Applied Probability and Stochastic Processes

2020
Buch

Herausgegeben von: Dr. V. C. Joshua; Prof. Dr. S. R. S. Varadhan; Prof. Dr. Vladimir M. Vishnevsky
Buchreihe: Infosys Science Foundation Series
Verlag: Springer Singapore
Enthalten in: Springer Professional "Wirtschaft+Technik"; Springer Professional "Technik"; Springer Professional "Wirtschaft"

Über dieses Buch

Dieses Buch versammelt ausgewählte Vorträge, die auf der Internationalen Konferenz über Fortschritte in angewandter Wahrscheinlichkeit und stochastischen Prozessen vom 7. bis 10. Januar 2019 am CMS College in Kerala, Indien, präsentiert wurden. Es zeigt qualitativ hochwertige Forschung auf dem Gebiet der angewandten Wahrscheinlichkeit und stochastischer Prozesse, indem es sich auf Techniken zur Modellierung und Analyse von Systemen konzentriert, die sich mit der Zeit entwickeln. Weiterhin werden die Anwendungen stochastischer Modellierung in der Warteschlangen-Theorie, Zuverlässigkeit, Inventar, Finanzmathematik, Operations Research und anderen Bereichen diskutiert. Dieses Buch richtet sich an ein breites Publikum, von Forschern, die sich für angewandte Wahrscheinlichkeiten, stochastische Modellierung in Bezug auf Warteschlangen-Theorie, Inventar und Zuverlässigkeit interessieren, bis hin zu solchen, die in Branchen wie Kommunikations- und Computernetzwerken, verteilten Informationssystemen, Kommunikationssystemen der nächsten Generation, intelligenten Transportnetzen und Finanzmärkten arbeiten.

Mit KI übersetzt

Inhaltsverzeichnis

Frontmatter

Shift–Coupling and Maximality

Abstract

We consider shift-coupling on groups. The theory is based on a key maximality result that does not rely on the group condition.

Hermann Thorisson

Diffusion Approximation Analysis of MultihopWireless Networks: Quality-of-Service and Convergence of Stationary Distribution

Abstract

Consider a multihop wireless network, with multiple source–destination pairs. We obtain a channel scheduling policy which can guarantee end-to-end mean delay for different traffic streams. We show the stability of the network for this policy by convergence to a fluid limit. It is intractable to obtain the stationary distribution of this network. Thus, we also provide a diffusion approximation for this scheme under heavy traffic. We further show that the stationary distribution of the scaled process of the network converges to that of the Brownian limit. This theoretically justifies the performance of the system. We verify the theoretical properties by means of simulations.

K. S. Ashok Krishnan, Vinod Sharma

Analysis of Retrial Queue with Heterogeneous Servers and Markovian Arrival Process

Abstract

Multi-server retrial queueing system with heterogeneous servers is analyzed. Customers arrive to the system according to the Markovian arrival process. Arriving primary customers and customers retrying from orbit occupy available server with the highest service rate, if any. Otherwise, the customers move to the orbit having an infinite capacity. Service times have exponential distribution. The total retrial rate infinitely increases when the number of customers in orbit increases. Behavior of the system is described by multi-dimensional continuous-time Markov chain which belongs to the class of asymptotically quasi-Toeplitz Markov chains. This allows to derive simple and transparent ergodicity condition and compute the stationary distribution of the chain. Presented numerical results illustrate the dynamics of some performance indicators of the system when the average arrival rate increases and the importance of account of correlation in the arrival process.

Liu Mei, Alexander Dudin

What is Standard Brownian Motion?

Abstract

In this expository note, we explain several different historical approaches to the construction of standard Brownian motion.

Krishna B. Athreya

Busy Period Analysis of Multi-Server Retrial Queueing Systems

Abstract

The literature on the busy period analysis in queueing theory is very limited due to the inherent complexity in its study. Recently, using the simulation approach the busy period for the classical multi-server queueing systems was studied by this author and some interesting observations were reported. In this paper we carry out a similar analysis but on a smaller scale in the case of multi-server retrial queueing systems. It should be pointed out that while the literature on retrial queueing system is vast, the same cannot be said about the busy period analysis in retrial queueing systems. Only a few papers with restricted assumptions are available in the literature. This paper is an attempt to fill the void.

