Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

Studies on the Role of Sediments on the Nutrient Dynamics and Fertility of Kuttanad Waters

In the present study the nutrient dynamics and fertility of Kuttanad waters is addressed. Kuttanad represent a wetland system with considerable agricultural activities. The hydrographical features of the Kuttanad waters are controlled by discharges from Manimala, Meenachil, Pamba, Achencoil and Muvattupuzha rivers and also by tidal intrusions of saline waters from Cochin backwaters during summers. The fertility of these water bodies were significantly high and supported good agricultural production. Kuttanad water forms the southern part of this aquatic systems and is considered as the most productive zones. As a part of the management scheme for a higher agricultural activity, the Thannermukkam bund was constructed to block and regulate the intrusion of saline water. The increased use of artificial fertilizers along with stagnant character of the water body in this area has resulted in sharp decline in the water quality, productivity and aquatic resources.

Nutrient Dynamics in the EEZ of the West Coast of India with Special Reference to the Oxygen Minimum Zone and Denitrification

The present work aims at deciphering the processes that control the nutrient distribution along the EEZ (Exclusive Economic Zone of India) of the west coast of India and to bring out its linkage with primary and secondary productivity. This work assume utmost importance as very few studies have hitherto focused entirely on the EEZ of the west coast of India to address the biochemical responses brought about by monsoons. The present study examines the seasonal variations in physicochemical parameters and associated primary biological responses along the west coast of India. This study targets to measure and understand the shelf ocean exchange in a typical coastal upwelling region of the southeast Arabian Sea, and the influence of convective mixing along the northern part of the west coast of India. The study focuses more directly on coastal upwelling along the southwest coast of India, within the EEZ. The effects of coastal upwelling, eddy formation and the offshore advection are apparent in the present investigation. This has consequences to fisheries and climate, in energy transfer to the food chain and the increased sequestering of carbon in the ocean. The study also focuses on the Oxygen Minimum Zone (OMZ) and dentrification observed along the EEZ of the west coast of India on a seasonal scale. In the study, an attempt is also made to demarcate the geographical boundaries of the denitrification zone in the EEZ of India and on the nature and magnitude of these variations, on a seasonal and inter annual scales

Studies on the Role of Sediments on the Nutrient Dynamics and Fertility of Kuttanad Waters

In the present study the nutrient dynamics and fertility of Kuttanad waters is addressed. Kuttanad represent a wetland system with considerable agricultural activities. The hydrographical features of the Kuttanad waters are controlled by discharges from Manimala, Meenachil, Pamba, Achencoil and Muvattupuzha rivers and also by tidal intrusions of saline waters from Cochin backwaters during summers. The fertility of these water bodies were significantly high and supported good agricultural production. Kuttanad water forms the southern part of this aquatic systems and is considered as the most productive zones. As a part of the management scheme for a higher agricultural activity, the Thannermukkam bund was constructed to block and regulate the intrusion of saline water. The increased use of artificial fertilizers along with stagnant character of the water body in this area has resulted in sharp decline in the water quality, productivity and aquatic resources.

Gamma stochastic volatility models

This paper presents gamma stochastic volatility models and investigates its distributional and time series properties. The parameter estimators obtained by the method of moments are shown analytically to be consistent and asymptotically normal. The simulation results indicate that the estimators behave well. The insample analysis shows that return models with gamma autoregressive stochastic volatility processes capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared stock index returns for the USA and UK. In comparison with GARCH and EGARCH models, the gamma autoregressive model picks up the persistence in volatility for the US and UK index returns but not the volatility persistence for the Canadian and Japanese index returns. The out-of-sample analysis indicates that the gamma autoregressive model has a superior volatility forecasting performance compared to GARCH and EGARCH models.

