Department of Mathematics

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An Adaptive Fractional Guard Channel Based CAC Scheme for Heterogeneous Traffic in Wireless Cellular Networks
(IEEE, 2019-03) Kulshrestha, Rakhee
In this paper, we propose an adaptive fractional guard channel based call admission scheme for heterogeneous traffic. We have developed a generalised model for investigating the quality of service (QoS) and the effect of mobility of subscribers through simulation and also analysed the results. We evaluate the proposed scheme by computing the new call blocking probability and handoff blocking probability. Moreover, our scheme being relevant to the choice of the wireless medium is extensible to LTE Networks that utilise MIMO wireless technology.
Analysis of G–queue with unreliable server
(Springer, 2012-12) Kulshrestha, Rakhee
This paper presents a model for a discrete time single server G-queue with two types of independent arrivals, namely positive and negative. The arrival of negative customer to queueing system removes one customer from the head of the queue (RCH), which causes server breakdown. The repair of the server is non-instantaneous and after repair server is assumed as good as new. The interarrival times of both positive and negative customers and the repair times of the server are geometrically distributed. We analyse the queueing system by using Matrix Geometric method. The expressions for various performance measures such as mean queue length, throughput, delay, etc. are derived and calculated numerically.
Analysis of Multiple Queue Model in Cellular Networks with Sub Rating of Channels
(King Abdulaziz University Journal, 2012) Kulshrestha, Rakhee
In cellular Networks we generally consider a single queue for each cell, some authors proposed a model with a dedicated queue for each transceiver in the cell. We have extended the idea of dedicated queue for each transceiver in the cell with sub-rating channels to improve the Quality of Service (QOS) of the system. In this paper we have compared three models, in model-I we used guard channels to give priority to handoff attempts and a buffer for finite size is provided to give priority to handoff data attempts, further in model-II we have taken sub-rating channel scheme (SCS). In subrating scheme a full rate channel is temporarily divided into two half rate channels in the blocked cell; one half rate channel serve the originating call and another serves handoff call. We proposed a dedicated queue for each transceiver in the cell with sub-rating in model-III. The Fixed Channel Assignment Scheme is considered for all models. The probabilities of handoff failure, blocking probability of new calls, forced termination of handoff calls, probability of noncompleted calls for all models are calculated for varying assumed of values arrival rate of new data calls, arrival rate of new voice calls, buffer size of channels and service rates. We compared and analyzed the numerical results to validate the proposed models.
Analysis of Spectrum Sensing and Spectrum Access in Cognitive Radio Networks With Heterogeneous Traffic and pp-Retry Buffering
(IEEE, 2022-07) Kulshrestha, Rakhee
It is well known that cognitive radio (CR) techniques have great potential to deal with the problem of radio spectrum scarcity. Spectrum sensing technique plays a critical role in enabling unlicensed secondary users (SUs) to utilize spectrum holes in cognitive radio networks (CRNs). However, a licensed primary user (PU) can be appropriately protected by simultaneously performing spectrum sensing and data transmission i.e., by using full-duplex (FD) mode. In this paper, we have proposed and analyzed a strategy which includes spectrum sensing and spectrum access mechanisms both. We consider heterogeneous traffic of real-time and non real-time SUs based on their different delay tolerance characteristics. We address the issue of false alarm rate (FAR) associated with FD sensing. Spectrum handoff and call buffering strategies with p -Retry policy are employed jointly so that SUs that would otherwise be blocked or forcibly dropped could be buffered and possibly served later. To evaluate the performance of the proposed strategy, five-dimensional continuous time Markov chain (CTMC) model is developed and the queueing-theoretic approach is utilized. Numerical results demonstrate the influence of spectrum sensing errors on the performance of such CRNs. Results also reveal that the provision of buffers under retrial policy increases the overall network resource utilization while decreasing blocking and dropping probabilities.