Srinivas R. Chakravarthy

Steady-State and Transient Analysis of a Single Channel Cognitive Radio Model with Impatience and Balking

Abstract

In this paper, motivated by an increasing interest in Cognitive Radio wireless transmission systems, we study a stochastic model of a single node of such a system with underlay transmission and balking. The considered model is essentially a single-server system with an ON–OFF type environment governing the service time intensity and triggering the balking events. We utilize the matrix analytic method for steady-state analysis, and perform transient analysis by Complete Level Crossing Information approach. The results of analysis are validated and illustrated by simulation.

Alexander Rumyantsev, Garimella Rama Murthy

Applications of Fluid Queues in Rechargeable Batteries

Abstract

In this paper, the transient solution of the amount of charge in a rechargeable battery of finite capacity is obtained. The level of charge in the battery is governed by different input and output processes and are dependent on the level of charge in the battery. This model has been already discussed in Jones et al. (Fluid queue models of battery life. In: IEEE 19th international symposium on modeling, analysis and simulation of computer and telecommunication systems (MASCOTS), pp. 278–285, 2011), and the distribution of the hitting time was found numerically. In this paper, the method chosen is based on probabilistic approach which allows us to achieve a closed form solution for the distribution of the level of charge in the battery at any time t. Numerical illustrations are presented to verify the analytical results.

Shruti Kapoor, S. Dharmaraja

Analysis of BMAP∕R∕1 Queues Under Gated-Limited Service with the Server’s Single Vacation Policy

Abstract

This paper deals with the finite-buffer single server vacation queues with batch Markovian arrival process (BMAP). The server follows gated-limited service discipline, i.e., the server can serve a maximum of L customers out of those that are waiting at the start of the busy period or all the waiting customers, whichever is minimum. It has been assumed that the server can take only one vacation, i.e., if no customers are found at the end of a vacation, the server remains idle until a batch of customers arrives. The service time and vacation time distributions are considered to possess rational Laplace–Stieltjes transform. The queue-length distribution at post-departure, arbitrary, and pre-arrival epochs has been obtained. Various performance measures like mean queue-length, mean waiting time of an arbitrary customer, and mean length of busy and idle periods have been derived for this model. Numerical results have been presented based on the analysis done.

Souvik Ghosh, A. D. Banik, M. L. Chaudhry

A Production Inventory System with Renewal and Retrial Demands

Abstract

This paper presents a continuous review inventory system with make-to-stock production facility. We assume that the arrival time points of demands form a renewal process and each demand requires only single item. The replenishment of stock is done by producing items one at a time. The production process is started when the inventory level drops to or below a prefixed inventory level, denoted by s(> 0), and is terminated when the maximum inventory level, namely S(> s), is reached. The inter-production time is assumed to be exponential. The customer, whose demand cannot be met during stock out period, enters an orbit of infinite size and from the orbit he sends signal to the inventory system to get his demand satisfied. The inter-retrial time between two successive retrials is assumed to follow exponential distribution. With suitable modeling process, we derived the joint probability distribution of number of customers in the orbit, status of the machine (producing or not) and the inventory level, using matrix geometric method.

G. Arivarignan, M. Keerthana, B. Sivakumar

A Queueing System with Batch Renewal Input and Negative Arrivals

Abstract

This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process, and join the queue/server for service. The negative arrivals are characterized by two independent Poisson arrival processes, a negative customer which removes the positive customer undergoing service, if any, and a disaster which makes the system empty by simultaneously removing all the positive customers present in the system. Using the supplementary variable technique and difference equation method we obtain explicit formulae for the steady-state distribution of the number of positive customers in the system at pre-arrival and arbitrary epochs. Moreover, we discuss the results of some special models with or without negative arrivals along with their stability conditions. The results obtained throughout the analysis are computationally tractable as illustrated by few numerical examples. Furthermore, we discuss the impact of the negative arrivals on the performance of the system by means of some graphical representations.

