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.

On Multi- Server Queues With Consultation With Main Server

Queueing Theory is the mathematical study of queues or waiting lines. Queues abound in every day life - in computer networks, in tra c islands, in communication of electro-magnetic signals, in telephone exchange, in bank counters, in super market checkouts, in doctor's clinics, in petrol pumps, in o ces where paper works to be processed and many other places. Originated with the published work of A. K. Erlang in 1909 [16] on congestion in telephone tra c, Queueing Theory has grown tremendously in a century. Its wide range applications includes Operations Research, Computer Science, Telecommunications, Tra c Engineering, Reliability Theory, etc.

Bivariate semi-Pareto distributions and processes

A bivariate semi-Pareto distribution is introduced and characterized using geometric minimization. Autoregressive minification models for bivariate random vectors with bivariate semi-Pareto and bivariate Pareto distributions are also discussed. Multivariate generalizations of the distributions and the processes are briefly indicated.

Photothermal and photoacoustic investigations on certain polymers and semi conducting materials

Material synthesizing and characterization has been one of the major areas of scientific research for the past few decades. Various techniques have been suggested for the preparation and characterization of thin films and bulk samples according to the industrial and scientific applications. Material characterization implies the determination of the electrical, magnetic, optical or thermal properties of the material under study. Though it is possible to study all these properties of a material, we concentrate on the thermal and optical properties of certain polymers. The thermal properties are detennined using photothermal beam deflection technique and the optical properties are obtained from various spectroscopic analyses. In addition, thermal properties of a class of semiconducting compounds, copper delafossites, arc determined by photoacoustic technique.Photothermal technique is one of the most powerful tools for non-destructive characterization of materials. This forms a broad class of technique, which includes laser calorimetry, pyroelectric technique, photoacollstics, photothermal radiometric technique, photothermal beam deflection technique etc. However, the choice of a suitable technique depends upon the nature of sample and its environment, purpose of measurement, nature of light source used etc. The polynler samples under the present investigation are thermally thin and optically transparent at the excitation (pump beam) wavelength. Photothermal beam deflection technique is advantageous in that it can be used for the detennination of thermal diffusivity of samples irrespective of them being thermally thick or thennally thin and optically opaque or optically transparent. Hence of all the abovementioned techniques, photothemlal beam deflection technique is employed for the successful determination of thermal diffusivity of these polymer samples. However, the semi conducting samples studied are themlally thick and optically opaque and therefore, a much simpler photoacoustic technique is used for the thermal characterization.The production of polymer thin film samples has gained considerable attention for the past few years. Different techniques like plasma polymerization, electron bombardment, ultra violet irradiation and thermal evaporation can be used for the preparation of polymer thin films from their respective monomers. Among these, plasma polymerization or glow discharge polymerization has been widely lIsed for polymer thin fi Im preparation. At the earlier stages of the discovery, the plasma polymerization technique was not treated as a standard method for preparation of polymers. This method gained importance only when they were used to make special coatings on metals and began to be recognized as a technique for synthesizing polymers. Thc well-recognized concept of conventional polymerization is based on molecular processcs by which thc size of the molecule increases and rearrangemcnt of atoms within a molecule seldom occurs. However, polymer formation in plasma is recognized as an atomic process in contrast to the above molecular process. These films are pinhole free, highly branched and cross linked, heat resistant, exceptionally dielectric etc. The optical properties like the direct and indirect bandgaps, refractive indices etc of certain plasma polymerized thin films prepared are determined from the UV -VIS-NIR absorption and transmission spectra. The possible linkage in the formation of the polymers is suggested by comparing the FTIR spectra of the monomer and the polymer. The thermal diffusivity has been measured using the photothermal beam deflection technique as stated earlier. This technique measures the refractive index gradient established in the sample surface and in the adjacent coupling medium, by passing another optical beam (probe beam) through this region and hence the name probe beam deflection. The deflection is detected using a position sensitive detector and its output is fed to a lock-in-amplifIer from which the amplitude and phase of the deflection can be directly obtained. The amplitude and phase of the deflection signal is suitably analyzed for determining the thermal diffusivity.Another class of compounds under the present investigation is copper delafossites. These samples in the form of pellets are thermally thick and optically opaque. Thermal diffusivity of such semiconductors is investigated using the photoacoustic technique, which measures the pressure change using an elcctret microphone. The output of the microphone is fed to a lock-in-amplificr to obtain the amplitude and phase from which the thermal properties are obtained. The variation in thermal diffusivity with composition is studied.