Applications of Mathematical Modeling, Machine Learning, and Intelligent Computing for Industrial Development
(CRC Press, 2023) Kulshrestha, Rakhee
The text focuses on mathematical modeling and applications of advanced techniques of machine learning, and artificial intelligence, including artificial neural networks, evolutionary computing, data mining, and fuzzy systems to solve performance and design issues more precisely. Intelligent computing encompasses technologies, algorithms, and models in providing effective and efficient solutions to a wide range of problems, including the airport’s intelligent safety system. It will serve as an ideal reference text for senior undergraduate, graduate students, and academic researchers in fields that include industrial engineering, manufacturing engineering, computer engineering, and mathematics. The book: Discusses mathematical modeling for traffic, sustainable supply chain, vehicular Ad-Hoc networks, and internet of things networks with intelligent gateways Covers advanced machine learning, artificial intelligence, fuzzy systems, evolutionary computing, and data mining techniques for real- world problems Presents applications of mathematical models in chronic diseases such as kidney and coronary artery diseases Highlights advances in mathematical modeling, strength, and benefits of machine learning and artificial intelligence, including driving goals, applicability, algorithms, and processes involved Showcases emerging real-life topics on mathematical models, machine learning, and intelligent computing using an interdisciplinary approach The text presents emerging real-life topics on mathematical models, machine learning, and intelligent computing in a single volume. It will serve as an ideal text for senior undergraduate students, graduate students, and researchers in diverse fields, including industrial and manufacturing engineering, computer engineering, and mathematics.
Bilevel control of degraded machining system with warm standbys, setup and vacation
(Elsevier, 2004-12) Kulshrestha, Rakhee
In this paper, we study (N, L) switch-over policy for machine repair model with warm standbys and two repairmen. The repairman (R1) turns on for repair only when N-failed units are accumulated and starts repair after a set up time which is assumed to be exponentially distributed. As soon as the system becomes empty, the repairman (R1) leaves for a vacation and returns back when he finds the number of failed units in the system greater than or equal to a threshold value N. Second repairman (R2) turns on when there are L(>N) failed units in the system and goes for a vacation if there are less than L failed units. The life time and repair time of failed units are assumed to be exponentially distributed. The steady state queue size distribution is obtained by using recursive method. Expressions for the average number of failed units in the queue and the average waiting time are established.
Blockchain-enabled solution for transparency and waste minimization in pharmaceutical supply chains
(Elsevier, 2025) Sangwan, Kuldip Singh; Kulshrestha, Rakhee
The pharmaceutical supply chain is a complex network involving multiple stakeholders and processes, making it susceptible to various inefficiencies and challenges such as counterfeiting, drug expiry, and inefficient inventory management. These challenges may lead to compromised patient safety and financial losses. Blockchain technology is a promising solution to these problems. This study develops a blockchain-enabled mathematical model for pharmaceutical supply chains. A distributed ledger is used to acquire the real-time drug transaction status throughout the supply chain. The study uses real-time data gathered from the distributed ledgers across the supply chain, ensuring optimum inventory with the minimization of expired drugs and transportation costs. By leveraging the proposed model, stakeholders can eliminate counterfeiting, reduce drug expiry, and ultimately ensure the integrity and safety of pharmaceutical products throughout their lifecycle. This model also helps manufacturers in decision making for drug manufacturing based on real-time data. Novelty of the study lies in real-time tracing and managing the drugs across the supply chain.