U. C. Gupta, Nitin Kumar, F. P. Barbhuiya

Asymptotic Analysis Methods for Multi-Server Retrial Queueing Systems

Abstract

In this paper, we consider a multi-server retrial queueing system of type M/M/N. We propose the asymptotic methods for analysis of the system under long delay and heavy load conditions. Application areas of each method are defined and numerical examples are given.

Ekaterina Fedorova, Anatoly Nazarov, Alexander Moiseev

On the Application of Dynamic Screening Method to Resource Queueing System with Infinite Servers

Abstract

Infinite-server queues are a widely used modelling tool thanks to their analytical tractability and their ability to provide conservative upper bounds for the corresponding multi-server queueing systems. A relatively new research field is represented by resource queues, in which every customer requires some volume of resources during her staying in the queue and frees it only at the end of the service. In a nutshell, in this paper the joint distribution of the processes describing the number of busy servers and the total volume of occupied resources is derived and the parameters of the corresponding bidimensional Gaussian distribution are explicitly calculated as a function of the arrival process characteristics and the service time and customers capacity distributions. The aim of this paper is twofold: on one side it summarizes in a ready-to-be-used way the main results for different arrival processes (namely, Poisson processes, renewal processes, MAP, and MMPP), on the other it provides a detailed description of the employed methodology, presenting the key ideas at the basis of powerful analysis tools (dynamic screening and asymptotic analysis methods), developed in the last two decades by Tomsk researchers.

Michele Pagano, Ekaterina Lisovskaya

“Controlled” Versions of the Collatz–Wielandt and Donsker–Varadhan Formulae

Abstract

This is an overview of the work of the authors and their collaborators on the characterization of risk-sensitive costs and rewards in terms of an abstract Collatz–Wielandt formula and in case of rewards, also a controlled version of the Donsker–Varadhan formula. For the finite state and action case, this leads to useful linear and dynamic programming formulations for the reward maximization problem in the reducible case.

Aristotle Arapostathis, Vivek S. Borkar

An (s, S) Production Inventory System with State Dependant Production Rate and Lost Sales

Abstract

In this paper, the system under study is a production inventory system that follows (s, S) replenishment policy and having state dependent production rate. The system considered has infinite capacity where customers arrive according to Poisson process. The service time follows exponential distribution. Further in the system, when the inventory level depletes to s, the production process is switched on and is kept on till the inventory level reaches its maximum capacity S. The production time follows exponential distribution with parameter θ _i, where i represents number of items in the inventory and 0 ≤ i ≤ S − 1. It is assumed that no new customers join the queue when there is void inventory. This yields an explicit product form solution for the steady state probability vector of the system, though there exists a dependence relationship between number of customers joining the queue and time interval for which the production process is turned on. Long run performance measures are computed and lost sales of the system is analysed. A comparison chart that points out the reduction of lost sales with state dependent production rate is also provided along with numerical illustrations for the performance measures. An expected cost function is constructed to numerically investigate the optimal (s, S) pair.

S. Malini, Dhanya Shajin

Analysis of a MAP Risk Model with Stochastic Incomes, Inter-Dependent Phase-Type Claims and a Constant Barrier

Abstract

Inspired by the problems with random income feature, this paper focuses on an insurance risk model with MAP inter-arrival time for premiums as well as claims. We study the model for a convex combination of two types of inter-dependent Phase-type claims, where the probability of claim switching is directly associated with the inter-arrival time of claims. Furthermore, the surplus process of this model is assumed to be restricted by a horizontal barrier “b” above the initial surplus “u”. The transient analysis of the corresponding Markovian fluid flow model is considered to develop the integral equations governing the Gerber–Shiu function and the expected discounted dividends paid until ruin. The closed-form solutions for these integral equations are obtained in terms of Lundberg roots. When the premium sizes are Phase-type distributed, the solutions are explicit at “u = b”. For “u ≤ b”, the solutions are explicit when the premium sizes are distributed exponentially. Finally, to validate and present the tractability of these solution expressions, some numerical illustrations are provided in individual cases.

