Dharmaraja Selvamuthu

Indian Institute of Technology Delhi | IIT Delhi · Department of Mathematics

The potential benefits of 5G networks, such as faster data speeds and improved user experiences, come with a critical challenge—efficiently preserving energy in base stations (BSs). Addressing this challenge is crucial, necessitating a focus on maximizing the energy efficiency of these stations. BSs play a vital role in providing coverage and capac...

This article investigates the pricing of variable annuity guarantees, with particularly emphasising on the Guaranteed Minimum Accumulation Benefit (GMAB) with several embedded options, like roll-up and ratchet. A continuous time model that integrates regime switching dynamics into the local volatility is proposed for the contract’s pricing. As loca...

Unmanned Aerial Vehicle (UAV) is a remotely controlled or autonomously operated aircraft used for various applications such as surveillance, communication, research, etc. UAVs are nowadays being recognized as potential threats, prompting a surge in the development of anti-UAV technologies. An anti-UAV system is designed to detect, track, and neutra...

In this paper, we look into the modeling of free space optical channel and design of the HAP-based wireless optical networks. For vertical beam propagation, the pressure and temperature gradients alter with height. Microscale variations in refractivity result in uncertainties that depend on elevation. As a result, irradiance fading variance caused...

The discrete-time Hawkes process (DTHP) is a sub-class of $g$-functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behaviour of the DTHP and its compensator. We...

This paper derives a closed-form expression for the default probability and the default correlation of firms under a structural model of credit risk. Specifically, the underlying firms are assumed to have the value process driven by a Hawkes jump-diffusion model with the continuous parts of the trajectories being driven by correlated Brownian motio...

A modified differentiated vacation queueing system with a close-down period and impatient customers is investigated in this research paper. The proposed model can be applied to study the energy management mechanisms of WiMAX and tethered high altitude platform (HAP) systems. In this system, the WiMAX mobile station (MS) switches to a close-down per...

In long term evolution-advanced (LTE-A) different radio access technologies coexist due to multi-node receivers and antennas. Under such a scenario, user experience, Quality of Service(QoS), and the loss becomes paramount goal. The main objective of this paper is to develop a new model such that it can serve a heterogeneous network environment and...

This chapter delves into some discrete and continuous distributions that are frequently encountered, while also examining their key characteristics.

Response surface methodology or in short RSM is a collection of mathematical and statistical tools and techniques that are useful in developing, understanding, and optimizing processes and products. Using this methodology, the responses that are influenced by several variables can be modeled, analyzed, and optimized.

Random experiments have sample spaces may not consist of numbers. For instance, in a coin-tossing experiment, the sample space consists of the outcomes “head" and “tail”, i.e., Since statistical methods primarily rely on numerical data, it becomes necessary to represent the outcomes of the sample space mathematically.

In order to study the effects of two or more factors on a response variable, factorial designs are usually used. By following these designs, all possible combinations of the levels of the factors are investigated. The factorial designs are ideal designs for studying the interaction effect between factors. By interaction effect, we mean that a facto...

In statistics, the capability to infer information about a population from a sample and assess the validity of those inferences is essential. Because of this, it is crucial to research the asymptotic behavior of r.v. sequences. The weak law of large numbers, the strong law of large numbers, and the central limit theorem (CLT), are some of the most...

Multiple r.v.s are often involved in various random experiments. For instance, an educator might examine the joint behavior of study time and grades, while a physician may investigate the joint behavior of blood pressure and weight. Similarly, an economist could study the joint behavior of business volume and profit. Indeed, most practical problems...

In the subject of statistical quality control, the word control bears a special technical meaning. A manufacturing process is said to be in control when a stable system of chance causes seems to be operating. However, this word is often misinterpreted by saying that a process is in control only when it has no variation.

Statistical quality control means application of statistical techniques for checking the quality of products. The products include manufactured goods such as computers, mobile phones, automobiles, clothing and services such as health care, banking, and public transportation. The word “quality” is defined in many ways. To some people, quality means...

In many real-life problems, the population parameter(s) is (are) unknown and someone is interested to obtain the value(s) of parameter(s). But, if the whole population is too large to study or the units of the population are destructive in nature or there is limited resources and manpower available then it is not practically convenient to examine e...

In this chapter, we will discuss another way to deal with the problem of making a statement about an unknown parameter associated with a probability distribution, based on a random sample. Instead of finding an estimate for the parameter, we shall often find it convenient to hypothesize a value for it and then use the information from the sample to...