Channel allocation and ultra-reliable communication in CRNs with heterogeneous traffic and retrials: A dependability theory-based analysis
(Elsevier, 2020-05) Kulshrestha, Rakhee
The current research efforts on Fifth Generation (5G) of wireless communication systems have identified the need for large extent improvements in accessibility and reliability of communication services. In this respect, Cognitive Radio (CR) has been envisioned as a key 5G enabler that allows dynamic spectrum access without causing interference to licensed (primary) users and can tackle the challenge of ultra reliable communication. Channel failures, which are generally caused due to hardware and software failure and/or due to intrinsic features such as fading and shadowing, can easily result in network performance degradation. In cognitive radio networks (CRNs), the connections of unlicensed (secondary) users are inherently vulnerable to breaks due to channel failures as well as licensed users’ arrivals. To explore the advantages of channel reservation and retrial phenomenon on performance improvement in error-prone channels, we propose and analyze dynamic spectrum access (DSA) scheme by also taking balking and reneging behavior into account. Moreover, since 5G networks should comprise heterogeneous applications that may have different Quality of Service (QoS), thus the present study facilitates the arrival of heterogeneous secondary users with access privilege variations. In addition, most previous works have studied the stationary performance of CRNs, however, those may not be adequate in practice, notably when the time horizon of operations is finite. This paper investigates the transient dynamics from the perspectives of dependability theory in CRNs. Furthermore, the whole system is modeled using a multi-dimensional continuous time Markov chain (CTMC) and numerical results illustrate the potential of the proposed scheme to achieve major gains in the performance of error-prone CRNs.
Channel Optimization for Wireless Data Broadcast
(IJCA, 2011) Kulshrestha, Rakhee
Recently data broadcast has emerged as powerful tool for information dissemination to massive number of clients equipped with portable gadgets. Wireless communication use air as medium for transferring data to exchange information between mobile client and remote server. To enhance communication capacities and avoid information clashing multichannel broadcast is preferred; which partition available air bandwidth in to small bandwidth air channels. In wireless environment plethora of data are transferred through air creating chaos on air channels. Hence broadcast channel is scared resource for wireless communication which greatly concern system performance by affecting data access time. This paper studies process of data scheduling and broadcasting for multichannel environment with optimal use of air channels. Various method of data placement over multichannel are studied and analytical model to find optimal number of air channel is developed. Simulation results of system performance in context of access time are inferred and presented.
A comparative study of ε-constraint, lp-metric, and weighted sum multi-objective optimization methods in a circular economy
(Elsevier, 2024) Kulshrestha, Rakhee; Sangwan, Kuldip Singh
Approximately 74.7 Mt (Million Metric Tonnes) of e-waste is expected to be produced in 2030, and laptop e-waste is one of the major constituents of this. The goal of this paper is to develop and optimize a mixed-integer linear programming (MILP) mathematical model for a laptop manufacturer in India, based on a framework that integrates secondary reuse concept associated with traditional circular economy waste avoidance strategies. The multi-objective solution techniques of ε-constraint, LP-metric, and weighted sum methods are used to optimize the circular economy model. The proposed model aids as a policy tool to decide the optimum number of inspection/collection centers, sales/distribution centers, disassembly centers, refurbishing centers, recycling centers, and their optimum locations and allocations. This study results suggest that reuse, secondary customer centers, refurbishing, and recycling of the laptops is not only economically beneficial to the organization but also environment friendly and helps to create more jobs in the rural economy.
Comparative study on spectrum sensing and modulation techniques in cognitive radio network
(IEEE, 2025-03) Kulshrestha, Rakhee
This paper conducts a comparative analysis of two prominent spectrum sensing methods, energy detection (ED) and matched filter detection (MFD), under different modulation schemes, specifically binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), and 64-quadrature amplitude modulation (QAM), in an Additive White Gaussian Noise (AWGN) channel. The study evaluates the performance of ED and MFD in terms of probability of detection, false alarm, and sensitivity to signal-to-noise ratio (SNR). Simulation results indicate that 64-QAM is the preferred modulation scheme for achieving superior spectral efficiency. The analysis leverages receiver operating characteristic (ROC) curves to highlight the trade-offs between the probability of detection and probability of false alarm. These findings provide critical insights into the selection of appropriate spectrum sensing techniques, enhancing overall spectrum utilization in cognitive radio network.