A. S. Dibu, M. J. Jacob

A PH Distributed Production Inventory Model with Different Modes of Service and MAP Arrivals

Abstract

This paper studies a production inventory model with retrial of customers under (s, S) policy. The arrival of customers is according to a Markovian Arrival Process with representation (D ₀, D ₁) and service times follow an exponential distribution. The production process follows a phase-type distribution. When the inventory level reduces to a pre-assigned level s due to demands, production starts and service is given at a reduced rate. This reduced rate continuous up to the zero level of inventory. The arriving customers are directed to a buffer of finite capacity equal to the current inventory level. An arriving customer, who notices the buffer full, proceeds to an orbit of infinite capacity with some probability and decides to leave the system with the complementary probability. An orbiting customer may retry from the orbit and inter-retrial times are exponentially distributed with linear rate. Various system performance measures of the model are defined. A suitable cost function is constructed and analyzed algorithmically. The optimum (s, S) pair is obtained. The effect of correlation between two successive inter-arrival times is also analyzed.

Salini S. Nair, K. P. Jose

On a Generalized Lifetime Model Using DUS Transformation

Abstract

In this paper, we propose a new lifetime distribution based on the generalized DUS transformation by using Weibull distribution as the baseline distribution. This new distribution exhibits various behaviour of hazard function like increasing, decreasing and inverse bathtub. Here we try to study the characteristics of the new distribution and also analyse a real data set to illustrate the flexibility of the model.

P. Kavya, M. Manoharan

Analysis of Inventory Control Model for Items Having General Deterioration Rate

Abstract

Deterministic inventory control models for stochastic deteriorating items have been extensively studied in the past. However, there is not much work reported to model situations where different phases of deterioration rate are prevalent. In this paper, we develop a deterministic inventory control model with stochastic deterioration incorporated through additive Weibull distribution. In this study, an elegant approach is proposed to consider a time-dependent demand in the planning process and we consider that the holding cost totally depends on time and shortages are allowed for this model. The objective is to minimize the total inventory cost of the proposed model. Finally, the formulated model is illustrated through numerical examples to determine the effectiveness of the proposed model.

V. P. Praveen, M. Manoharan

A Two-Server Queueing System with Processing of Service Items by a Server

Abstract

We consider a two-server (S ₁ and S ₂) queueing system in which the customers arrive according to Markovian arrival process. Each customer is to be provided with a processed item (inventory) at the end of his service. S ₁ provides service alone, whereas S ₂ provides service and also processes the items required to serve the customers. The maximum number of processed item permitted is L. The processing time follows phase type distribution. When the inventory level hits L, S ₂ starts serving customers if any waiting; else stays idle. S ₁ is dedicated to service only. Service is rendered only if there are processed items. Also, when a customer arrives to the system when both servers are idle, S ₁ provides him service and S ₂ continuously remains idle even if it has completed the processing of L items. The duration of service time given by both servers follows phase type distributions of same order, but S ₁ provides service at a slower rate than S ₂. If the inventory level drops to a predetermined level s due to a service completion by S ₂, then he starts processing items. If the inventory level drops to level s due to a service completion by S ₁, then the customer served by S ₂ is shifted to S ₁ to provide him the residual service; S ₂ starts processing items. The arrival process is independent of the inventory processing and service process. The long run behavior of the system is analyzed under condition for stability. We derive some important distributions associated with the model. Numerical investigation of the optimal values of L and s is provided.

A. Krishnamoorthy, Divya V.

A Two-Stage Tandem Queue with Specialist Servers

Abstract

The queueing system considered consist of two multi-server stations in series. Customers arrive according to a Markovian Arrival Process to an infinite capacity queue at the first station. There are c servers who provide identical exponentially distributed service at the first station. A customer at the head of the queue can enter into service if any one of the servers at the first stage is idle. At the second station there are N identical servers called specialist servers . The service time distribution of specialist severs is phase type. There is a finite buffer in between the two stations. On completion of service at first stage, a customer needs service at the second station with probability p or leaves the system with probability 1 − p. In the former case, the customer joins the second station for service in case the waiting room is not full, else he is lost to the system. A customer in the finite buffer can enter into service if at least one of these servers is free. Stability of the system is established and stationary distribution is obtained using Matrix Analytic Methods. We compute distribution of waiting time of customers in the first queue, the mean number of customers lost due to capacity restriction of the waiting space of the second station and the mean waiting time of customers who get into service at the second station. An optimization problem on the capacity of second waiting station is also analyzed.