If mathematics is the queen of sciences, then probability is the queen of applied mathematics. The concept of probability originated in the seventeenth century and can be traced to games of chance and gambling. Games of chance include actions like drawing a card, tossing a coin, selecting people at random and noting number of females, number of cal...

Now, we are ready to discuss the relationship between probability and statistical inference. The two key facts to statistical inference are (a) the population parameters are fixed numbers that are usually unknown and (b) sample statistics are known for any sample. For different samples, we get different values of the statistics and hence this varia...

Often, we wish to investigate the effect of a factor (independent variable) on a response (dependent variable). We then carry out an experiment where the levels of the factor are varied. Such experiments are known as single-factor experiment. There are many designs available to carry out such experiment. The most popular ones are completely randomi...

Statistics is an art of learning from data. One of the tasks to be performed after collecting data from any observed situation, phenomena, or interested variable is to analyze that data to extract some useful information. Statistical analysis is one of the most applied tools in the industry, decision-making, planning, public policy, etc. Many pract...

It is quite often that one is interested to quantify the dependence (positive or negative) between two or more random variables. The basic role of covariance is to identify the nature of dependence. However, the covariance is not an appropriate measure of dependence since it is dependent on the scale of observations. Hence, a measure is required wh...

Maximizing energy efficiency in User Equipment (UE) is a critical concern due to the limited power sources available in these devices. This holds true for both LTE-A and LTE-5G networks. To assess energy efficiency in these networks, we’ve developed three stochastic models: the Markov model, semi-Markov model, Markov regenerative process (MRGP) mod...

In this chapter, we consider time-dependent and stationary characteristics of a reparable k-out-of-n models. The preliminaries 3.1 provides a definition of the types of system recovery after a complete failure, as well as additional notations. The time-dependent probabilities for two repair scenarios are considered in Sect. 3.2. The stationary char...

This chapter is devoted to the development of mathematical methods for Preventive Maintenance (PM) organization for k-out-of-n model using a different optimization criteria. In Sect. 4.1 we consider PM organization with respect to maximization of the availability criteria. Section 4.2 continues these investigations for a cost-type criterion. The PM...

This chapter considers the reliability function of a k-out-of-n model under conditions where the recovery of intermediate failures is either allowed or not. Various scenarios of the dependence of the system failure on the failure of its components are considered. Analytical expressions and algorithms are presented for calculating the reliability fu...

This chapter aims to demonstrate some new approaches to investigation of k-out-of-n models. Section 5.1 considers the capabilities of decomposable semi-regenerative processes. In Sects. 5.2 and 5.3, some simulation methods and machine learning techniques are considered to assess the probabilistic and time characteristics of the reliability of repai...

This chapter is devoted to the tethered high-altitude telecommunications platforms and their reliability study using k-out-of-n models.

This book provides a systematic presentation of the major results in the field of the theory of k-out-of-n systems obtained in recent years and their applications for the reliability assessment of high-altitude unmanned platforms. Mathematical models, methods, and algorithms, presented in the book, will make a significant contribution to the develo...

With the increasing prevalence of wireless sensor networks, the uninterrupted operation of these networks becomes essential. To ensure continuous functionality, wireless networks rely on available base stations (BSs). However, the persistent operation of BSs comes at the cost of substantial energy consumption. Consequently, given the surge in wirel...

Narrowband Internet of Things (NB‐IoT) embodies the vision of connecting virtually anything with everything and aims to support a massive number of devices for small data transmission. However, an efficient power‐saving model for battery‐operated NB‐IoT devices is the need of the hour. In addition to the legacy discontinuous reception (DRX) scheme,...

The intensification of mobile broadband services and user experience is explicitly dependent on the increased battery life of user equipment (UE) and minimized delay in service. In 5G New Radio (NR), in addition to the Discontinuous Reception (DRX) scheme, Bandwidth Part (BWP) switching plays a significant role in reducing UE power consumption. The...

Base stations (BSs) sleeping strategy has been widely analyzed nowadays to save energy in 5G cellular networks. 5G cellular networks are meant to deliver a higher data speed rate, ultra-low latency, more reliability, massive network capacity, more availability, and a more uniform user experience. In 5G cellular networks, BSs consume more power whic...

Reducing energy consumption is the vital goal of green communication. Base station (BS) is a radio receiver/transmitter that serves as the hub of the local wireless network. It is a gateway between a wired network and the wireless network. BS consumes high energy to receive and transfer the signals. Power consumption in base station can be minimize...

