Stochastic processes and their applications time dependent solutions for some queueing and inventory models

The objective of this thesis is to study the time dependent behaviour of some complex queueing and inventory models. It contains a detailed analysis of the basic stochastic processes underlying these models. In the theory of queues, analysis of time dependent behaviour is an area.very little developed compared to steady state theory. Tine dependence seems certainly worth studying from an application point of view but unfortunately, the analytic difficulties are considerable. Glosod form solutions are complicated even for such simple models as M/M /1. Outside M/>M/1, time dependent solutions have been found only in special cases and involve most often double transforms which provide very little insight into the behaviour of the queueing systems themselves. In inventory theory also There is not much results available giving the time dependent solution of the system size probabilities. Our emphasis is on explicit results free from all types of transforms and the method used may be of special interest to a wide variety of problems having regenerative structure.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Probability Theory. Stochastic Processes And Their Applications Probabilistic Analysis Of Some Queueing And Inventory Models

In this thesis we attempt to make a probabilistic analysis of some physically realizable, though complex, storage and queueing models. It is essentially a mathematical study of the stochastic processes underlying these models. Our aim is to have an improved understanding of the behaviour of such models, that may widen their applicability. Different inventory systems with randon1 lead times, vacation to the server, bulk demands, varying ordering levels, etc. are considered. Also we study some finite and infinite capacity queueing systems with bulk service and vacation to the server and obtain the transient solution in certain cases. Each chapter in the thesis is provided with self introduction and some important references

Tide And River Runoff Interactions In The Cochin Estuary

Hydrodynamic characteristics of an estuary resulting from interaction of tide and river runoff are important since problems regarding flood, salinity intrusion, water quality, ecosystem and sedimentation are ubiquitous. The present study focuses on such hydrodynamic aspects in the Cochin estuary. Most of the estuaries that come under the influence of Indian Summer Monsoon and for which the salinity is never in a steady state at any time of the year are generally shallow and convergent, i.e. the width decreases rapidly from mouth to head. In contrast, Cochin estuary is wider towards the upstream and has no typical river mouth, where the rivers are joining the estuary along the length of its channel .Adding to the complexity it has dual inlets and the tidal range is 1 m which is lower than other Indian estuaries along west coast. These typical physical features lead to its unique hydrodynamic characteristics. Therefore the thesis objectives are: I) to study the influence of river runoff on tidal propagation using observations and a numerical model ii) to study stratification and property distributions in Cochin estuary iii) to understand salinity distributions and flushing characteristics iv) to understand the influence of saltwater barrage on tides and salinity v) To evaluate several classification schemes for the estuary

Hydrogeological, Geophysical And Geochemical Studies In Parts Of Coastal And Midland Areas, Central Kerala - A Gis Approach

The present study deals with the different hydrogeological characteristics of the coastal region of central Kerala and a comparative analysis with corresponding hard rock terrain. The coastal regions lie in areas where the aquifer systems discharge groundwater ultimately into the sea. Groundwater development in such regions will require a precise understanding of the complex mechanism of the saline and fresh water relationship, so that the withdrawals are so regulated as to avoid situations leading to upcoming of the saline groundwater bodies as also to prevent migration of sea water ingress further inland. Coastal tracts of Kerala are formed by several drainage systems. Thick pile of semi-consolidated and consolidated sediments from Tertiary to Recent age underlies it. These sediments comprise phreatic and confined aquifer systems. The corresponding hard rock terrain is encountered with laterites and underlined by the Precambrian metamorphic rocks. Supply of water from hard rock terrain is rather limited. This may be due to the small pore size, low degree of interconnectivity and low extent of weathering of the country rocks. The groundwater storage is mostly controlled by the thickness and hydrological properties of the weathered zone and the aquifer geometry. The over exploitation of groundwater, beyond the ‘safe yield’ limit, cause undesirable effects like continuous reduction in groundwater levels, reduction in river flows, reduction in wetland surface, degradation of groundwater quality and many other environmental problems like drought, famine etc.

