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October 1996 - present
Publications
Publications (58)
This article investigates an M/M/2/K heterogeneous queueing system, specifically focusing on two aspects of customer impatience: reverse balking and reneging till the end of service (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackag...
This article focuses on both classical and Bayesian inference of traffic intensity in a single-server Markovian queueing model considering balking. To reflect real-world situations, the article introduces the concept of balking, where customers opt not to join the queue due to the perceived waiting time. The essence of this article involves a compr...
This article investigates a novel M/M/1 queueing model incorporating the concept of balking, where customers decide not to join a queue because it appears too long or the waiting time seems too excessive. The study focuses on estimating traffic intensity (q) and key performance measures, including the average number of customers in the system (L s)...
This article addresses the pressing issue of customer impatience and dissatisfaction with queueing systems, a critical aspect of modern businesses. It delves into specific aspects of customer behavior, viz., reverse balking, reneging, and retention of reneged customers, which significantly influence queue dynamics. A novel finite-buffer two-server...
For operating any new finite capacity (say K) queuing system in which customers arrive according to a Poisson process and are served by a single server under exponential service time (in Kendall’s notation M/M/1/K system), the assumption of fixing K and estimating the parameter traffic intensity \(\rho\), is quite practical. But in situation of any...
When we study any queuing system, the performance measures reflect different features of the system. In the classical M/M/1 queuing system, traffic intensity is perhaps the most important performance measure. We propose a fresh and simple estimator for the same and show that it has nice properties. Our approach is frequentist. This approach has the...
This is about NIRF ranking of universities
Queuing models where arrival rates go down consequent to increase in the number of customers are called systems with discouraged arrivals. Discouraged arrivals are distinct from balking in the sense that balking implies that arriving customers do not join. In this paper, we model a single server finite buffer Markovian queuing model with discourage...
In this paper we consider multi-server single queue system in which inter-arrival and service times are exponentially distributed. When assessing the performance of such queuing model, information regarding the parameter traffic intensity (ρ), also called the utilization factor of the service station, is very essential. The unknown factor ρ is ther...
The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance co...
Reneging and Balking are two facts of customer impatience. In traditional queuing literature, customer impatience was not often considered. However, for the last few decades, queuing theorists have been trying to integrate aspect of balking and reneging into modeling of queues in a holistic way. This paper is an extension of the work in the same di...
Extended Abstract:
Aim: To propose a practical guiding rule for implementing the procedure outlined by Zheng and Seila (2000) for estimating various performance measures of the classical M/M/1 queuing model using the frequentist framework.
Motivation: There are four popular performance measures of interest in the M/M/1 queuing system viz. avera...
Extended abstract:
This paper deals statistical inference in the single server queuing model in which inter-arrival and service times are exponentially distributed (Markovian) using data on queue size (number of customers present in the queue) observed at any random point of time.
We develop estimates of traffic intensity (ρ) as well as L and Lq...
In a queuing system, it is essential to carry out statistical analysis for assessing the performance of the queuing system. In this article, estimation of two important performance measures viz expected number of customers in the system (L) and mean queue length (Lq) have been studied from classical framework, particularly for steady state M/M/1 qu...
Extended Abstract:
Aim: Construction of estimator - point as well as interval, hypothesis testing and methods relating to determination of sample size in the context of statistical inference of traffic intensity parameter of the M/M/1 queuing model.
Method: We construct the estimator by leveraging a trick wherein we have exploited the relationshi...
In the modeling of many queuing systems, it is assumed that customers who arrive stay on till they receive service. In real life, this does not always happen. Arriving customer may decide against joining the system. In queuing parlance, this is known as balking. In this paper, we shall assume that customers may balk if service is not instantly avai...
In this paper we present a picture of BMI variation among major states of India and to identify states with high as well as low BMI. This allows for implementation of necessary public health strategy to combat the devastating health consequences of both extremes of BMI. The analysis is based on a country wide large scale survey. An additional aim i...
In the analysis of queuing systems with reneging customers, it is traditionally assumed that the reneging rate remains constant irrespective of the position of the customer. In real life this is seldom true. This paper is an attempt to model such a reneging phenomenon along with balking in the M/M/1 queue. The reneging rates are a function of the p...