Drying is an important process in the tea processing industry. Drying arrests enzymatic reactions to produce a stable product with increased shelf life. Development of the quality attributes such as taste, fragrance, color, etc. in tea is initiated during processing steps prior to drying, which undergoes the final stage of development during drying...

An inverse Hawkes process is a process having constant intensity and stochastic jump size, depending on the past number of jumps, while a Hawkes process has the intensity which is stochastic. An extended inverse Hawkes process is a process obtained by combining a Hawkes process and an inverse Hawkes process. The focus of this paper is to investigat...

Fifth‐generation (5G) networks deal with high‐frequency data rates, ultra‐low latency, more reliability, massive network capacity, more availability, and a more uniform user experience. To validate the high‐frequency rates, 5G networks engage beam searching operation. By adopting a beam searching state between the short and long sleep, one can redu...

Base Stations (BSs) sleeping strategy is an efficient way to obtain the energy efficiency of cellular networks. To meet the increasing demand of high-data-rate for wireless applications, small cell BSs provide a promising and feasible approach but that consumes more power. Hence, energy efficiency in small cell BSs is a major issue to be concerned....

This study proposed and evaluated a new insurance product, i.e., the variable annuity product, accompanied by the health status and the guaranteed lifelong withdrawal benefit (GLWB). Due to specific problems, the insurance sector is now one of the riskiest industries. The aging of the population and rising medical service costs as a result of techn...

This study investigates the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifetime withdrawal benefit (GLWB) rider. VAs are annuities in which the value is linked to a bond and equity sub‐account fund. The guaranteed lifetime withdrawal benefit rider regularly provides a series of payments to the policyholder for th...

This work focuses over the performability analysis of a multi-server retrial queueing model with phase-type inter-retrial times in cellular networks. It is considered that the pattern of the new call arrival and handoff call arrival follows marked Markovian arrival process. The service times of both types of calls are phase-type (PH) distributed wi...

In the world of broadband network, Long Term Evolution-Advanced (LTE-A) is facing a large demand due to its high-speed wireless data transmission, extensive coverage from base stations, and a luxury of upgrading protocol software. However, its efficiency depends mainly on the two significant attributes which are reliability and survivability. Furth...

This paper is devoted to the study of the number of customers in infinite-server systems driven by Hawkes processes. In these systems, the self-exciting arrival process is assumed to be represented by a Hawkes process and the self-exciting service process by a state-dependent Hawkes process (sdHawkes process). Under some suitable conditions, for th...

This paper is devoted to the study of the number of customers in infinite-server systems driven by Hawkes processes. In these systems, the self-exciting arrival process is assumed to be represented by a Hawkes process and the self-exciting service process by a state-dependent Hawkes process (sdHawkes process). Under some suitable conditions, for th...

The intensification of mobile broadband services and user experience is explicitly dependent on increased battery life of user equipment (UE) and minimized delay in service. In 5G New Radio (NR), in addition to Discontinuous Reception (DRX) scheme, Bandwidth Part (BWP) switching plays a significant role in reducing UE power consumption. The dynamic...

Pricing a variable annuity (VA) is traditionally based on models with standard Brownian motion (BM). The assumption of independent increments in the BM is not always realistic as the price process of the risky assets exhibit a long‐range dependency. To model such assets, a fractional Brownian motion (FBM) with Hurst parameter 12,1$$ \left(\frac{1}{...

Energy saving in User Equipment (UE) is one of the important issues for limited sources of power in the device. It is critical for the UE to maximize its energy efficiency. In this paper, we have presented two stochastic models, namely the Markov model and semi-Markov model, for the UE based on the states of discontinuous reception (DRX) mechanism,...

This paper studies the behavior of a batch arrival single server retrial queueing model under three different vacation policies. Three types of vacation policies, single vacation, multiple vacations, and atmost J-vacations with impatient customers in general retrial times are considered. The probability generating function and marginal generating f...

An M/M/1 dual-stage vacation queueing system with a system disaster is analysed in this paper. This work is motivated by the dual-stage sleep mode mechanism in the MAC (Media Access Control) and the physical layer of a WiMAX system with Denial of Service. In this model, the server switches to two types of vacation called stage-I and stage-II vacati...

The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed...

The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed...

The management of energy consumption in agriculture is a worldwide concern because of the adverse effects of CO2 emissions from fossil fuels, which are generally used as an energy source for various applications in agriculture. Renewable energy technologies are promoted in many parts of the world for various agriculture applications for mitigating...

