricing, now for general homogenous payoff functions. Clarity is primed as the multivariate log-Gaussian and exponential Poisson cases are worked out. Numeraire invariance is emphasized as the primary means to reduce dimensionality by one to the projective space where the SDE dynamics are specified and the PDEs solved (or expectations explicitly calculated). Predictable representation of a homogenous payoff with deltas (hedge ratios) as partial derivatives or partial differences of the option price function is highlighted. Equivalent martingale measures are utilized to show unique pricing with bounded deltas (and in the nondegenerate case unique hedging) and to exhibit the PDE or closed-form solutions as numeraire-deflated conditional expectations in the usual way. Homogeneity, change of numeraire, and extension to dividends are discussed.

The contract is described and market examples given. Essential theoretical developments are introduced and cited chronologically. The principles and techniques of hedging and unique pricing are illustrated for the two simplest nontrivial examples: the classical Black-Scholes/Merton/Margrabe exchange option model brought somewhat up-to-date from its form three decades ago, and a lesser exponential Poisson analogue to illustrate jumps. Beyond these, a simplified Markovian SDE/PDE line is sketched in an arbitrage-free semimartingale setting. Focus is maintained on construction of a hedge using Ito's formula and on unique pricing, now for general homogenous payoff functions. Clarity is primed as the multivariate log-Gaussian and exponential Poisson cases are worked out. Numeraire invariance is emphasized as the primary means to reduce dimensionality by one to the projective space where the SDE dynamics are specified and the PDEs solved (or expectations explicitly calculated). Predictable representation of a homogenous payoff with deltas (hedge ratios) as partial derivatives or partial differences of the option price function is highlighted. Equivalent martingale measures are utilized to show unique pricing with bounded deltas (and in the nondegenerate case unique hedging) and to exhibit the PDE or closed-form solutions as numeraire-deflated conditional expectations in the usual way. Homogeneity, change of numeraire, and extension to dividends are discussed.

It is studied the time dependent description of electron-molecule collision complexes is studied. It is shown that the equation of motion for the. wave packet is non-Markovian, that is, the time development depends on the previous history of the system. The integro-differential equation of motion is explicitly solved.

This contribution proposes a decompositional iterative method with low memory requirements for the steadystate analysis ofKronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case. © 2008, Kent State University.

This paper presents a probabilistic model for the service life assessment of bridge deteriorating truss. Damage evolution of each structural member is dealt as a transition process through different states of performance. The transition process is modeled as a Markovian renewal process which formulation allows considering eventual improvements of the structural performance. In this way, the model is used to set up selective maintenance and/or rehabilitation interventions. Then the preventive maintenance scenarios selected are economically compared. © 2012 Taylor & Francis Group.