Cost scrutiny of discrete-time priority queue with cluster arrival and Bernoulli feedback
(Springer, 2024-03) Kulshrestha, Rakhee
This work describes the economic feasibility of a single server discrete-time queueing model, (Geo/G/1) where interarrival times have a geometric distribution, and service times have a general distribution. This work is motivated by the case of discrete-time queueing models under priority scheme for solving many congestion issues of the telecommunication system wherein few calls are treated as prioritized calls and system manager may handle it properly. Herein a state-dependent arrival policy is used. It is assumed that the clients arrive in groups of varying sizes, and incorporates only one server queueing system with unlimited capacity. Under a discrete-time system with Markovian service practice, clients are serviced one at a time. If a client is dissatisfied with his service, he will most likely be directed back to the front of the queue. This concept is commonly referred to as Bernoulli feedback (BF) in queueing scenario. Just after every service, it is presumed that the server either starts to identify the next client to be serviced with some probability, or the server starts a solo vacation procedure with its complementary probability and this process is referred as Bernoulli vacation (BV). In addition, preferred and impatient clients are examined too. We investigate the Markov chain that underpins the queueing system in question, and its normalizing condition. The average number of consumers in the queue and the system are found using a generating function method. The numeral expositions are ascertained to delve the impact of different parameters on various performance metrics which can give information to system management in order to monitor the system's functioning condition and decrease congestion. We then used direct search method (DSM) and Particle Swarm Optimization (PSO) approaches to present a comparative study to assist system administrators or decision-makers by economically regulating the system. Furthermore, the results of the provided model are contrasted to those of a soft computing approach termed as ANFIS (Adaptive Neuro-Fuzzy Inference System).
Data Broadcast Management in Wireless Communication: An Emerging Research Area
(IGI Global, 2011) Kulshrestha, Rakhee
The data broadcast policies have been developed for single channel and multi channel with various scheduling and indexing techniques. For the data management policies which consider the different broadcast cycles for different broadcast operators, it can be said that traditional types of data management policies are known previously, and the policies of Central Server (CS) and Unified Index Hub (UIH), which consider single broadcast cycle for all operators, are recent. This chapter presents both strategies very simply for better understanding, discusses the work done in the past and present on data broadcast management, along with suggestions for the future possibilities to explore the field.
Discrete-Time Analysis of Communication Networks with Second Optional Service and Negative User Arrivals.
(Springer, 2020-04) Kulshrestha, Rakhee
Unreliable G-queues with the option of an additional service are appropriate mathematical models for communication networks, and hence, their performance evaluation is important for theory and applications. The present work investigates a Geo/Geo/1 G-queue with second optional service (SOS) and unreliable server. We assume that in addition to normal (positive) arriving customers, negative customers also arrive in the system. A customer in service is taken away upon a negative customer arrival, which also causes the failure of server. We consider that all arriving customers are provided with the essential service, which is known as first essential service (FES) and some customer’s desire for an optional service after essential service with a certain probability, which is known as second optional service (SOS). The steady-state probabilities and expected number of customers in the system, throughput, and delay are derived using the matrix geometric method. Further, numerical simulations are computed to illustrate the joint influence of an optional service and the unreliable server on the performance of the communication networks.
Economic and reliability analysis of discrete-time G-queue with multi-optional services and Bernoulli feedback
(Springer, 2025-07) Kulshrestha, Rakhee
Cellular networks play a crucial role in modern telecommunications, supporting growing numbers of mobile users and various call types ranging from voice calls to multimedia data sessions. Efficient call handling is essential to ensure reliable and timely connections, optimal resource utilization, and a satisfactory Quality of Service (QoS). This study analyzes various call types in cellular networks using a discrete-time queueing model. Specifically, we investigate a discrete-time Geo/Geo/1 G-queue characterized by an unreliable server, k-optional services, and Bernoulli feedback mechanisms. Furthermore, within the framework of this queuing model, various call types are treated as positive customers, while virus attacks are considered negative customers. The arrival of a negative customer interrupts an ongoing service, leading to a server failure. Additionally, we assume that all arriving customers (positive) must undergo the First Essential Service (FES). After completing the FES, the server offers further services, allowing customers to either select one of the k-optional services, rejoin the queue for another FES, or leave the system if they do not wish to utilize additional services. Then, the entire system is modeled as a two-dimensional discrete-time Markov chain, and the matrix-geometric method is utilized to compute the steady-state probability vector, which is then employed to evaluate the numerical results of various performance metrics that depend on the queueing and reliability analysis. Finally, a cost model is established, and the Quasi-Newton method and Particle swarm optimization (PSO) technique are employed to achieve optimal operating conditions with minimal expected cost.
Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment
(Science PC, 2016-10) Kulshrestha, Rakhee
The mathematical model for analyzing the transmission dynamics of HIV/AIDS epidemic with treatment is studied by considering the three latent compartments for slow, medium and fast progresses of developing the AIDS. By constructing the system of differential equations for the different population groups namely susceptible, three types of latent individuals, symptomatic stage group and full blown AIDS individuals, the mathematical analysis is carried out in order to understand the dynamics of disease spread. By determining the basic reproduction number (R0), the model examines the two equilibrium points (i) the disease free equilibrium and (ii) the endemic equilibrium. It is established that if R0 <1, the disease free equilibrium is locally and globally asymptotically stable. The stability of endemic equilibrium has also been discussed.
Forecasting of Solar Irradiances using Time Series and Machine Learning Models: A Case Study from India
(Springer, 2022-10) Kulshrestha, Rakhee; Pasari, Sumanta
With the focus on renewable energy resources due to environmental reasons, reliable forecasting of renewable energy has great societal importance. This study focuses on the analysis and forecasting of GHI data at two different locations in India, namely Pokhran and Bitta. Since the GHI time series plots exhibit seasonality and randomness, the time series SARIMA model along with two machine learning models, namely MLP and LSTM, are implemented for daily, weekly and monthly forecasting. The efficacy of these competitive models is assessed using MAPE and RMSE values. We also perform residual analysis as a post processing step of the implemented models. For monthly forecasting, the SARIMA model has the best performance, as it precisely captures monthly seasonality in comparison to the machine learning models. However, for short term daily forecasting, machine learning models provide much better estimates with MLP as the most desirable one. Since the SARIMA model fails to fully capture the high amount of fluctuation (mostly, seasonal fluctuation) in the daily and weekly observations, we additionally implement an ARIMA model with sliding windows to improve modelling efficacy. The present study therefore provides a clear guideline on the selection of forecasting models based on the desired time horizon.
Mathematical Modeling and Computation of Real-Time Problems An Interdisciplinary Approach
(CRC Press, 2021) Kulshrestha, Rakhee; Shekhar, Chandra
This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems. The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research. The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.
Modelling and simultaneous optimization of environmental, economic, and technological factors in machining
(Springer, 2023-10) Sangwan, Kuldip Singh; Kulshrestha, Rakhee
In the current era, manufacturing industries are facing multifaceted challenges related to increasing environmental awareness, decreasing economic gains, and technology obsolesce. These challenges become more apparent during the machining of difficult-to-machine materials due to high tool wear rates, high cutting forces, undesirable surface quality, high tool replacement costs, and a stagnating productivity. The developed approach aims at improving environmental, economic, and technological factors by optimizing four performance characteristics–energy demand, surface roughness, tool wear, and material removal rate during the milling of H13 tool steel by using an integrated artificial neural network and genetic algorithm. The proposed methodology provides Pareto solutions for minimum energy demand, surface roughness, & tool wear, and maximum material removal rate. The novelty of this work lies in generating Pareto fronts for analyzing conflicting responses, and determining preferred solutions without sacrificing environmental, technological, and economic considerations, simultaneously. The present work will be significant to practitioners in adopting better management strategies and simultaneously dealing with these challenges. The potential of the research lies in directly integrating the proposed optimization module with the machine tool system to serve as an online tool for machine tool process optimization.
A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy
(Emerald, 2024-05) Kulshrestha, Rakhee; Sangwan, Kuldip Singh
This paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.