EXTENDED ABSTRACT
Objective: We aim to quantify the proportion of chronic diseases that are attributable to a specific modifiable risk factor. The quantification is done separately for diabetes, cardiovascular and cancer.
Methods: A statistical construct that can be used to quantify the proportion is Population Attributable Fraction (PAF). The PA...
Extended Abstract:
Objective: To identify and quantify the risk factors of leading chronic disease of India viz heart disease, diabetes and cancer based on a relatively recent large scale nationally representative survey. An additional aim is to assess and compare the influence of modifiable risk factors among different age groups and different ar...
In the modeling of many queuing systems, it is assumed that customers who arrive stay on till they receive service. In real life, this does not always happen. Arriving customer may decide against joining the system. In queuing parlance, this is known as balking. In this paper, we shall assume that customers may balk if service is not instantly avai...
Of all statistical distributions, the standard normal is perhaps the most popular and widely used. Its use often involves computing the area under its probability curve. Unlike many other statistical distributions, there is no closed form theoretical expression for this area in case of the normal distribution. Consequently it has to be approximated...
Extended Abstract:
Aim: The present paper endeavours to examine whether the theoretical frameworks used in dropout literature (Weber, 1989; Rumberger, 1983; Rumberger, 2001) can be used to explain the high dropout rate of disadvantaged sections of the society.
Motivation: While there has been considerable progress in literacy in India since inde...
Chronic diseases are the leading causes of death in developed as well as developing countries.
Reneging involves the phenomenon of customers joining a queuing system but departing without completely receiving service. There are situations where customers begin receiving service but disengage before service completion. Emergency patients attended by critical care professionals are of such type. This paper deals with the analysis of Markovian...
Reneging involves the phenomenon of customers joining a queuing system but departing without completely receiving service. There are situations where customers begin receiving service but disengage before service completion. Emergency patients attended by critical care professionals are of such type. This paper deals with the analysis of Markovian...
In operational meteorology, forecasting heavy rainfall (HRF) events has been a long-standing challenge in India. This is especially true in certain regions where the physical geography lends itself to the creation of such HRF events. Northeast India (NEI) is one such region within the Asian monsoon zone, which receive very HRF during the pre-monsoo...
Queuing models with impatient customers have many applications. The common modes of impatience are reneging and balking, both of which have been considered in this paper. The model assumes a multi server queuing scenario with limited waiting space where arrival, service and reneging events are all generated by independent Poisson process and custom...
In the analysis of reneging behavior, one approach is to assume random patience time. Each customer is assumed to follow identical distribution of patience time. However, there are many real life queuing systems where this assumption is not satisfied. Customers waiting in the system are often aware of their position in it and hence the reneging rate...
Queuing models with impatient customers have many applications. The common modes of impatience are reneging and balking, both of which have been considered in this paper. The model assumes a multi server queuing scenario with limited waiting space where arrival, service and reneging events are all generated by independent Poisson process and custom...
In the analysis of reneging behavior, one approach is to assume random patience time. Each customer is assumed to follow identical distribution of patience time. However, there are many real life queuing systems where this assumption is not satisfied. Customers waiting in the system are often aware of their position in it and hence the reneging rat...
Queuing models with impatient customers have many applications. The common modes of impatience are reneging and balking, both of which have been considered in this paper. The model assumes a multi server queuing scenario with limited waiting space where arrival, service and reneging events are all generated by independent Poisson process and custom...
Objective: There is increasing evidence to suggest that the epidemiologic transition is well underway in India and other less industrialized countries. Hence there is a need to review the status of our understanding of the impending epidemic of non-communicable chronic diseases (NCD) in India, given their chronic nature and their impact on society....
Extended Abstract:
Objectives: The broad objective is to analyze a multiserver Markovian finite buffer queuing model in the presence of balking and reneging. Balking is assumed to be state dependent where as reneging is assumed to be state independent. Specific objective include design of non-traditional performance measures which captures various...
In the context of our fast-paced world, customer impatience in queuing systems is a reality. In this paper, we analyze a queuing system with Erlangian service discipline assuming that customers may renege. Analysis in steady state is presented. Relevant performance measures have been discussed.
Extended Abstract:
Cumulative distribution functions of some central sampling distributions viz. chi-sq, F distribution and t-distribution do not have closed form representation. Hence an approximate formula can be of immense use for computational work. In this paper, we review the development of literature of approximations to the cumulative dist...