Bioactive Metabolites and Biomarkers from Rhizophoraceae mangroves- A Chemotaxonomic Approach

Mangroves are specialised ecosystems developed along estuarine sea coasts and river mouths in tropical and subtropical regions of the world, mainly in the intertidal zone. Hence, the ecosystem and its biological components is under the influence of both marine and freshwater conditions and has developed a set of physiological adaptations to overcome problems of anoxia, salinity and frequent tidal inundations. This has led to the assemblage of a wide variety of plant and animal species of special adaptations suited to the ecosystem. The path of photosynthesis in mangroves is different from other glycophytes. There are modifications or alterations in other physiological processes such as carbohydrate metabolism or polyphenol synthesis. As they survive under extreme conditions of salinity, temperature, tides and anoxic soil conditions they may have chemical compounds, which protect them from these destructive elements. Mangroves are necessarily tolerant of high salt levels and have mechanisms to take up water despite strong osmotic potentials. Some also take up salts, but excrete them through specialised glands in the leaves. Others transfer salts into senescent leaves or store them in the bark or the wood. Still others simply become increasingly conservative in their water use as water salinity increases. A usual transportation or biosynthetic path as other plants cannot be expected in mangrove plants. In India, the states like West Bengal, Orissa, Andhra Pradesh, Tamil Nadu, Andaman and Nicobar Islands, Kerala, Goa, Maharashtra, and Gujarat occupy vast area of mangroves. Kerala has only 6 km2 total mangrove area with Rhizophora apiculata, Rhizophora mucronata, Bruguiera gymnorrhiza, Bruguiera cylindrica, Avicennia officinalis, Sonneratia caseolaris, Sonneratia apetala and Kandelia candal, as the important species present, most of which belong to the family Rhizophoraceae.Rhizophoraceae mangroves are ranked as “major elements of mangroves” as they give the real shape of this unique and interesting ecosystem and these mangrove species most productive and typical characteristic ecosystem of World renowned. It was found that the Rhizophoraceae mangrove extracts exhibit several bioactive properties. Various parts of these mangroves are used in ethnomedicinal practices. Even though extracts from these mangroves possess therapeutic activity against humans, animal and plant pathogens, the specific metabolites responsible for these bioactivities remains to be elucidated. Various parts of these mangroves are used in ethnomedicinal practices. There is a gap of information towards the chemistry of Rhizophoraceae mangroves from Kerala. Thorough phytochemical investigation can achieve the validity of ethnomedicines as well as apply the use of mangrove plants in the development of new drugs. Such studies can pave a firm base for their use in biomarker and chemotaxonomic studies as well as for the better management of the existing mangrove ecosystem. In this study, the various chemical parameters including minerals, biochemical components, bioactive and biomarker molecules were used to classify and assess the possible potentials of the mangrove plants of the true mangrove family Rhizophoraceae from Kochi.

Studies on Bio-Geochemistry, Bio-Optical Properties and Satellite Validation of Coastal Waters of South Eastern Arabian Sea

In situ methods used for water quality assessment have both physical and time constraints. Just a limited number of sampling points can be performed due to this, making it difficult to capture the range and variability of coastal processes and constituents. In addition, the mixing between fresh and oceanic water creates complex physical, chemical and biological environment that are difficult to understand, causing the existing measurement methodologies to have significant logistical, technical, and economic challenges and constraints. Remote sensing of ocean colour makes it possible to acquire information on the distribution of chlorophyll and other constituents over large areas of the oceans in short periods. There are many potential applications of ocean colour data. Satellite-derived products are a key data source to study the distribution pattern of organisms and nutrients (Guillaud et al. 2008) and fishery research (Pillai and Nair 2010; Solanki et al. 2001. Also, the study of spatial and temporal variability of phytoplankton blooms, red tide identification or harmful algal blooms monitoring (Sarangi et al. 2001; Sarangi et al. 2004; Sarangi et al. 2005; Bhagirathan et al., 2014), river plume or upwelling assessments (Doxaran et al. 2002; Sravanthi et al. 2013), global productivity analyses (Platt et al. 1988; Sathyendranath et al. 1995; IOCCG2006) and oil spill detection (Maianti et al. 2014). For remote sensing to be accurate in the complex coastal waters, it has to be validated with the in situ measured values. In this thesis an attempt to study, measure and validate the complex waters with the help of satellite data has been done. Monitoring of coastal ecosystem health of Arabian Sea in a synoptic way requires an intense, extensive and continuous monitoring of the water quality indicators. Phytoplankton determined from chl-a concentration, is considered as an indicator of the state of the coastal ecosystems. Currently, satellite sensors provide the most effective means for frequent, synoptic, water-quality observations over large areas and represent a potential tool to effectively assess chl-a concentration over coastal and oceanic waters; however, algorithms designed to estimate chl-a at global scales have been shown to be less accurate in Case 2 waters, due to the presence of water constituents other than phytoplankton which do not co-vary with the phytoplankton. The constituents of Arabian Sea coastal waters are region-specific because of the inherent variability of these optically-active substances affected by factors such as riverine input (e.g. suspended matter type and grain size, CDOM) and phytoplankton composition associated with seasonal changes.