Stochastic Modelling Using Markov Chains

Department of Statistics, Cochin University of Science and Technology

A Study of Single Stage Semi‐Dry Anaerobic Digestion of Organic Fraction of Municipal Solid Waste

Solid waste generation is a natural consequence of human activity and is increasing along with population growth, urbanization and industrialization. Improper disposal of the huge amount of solid waste seriously affects the environment and contributes to climate change by the release of greenhouse gases. Practicing anaerobic digestion (AD) for the organic fraction of municipal solid waste (OFMSW) can reduce emissions to environment and thereby alleviate the environmental problems together with production of biogas, an energy source, and digestate, a soil amendment. The amenability of substrate for biogasification varies from substrate to substrate and different environmental and operating conditions such as pH, temperature, type and quality of substrate, mixing, retention time etc. Therefore, the purpose of this research work is to develop feasible semi-dry anaerobic digestion process for the treatment of OFMSW from Kerala, India for potential energy recovery and sustainable waste management. This study was carried out in three phases in order to reach the research purpose. In the first phase, batch study of anaerobic digestion of OFMSW was carried out for 100 days at 32°C (mesophilic digestion) for varying substrate concentrations. The aim of this study was to obtain the optimal conditions for biogas production using response surface methodology (RSM). The parameters studied were initial pH, substrate concentration and total organic carbon (TOC). The experimental results showed that the linear model terms of initial pH and substrate concentration and the quadratic model terms of the substrate concentration and TOC had significant individual effect (p < 0.05) on biogas yield. However, there was no interactive effect between these variables (p > 0.05). The optimum conditions for maximizing the biogas yield were a substrate concentration of 99 g/l, an initial pH of 6.5 and TOC of 20.32 g/l. AD of OFMSW with optimized substrate concentration of 99 g/l [Total Solid (TS)-10.5%] is a semi-dry digestion system .Under the optimized condition, the maximum biogas yield was 53.4 L/kg VS (volatile solid).. In the second phase, semi-dry anaerobic digestion of organic solid wastes was conducted for 45 days in a lab-scale batch experiment for substrate concentration of 100 g/l (TS-11.2%) for investigating the start-up performances under thermophilic condition (50°C). The performance of the reactor was evaluated by measuring the daily biogas production and calculating the degradation of total solids and the total volatile solids. The biogas yield at the end of the digestion was 52.9 L/kg VS for the substrate concentration of 100 g/l. About 66.7% of volatile solid degradation was obtained during the digestion. A first order model based on the availability of substrate as the limiting factor was used to perform the kinetic studies of batch anaerobic digestion system. The value of reaction rate constant, k, obtained was 0.0249 day-1. A laboratory bench scale reactor with a capacity of 36.8 litres was designed and fabricated to carry out the continuous anaerobic digestion of OFMSW in the third phase. The purpose of this study was to evaluate the performance of the digester at total solid concentration of 12% (semi-dry) under mesophlic condition (32°C). The digester was operated with different organic loading rates (OLRs) and constant retention time. The performance of the reactor was evaluated using parameters such as pH, volatile fatty acid (VFA), alkalinity, chemical oxygen demand (COD), TOC and ammonia-N as well as biogas yield. During the reactor’s start-up period, the process is stable and there is no inhibition occurred and the average biogas production was 14.7 L/day. The reactor was fed in continuous mode with different OLRs (3.1,4.2 and 5.65 kg VS/m3/d) at constant retention time of 30 days. The highest volatile solid degradation of 65.9%, with specific biogas production of 368 L/kg VS fed was achieved with OLR of 3.1 kg VS/m3/d. Modelling and simulation of anaerobic digestion of OFMSW in continuous operation is done using adapted Anaerobic Digestion Model No 1 (ADM1).The proposed model, which has 34 dynamic state variables, considers both biochemical and physicochemical processes and contains several inhibition factors including three gas components. The number of processes considered is 28. The model is implemented in Matlab® version 7.11.0.584(R2010b). The model based on adapted ADM1 was tested to simulate the behaviour of a bioreactor for the mesophilic anaerobic digestion of OFMSW at OLR of 3.1 kg VS/m3/d. ADM1 showed acceptable simulating results.

Development of ready-to-eat extruded fish based noodles in semi-rigid containers”

Fish and fishery products are having a unique place in global food market due to its unique taste and flavour; moreover, the presence of easily digestible proteins, lipids, vitamins and minerals make it a highly demanded food commodity.Fishery products constitute a major portion of international trade, which is a valuable source of foreign exchange to many developing countries.Several new technologies are emerging to produce various value added products from food; “extrusion technology” is one among them. Food extruder is a better choice for producing a wide variety of high value products at low volume because of its versatility. Extruded products are shelf-stable at ambient temperature. Extrusion cooking is used in the manufacture of food products such as ready-to-eat breakfast cereals, expanded snacks, pasta, fat-bread, soup and drink bases. The raw materialin the form of powder at ambient temperature is fed into extruder at a known feeding rate. The material first gets compacted and then softens and gelatinizes and/or melts to form a plasticized material, which flows downstream into extruder channel and the final quality of the end products depends on the characteristics of starch in the cereals and protein ingredient as affected by extrusion process. The advantages of extrusion process are the process is thermodynamically most efficient, high temperature short time enables destruction of bacteria and anti-nutritional factors, one step cooking process thereby minimizing wastage and destruction of fat hydrolyzing enzymes during extrusion process and enzymes associated with rancidity.