Extended Abstract: Objectives: The broad objective is to analyze a multiserver Markovian finite buffer queuing model in the presence of balking and reneging. Balking is assumed to be state dependent where as reneging is assumed to be state independent. Specific objective include design of non-traditional performance measures which captures various...
In reneging literature, the reneging distribution is often assumed to be deterministic or random. In case of random reneging, it is assumed that the distribution is state independent so that customers have the same reneging rate irrespective of their position in the system. However, one can commonly observe many queuing systems where customers are...
In the analysis of many queuing systems, it is assumed that customers who arrive stay on till they receive service. In real life, this does not always happen. We shall assume that customers may balk if service is not instantly available on arrival. Even if a customer joins the system, the customer may renege. In this paper, we consider a multi serv...
Extended abstract:
In reneging literature, the reneging distribution is often assumed to be deterministic or random. In case of random reneging, it is assumed that the distribution is state independent so that customers have the same reneging rate irrespective of their position in the system. However, one can commonly observe many queuing systems...
In the analysis of many queuing systems, it is assumed that customers who arrive stay on till they receive service. In real life, this does not always happen. We shall assume that customers may balk if service is not instantly available on arrival. Even if a customer joins the system, the customer may renege. In this paper, we consider a multi serv...
In this paper, a single server finite buffer Markovian queuing system is analyzed with the additional restriction that customers may balk as well as renege. Reneging considered in literature is usually of position independent type where the reneging rate is constant irrespective of the position of the customer in the system. However there are many...
In this article, we present a new approximation to the cumulative distribution function of standard normal distribution. The approximation is fairly accurate with minimum accuracy of seven decimal digits. To the best of our knowledge, this formula outperforms other such approximations available in literature.
PS: A pdf of full text of the publishe...
This study seeks to examine and quantify the effect of various socio-economic, demographic and cultural factors on the prevalence of chronic diseases among a representative sample of adult population from Guwahati, the capital city of Assam. The data source used in this study is a primary one collected through a household survey. In all, 6343 respo...
Extended Abstract:
Objective :
The purpose of this paper is to outline a Bayesian method for estimating of the probability of an individual being afflicted by a particular chronic disease keeping in view his/her demographic characteristics and his/her practice of risky health behaviours. We demonstrate our method by applying it to a primary data...
Purpose
To analyze the patient demography and the various fluorescein angiography (FA) features of diffuse retinal pigment epitheliopathy (DRPE) cases among the inhabitants of the Brahmaputra Valley of India and to see if there is any ethnic variation in its clinical presentation and risk factors.
Methods
This is a retrospective study in a clinica...
The use of stochastic models and performance measures for the analysis of real life queuing scenarios are based on the fundamental
premise that parameters values are known. This is a rarity since more often than not, parameters are usually unknown and require
to be estimated. This paper presents techniques for the same from Bayesian perspective. Th...
This paper analyzes a single server Markovian queuing system with the added complexity of customers who are prone to giving up whenever its waiting time is larger than a random threshold - his patience time. I assume that these individual patience times are independent and identically distributed exponential random variables. Application of such qu...
Applications of queueing models for analyzing real-life scenarios are based on the fundamental premise that parameter values are known. This is a rarity and more often than not, such parameters require to be estimated. Any analyst with field level experience will corroborate this. How are such estimates to be obtained? What are the procedures to be...
Over the years, a number of approximations to the cdf of the Normal distribution have been proposed. How does one make a choice among them? This paper compares their performance with a view to identifying the best among them. Our analysis reveals that a uniformly best approximation formula does not exist. Locally best are identified. Finally we com...
While progress in improving literacy in India has been remarkable, the phenomenon of school dropouts has remained a blot in the face of an otherwise commendable performance. Dropout rates have undoubtedly come down but are still high enough for us to sit up and take notice. Sex differentials have also reduced. But rates for females have consistentl...
Analysis of the fundus and fluorescein angiography (FA) features of the asymptomatic eyes in patients of central serous chorioretinopathy (CSC) at initial visit and estimation of the overall magnitude of bilateral pathology.
Retrospective observational case series that reviewed the medical records and FA features of 229 consecutive patients between...
The Exponentiated Weibull family is an extension of the Weibull family obtained by adding an additional shape parameter. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates which are quite common in reliability and biological studies. As with any other distribution, many of its...