Stochastic Modelling Using Markov Chains

Department of Statistics, Cochin University of Science and Technology

Nutrient Mobility in Chalakudy River,Typified With Riparian Buffer Zone and Its Adjoining Estuary:Spatiotemporal Manifestation

This study was aimed at to characterize the spatio-temporal trends in the distributional characteristics of various species of nitrogen and phosphorus as well as to elucidate the factors and processes aflecting these nutrients in the dissolved, particulate and sedimentary phases of a river estuarine system. The main area of study is Chalakudy river in Kerala, which is a fresh water system originating from Anamalai hills and ending at Arabian Sea. Its basin is between I00 05 ’ to I00 35’ North latitude and 76” 15 ’ to 760 55’ East longitude. Being a riparian bufler zone, the dynamics of nutrient mobility tend to be more complex and variable in this river-estuarine system.The diflerent species of nitrogen estimated from the filtrate were nitrite-N, nitrateN, ammonia-N, urea-N, total nitrogen and residual nitrogen. The diflerent forms of phosphorus estimated from the filtrate were phosphate-P, total-P and residualP. Pre weighed sediments as well as particulate matter were analysed for quantijying nitrite-N, nitrate-N, ammonia-N and urea-N. Total nitrogen was estimated after digestion with potassium persulfate. Fractionation of phosphorus in sediment/particulate matter was performed by applying sequential extraction procedure. The dijferent forms of phosphorus thus estimated were loosely bound (exchangeable) P, Fe/Al bound P, polyphosphates, Ca bound P and refractory P. Sedimental total P was also measured directly by applying digestion method.The analyses carried out in this bimonthly annual survey have revealed specific information on the latent factors influencing the water quality pattern ofthe river. There was dependence among the chemical components of the river sediment and suspended matter, reflecting the water quality. A period of profound environmental change occurred and changes in various species had been noted in association with seasonal variations in the waterway, especially following enhanced river runoff during the monsoon. The results also successfully represented the distribution trend of nutrients during the rainy as well as dry season. Thus, the information gathered in this work will also be beneficial for those interested or involved in river management, conservation, regulation and policy making in regional and national levels.

Stochastic Inventory with/without Service Time, Reneging and Retrial of Customers

This thesis Entitled Stochastic modelling and analysis.This thesis is divided into six chapters including this introductory chapter. In second chapter, we consider an (s,S) inventory model with service, reneging of customers and finite shortage of items.In the third chapter, we consider an (s,S) inventoiy system with retrial of customers. Arrival of customers forms a Poisson process with rate. When the inventory level depletes to s due to demands, an order for replenishment is placed.In Chapter 4, we analyze and compare three (s,S) inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. In chapter 5, we analyze and compare three production inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed.In chapter 6, we consider a PH /PH /l inventory model with reneging of customers and finite shortage of items.

Implications of Hydrobiology and Nutrient dynamics on trophic structure and interactions in Cochin backwaters

In the present thesis entitled” Implications of Hydrobiology and Nutrient dynamics on Trophic structure and Interactions in Cochin backwaters”, an attempt has been made to assess the influence of general hydrography, nutrients and other environmental factors on the abundance, distribution and trophic interactions in Cochin backwater system. The study was based on five seasonal sampling campaigns carried out at 15 stations spread along the Cochin backwater system. The thesis is presented in the following 5 chapters. Salient features of each chapter are summarized below: Chapter 1- General Introduction: Provides information on the topic of study, environmental factors, back ground information, the significance, review of literature, aim and scope of the present study and its objectives.Chapter 2- Materials and Methods: This chapter deals with the description of the study area and the methodology adopted for sample collection and analysis. Chapter 3- General Hydrograhy and Sediment Characteristics: Describes the environmental setting of the study area explaining seasonal variation in physicochemical parameters of water column and sediment characteristics. Data on hydrographical parameters, nitrogen fractionation, phosphorus fractionation and biochemical composition of the sediment samples were assessed to evaluate the trophic status. Chapter 4- Nutrient Dynamics on Trophic Structure and Interactions: Describes primary, secondary and tertiary production in Cochin backwater system. Primary production related to cell abundance, diversity of phytoplankton that varies seasonally, concentration of various pigments and primary productivitySecondary production refers to the seasonal abundance of zooplankton especially copepod abundance and tertiary production deals with seasonal fish landings, gut content analysis and proximate composition of dominant fish species. The spatiotemporal variation, interrelationships and trophic interactions were evaluated by statistical methods. Chapter 5- Summary: The results and findings of the study are summarized in the fifth chapter of the thesis.

Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.