T. S. Sinu Lal, A. Krishnamoorthy, V. C. Joshua, Vladimir Vishnevsky

The MAP/(PH,PH,PH)/1 Model with Self-Generation of Priorities, Customer Induced Interruption and Retrial of Customers

Abstract

In this article, we consider a MAP/(PH,PH,PH)/1 model to which customers arrive, according to the Markovian arrival process. At the time of arrival, all customers viewed as ordinary. If the server is busy, the arriving customers enter an orbit of infinite capacity. Each customer in orbit tries, independently of each other, to access the server at a constant rate. Each customer in orbit, regardless of others, generates priority with inter occurrence time exponentially distributed with parameter γ. A priority generated customer is immediately taken for service if the server is free. Else such customer is placed in a waiting space A ₁ of capacity one which is reserved only for priority generated customers. We consider a customer induced interruption while service is going on. The interruption occurs according to a Poisson process. The interrupted customers will enter into a buffer B ₁ of finite capacity K and they will spend a random period for completion of interruption. The duration of the interruption of customers in B ₁ follows an exponential distribution. The service facility consists of one server and period of service times of ordinary, priority, and interruption completed customers follow phase-type distribution with appropriate representations. Various performance measures obtained and suitable profit function for getting optimal buffer size K is also derived.

Jomy Punalal, S. Babu

Valuation of Reverse Mortgage

Abstract

This article provides an analytic valuation formula for reverse mortgage. We achieve this by utilizing the principle of balance between the expected gain and expected payment. The underlying model employs a jump-diffusion process to represent the dynamics of the house price, the Vasicek model to drive the instantaneous interest rate, and a bivariate distribution function to describe the longevity risk. We obtain, in particular, the formulas for the lump sum payment, joint annuity, increasing (decreasing) annuity, level annuity of reverse mortgage, and the valuation equation that the variable payment annuities satisfy. We then discuss the monotonicity of the lump sum, annuity, and annuity payment factors with respect to the parameters associated with the home price and the interest rate model. Finally, we analyze the sensitivity of the joint annuity with respect to the parameters associated with the home price, interest rate, and lifetime model. The numerical analysis supports our theoretical results.

D. Kannan, Lina Ma

Stationary Distribution of Discrete-Time Finite-Capacity Queue with Re-sequencing

Abstract

The discrete-time re-sequencing model, consisting of one high and one low priority finite-capacity queue and a single server, which serves the low priority queue if and only if the high priority queue is empty, is being considered. Two types of customers, regular and re-sequencing, arrive at the system. The arrival and service processes are geometric, i.e. in each time slot at most one customer of each type may arrive at the system and at most one customer may be served. A regular customer upon arrival occupies one place in the high priority queue. An arriving re-sequencing customer moves one customer from the high priority queue (if it is not empty) to the low priority queue and itself leaves the system. A regular customer which sees the high priority queue full and a re-sequenced customer which sees the low priority queue full, are lost. Using the generating function method the recursive procedure for the computation of the joint stationary distribution of the number of customers in the high and in the low priority queues is derived.

Rostislav Razumchik, Lusine Meykhanadzhyan

The Polaron Measure

Abstract

{x(t) − x(s)} are the increments of the three dimensional Brownian motion over the intervals [s, t]. $F(T,\omega )=\int \int _{-T\le s<t\le T}{e^{-|t-s|}\over |x(t)-x(s)|} dtds $. Q _α,T is defined as the measure with Radon–Nikodym derivative [Z(T, α)]⁻¹ $\exp [\alpha F(T,\omega )]$ with respect to Brownian Motion, Z(α, T) being the normalization constant $Z(T,\alpha )=E[\exp [\alpha F(T,\omega )]]$. We are interested in the existence of the Polaron measure Q _α =lim_T→∞Q _α,T, the validity of central limit theorem for $(2T)^{-{1\over 2}} (x(T)-x(-T))$ under Q _α,T as well as Q _α and the behavior of Q _α for large α.