This article studies the problem of hedging a defaultable claim via the maximization of the mean value of exponential utility, over a set of admissible strategies. The dynamics of the underlying asset is assumed to be governed by mutually exciting Hawkes processes, which captures the jumps clustering phenomenon observed in the market. The resulting...

In this work, the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifelong withdrawal benefit (GLWB) rider has been considered. VAs are annuities whose value is linked with a sub-account fund consisting of bonds and equities. The GLWB rider provides a series of regular payments to the policyholder during the policy du...

This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times, in particular, forward and backward recurrence processes. We obtain the transient solution of the process in the form of a generalized Markov renewal equation. A distinguishing feature is that Markov and semi-Markov processes result as special c...

In tea production, India ranks second largest in the world, after China. Indian tea industry is one of the largest in the world and with over 13,000 gardens and produces 1350 million kg of tea leaves. Tea production and processing require electrical and thermal energy in various processes such as irrigation, withering, rolling, fermentation, drying...

This work focuses over the performability analysis of a multi-server retrial queueing model with phase-type inter-retrial times in cellular networks. It is considered that the pattern of the new call arrival and handoff call arrival follows Markovian arrival process (MAP). The service times of both types of calls are phase-type (PH ) distributed wi...

In this study, we extend upon the model by Haring et al. (2001) by introducing retrial phenomenon in multi-server queueing system. When at most g number of guard channels are available, it allows new calls to join the retrial group. This retrial group is called orbit and can hold a maximum of m retrial calls. The impact of retrial over certain perf...

This article studies the problem of valuation of equity-indexed annuities (EIA) when the stock index follows a Hawkes jump-diffusion model to account for the jump risk and clustering of index price jumps. Further, the interest rate is assumed to be driven by Vasicek type model, correlated to the dynamics of the stock index. In the proposed framewor...

We consider a continuous-time Ehrenfest model defined over the integers from -N to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe instantaneously resets the process to state 0. We investigate both the transient and steady-state probabilities of the above model. Further, the first passage time through state...

In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered duration-dependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To m...

Abstract This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds. The criteria to optimize the credit portfolio is based on l ∞ -norm risk measure and the proposed optimization model is formulated as a linear programming problem. The input parameters to the optimization model are r...

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 l...

This article deals with batch arrival single server queue with random vacation policy, in which the server takes the maximum number of random vacations till it finds some customers waiting in a queue at a vacation completion epoch. If no arrival occurs after completing maximum number of random vacations, the server stays dormant in the system and w...

In the tertiary education institutions, rankings have started gaining ample attention all over the world. This has created a profound impact on the indian higher education system. As a result of that, in 2015, the government of India announced National institutional ranking framework (NIRF) to rank the indian institutions. NIRF is based on multiple...

Abstract Introduction Nowadays, the most significant challenges in the stock market is to predict the stock prices. The stock price data represents a financial time series data which becomes more difficult to predict due to its characteristics and dynamic nature. Case description Support Vector Machines (SVM) and Artificial Neural Networks (ANN) ar...

This work begins with the understanding of the fundamentals of blood banking by analyzing various aspects of its supply chain and then examines the current scenario of blood shortage in India. A mathematical model is proposed to curb the mismatch between surplus and shortage of blood units at blood banks. This proposed model has three main echelons...

In optimization models based on stochastic programming, we often face the problem of representing expectations in proper form known as scenario generation. With advances in computational power, a number of methods starting from simple Monte-Carlo to dedicated approaches such as method of moment-matching and scenario reduction are being used for mul...

Agriculture has occupied a crucial position in India’s economic development and economy since past times. In recent times, Government of India, concerned with the welfare of the farming community, have either encouraged or directly participated in setting up of risk-sharing institutions. Crop insurance is a basic tool by which farmers can stabilize...

Several factors, including weather vagaries, possess a serious threat to agricultural crop production in India and also are noteworthy risks to the economy. Crop yield depends on nutrition level of soils, fertilizer availability and cost, pest control, agro-meteorological input parameters like temperature, rainfall and other factors. Further, each...

Now, we are ready to discuss the relationship between probability and statistical inference. The two key facts to statistical inference are (a) the population parameters are fixed numbers that are usually unknown and (b) sample statistics are known for any sample. For different samples, we get different values of the statistics and hence this varia...

Often, we wish to investigate the effect of a factor (independent variable) on a response (dependent variable). We then carry out an experiment where the levels of the factor are varied. Such experiments are known as single-factor experiment. There are many designs available to carry out such experiment. The most popular ones are completely randomi...