Chiranjib Mukherjee, S. R. S. Varadhan

Batch Arrival Multiserver Queue with State-Dependent Setup for Energy-Saving Data Center

Abstract

Queues with setup time are extensively studied because they have application in performance evaluation of power-saving data centers. In data centers, there are a huge number of servers which consume a large amount of energy. In the current technology, an idle server still consumes about 60% of the energy when it is busy. Thus, a simple way to save energy is to turn off idle servers. However, when there are some waiting jobs, we have to turn on the OFF servers in order to reduce the waiting time. A server needs some setup time to be active during which it consumes energy but cannot process jobs. Therefore, there exists a trade-off between power consumption and delay performance. Gandhi et al. (Eval Rev 38:48–50, 2010; Perform Eval 67:1123–1138, 2010) analyze this trade-off using an M/M/c queue with staggered setup (one server in setup at a time). In this paper, using an alternative approach, we obtain generating functions for the joint stationary distribution of the number of active servers and that of jobs in the system for a more general model with batch arrivals and state-dependent setup time. We further obtain moments for the joint queue length. Numerical results reveal that under the same traffic intensity, the mean power consumption decreases with the mean batch size. One of the main theoretical contributions is a new conditional decomposition formula showing that the number of waiting customers under the condition that all servers are busy can be decomposed to the sum of two independent random variables with clear physical interpretation.

Tuan Phung-Duc

Weak Convergence of Probability Measures of Trotter–Kato Approximate Solutions of Stochastic Evolution Equations

Abstract

The paper considers semilinear stochastic evolution equations in real Hilbert spaces. The goal here is to establish the weak convergence of probability measures induced by mild solutions of Trotter–Kato approximating equations.

T. E. Govindan

Stochastic Multiphase Models and Their Application for Analysis of End-to-End Delays in Wireless Multihop Networks

Abstract

This paper presents a study of applying open queueing networks with MAP∕PH∕1∕N nodes for estimation of performance characteristics of wireless networks with linear topology using either relay, or DCF channels. Basic properties of such queueing networks are outlined along with Markovian arrival processes (MAPs) and phase-type (PH) distributions fitting methods. Due to exponential growth of the system state space in MAP∕PH∕1∕N →⋯ →•∕PH∕1∕N queueing networks, the exact calculation of its characteristics is practically impossible for an arbitrary large number of nodes, and we propose an algorithm which finds approximated results by iterative estimations of node parameters using departure processes approximations with MAPs of smaller order. We use this approach to get numerical results, which are further compared with the data obtained by Monte-Carlo method. The comparison shows that the results obtained by both methods are very close to each other, while the iterative approach requires significantly less time. The paper provides results of fitting transmission delays using PH distributions and end-to-end delays estimations for wireless networks with simple relay and IEEE 802.11 DCF channels. All numerical results are validated using a simulation model.

Vladimir Vishnevsky, Andrey Larionov

Variance Laplacian: Quadratic Forms in Statistics

Abstract

In this research paper, it is proved that the variance of a discrete random variable, Z can be expressed as a quadratic form associated with a Laplacian matrix i.e.

$$\displaystyle \mbox{ Variance }[Z]=X^{T} G X $$

G is Laplacian matrix whose elements are expressed in terms of probabilities. We formally state and prove the properties of Variance Laplacian matrix, G. Some implications of the properties of such matrix to statistics are discussed. It is reasoned that several interesting quadratic forms can be naturally associated with statistical measures such as the covariance of two random variables. It is hoped that VARIANCE LAPLACIAN MATRIX G will be of significant interest in statistical applications. The results are generalized to continuous random variables also. It is reasoned that cross-fertilization of results from the theory of quadratic forms and probability theory/statistics will lead to new research directions.

Garimella Rama Murthy

On the Feynman–Kac Formula

Abstract

In this article given y : [0, η) → H, a continuous map into a Hilbert space H, we study the equation

$$\displaystyle \hat y(t)= e^{ \int \limits _0^t c(s,\hat y)ds}y(t), $$

where c(s, ⋅) is a given “potential” on C([0, η), H). Applying the transformation $y \rightarrow \hat y$ to the solutions of the SPDE and SDE underlying a diffusion, we study the Feynman–Kac formula.

B. Rajeev

Heterogeneous System GI/GI(n)∕∞ with Random Customers Capacities

Abstract

In the paper, we consider a queuing system with n types of customers. We assume that each customer arrives at the queue according to a renewal process and takes a random resource amount, independent of their service time. We write Kolmogorov integro-differential equation, which, in general, cannot be analytically solved. Hence, we look for the solution under the condition of infinitely growing a service time, and we obtain multi-dimensional asymptotic approximations. We show that the n-dimensional probability distribution of the total resource amounts is asymptotically Gaussian, and we look at its accuracy via Kolmogorov distance.

Ekaterina Lisovskaya, Svetlana Moiseeva, Michele Pagano, Ekaterina Pankratova

Metadaten
Barrierefreiheit

Titel: Applied Probability and Stochastic Processes
Herausgegeben von: Dr. V. C. Joshua
Prof. Dr. S. R. S. Varadhan
Prof. Dr. Vladimir M. Vishnevsky
Verlag: Springer Singapore
Electronic ISBN: 978-981-15-5951-8
Print ISBN: 978-981-15-5950-1
DOI: https://doi.org/10.1007/978-981-15-5951-8

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Inhaltsverzeichnis

Frontmatter

Shift–Coupling and Maximality

Diffusion Approximation Analysis of MultihopWireless Networks: Quality-of-Service and Convergence of Stationary Distribution

Analysis of Retrial Queue with Heterogeneous Servers and Markovian Arrival Process

What is Standard Brownian Motion?

Busy Period Analysis of Multi-Server Retrial Queueing Systems

Steady-State and Transient Analysis of a Single Channel Cognitive Radio Model with Impatience and Balking

Applications of Fluid Queues in Rechargeable Batteries

Analysis of BMAP∕R∕1 Queues Under Gated-Limited Service with the Server’s Single Vacation Policy

A Production Inventory System with Renewal and Retrial Demands

A Queueing System with Batch Renewal Input and Negative Arrivals

Asymptotic Analysis Methods for Multi-Server Retrial Queueing Systems

On the Application of Dynamic Screening Method to Resource Queueing System with Infinite Servers

“Controlled” Versions of the Collatz–Wielandt and Donsker–Varadhan Formulae

An (s, S) Production Inventory System with State Dependant Production Rate and Lost Sales

Analysis of a MAP Risk Model with Stochastic Incomes, Inter-Dependent Phase-Type Claims and a Constant Barrier

A PH Distributed Production Inventory Model with Different Modes of Service and MAP Arrivals

On a Generalized Lifetime Model Using DUS Transformation

Analysis of Inventory Control Model for Items Having General Deterioration Rate

A Two-Server Queueing System with Processing of Service Items by a Server

A Two-Stage Tandem Queue with Specialist Servers

The MAP/(PH,PH,PH)/1 Model with Self-Generation of Priorities, Customer Induced Interruption and Retrial of Customers

Valuation of Reverse Mortgage

Stationary Distribution of Discrete-Time Finite-Capacity Queue with Re-sequencing

The Polaron Measure

Batch Arrival Multiserver Queue with State-Dependent Setup for Energy-Saving Data Center

Weak Convergence of Probability Measures of Trotter–Kato Approximate Solutions of Stochastic Evolution Equations

Stochastic Multiphase Models and Their Application for Analysis of End-to-End Delays in Wireless Multihop Networks

Variance Laplacian: Quadratic Forms in Statistics

On the Feynman–Kac Formula

Heterogeneous System GI/GI(n)∕∞ with Random Customers Capacities

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