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.

Queueing Theory And Other Applications Of Stochastic Processes Queueing And Inventory Models With Rest Periods

In this thesis we study the effect of rest periods in queueing systems without exhaustive service and inventory systems with rest to the server. Most of the works in the vacation models deal with exhaustive service. Recently some results have appeared for the systems without exhaustive service.

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

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

Optimization of carbon and nitrogen sources and growth factors for the production of an aquaculture probiotic (Pseudomonas MCCB 103) using response surface methodology

Aim: To develop a new medium for enhanced production of biomass of an aquaculture probiotic Pseudomonas MCCB 103 and its antagonistic phenazine compound, pyocyanin. Methods and Results: Carbon and nitrogen sources and growth factors, such as amino acids and vitamins, were screened initially in a mineral medium for the biomass and antagonistic compound of Pseudomonas MCCB 103. The selected ingredients were further optimized using a full-factorial central composite design of the response surface methodology. The medium optimized as per the model for biomass contained mannitol (20 g l)1), glycerol (20 g l)1), sodium chloride (5 g l)1), urea (3Æ3 g l)1) and mineral salts solution (20 ml l)1), and the one optimized for the antagonistic compound contained mannitol (2 g l)1), glycerol (20 g l)1), sodium chloride (5Æ1 g l)1), urea (3Æ6 g l)1) and mineral salts solution (20 ml l)1). Subsequently, the model was validated experimentally with a biomass increase by 19% and fivefold increase of the antagonistic compound. Conclusion: Significant increase in the biomass and antagonistic compound production could be obtained in the new media. Significance and Impact of the Study: Media formulation and optimization are the primary steps involved in bioprocess technology, an attempt not made so far in the production of aquaculture probiotics

Optimization of medium for the production of a novel aquaculture probiotic, Micrococcus MCCB 104 using central composite design

A marine isolate of jáÅêçÅçÅÅìë MCCB 104 has been identified as an aquaculture probiotic antagonistic to sáÄêáç. In the present study different carbon and nitrogen sources and growth factors in a mineral base medium were optimized for enhanced biomass production and antagonistic activity against the target pathogen, sáÄêáç=Ü~êîÉóá, following response surface methodology (RSM). Accordingly the minimum and maximum limits of the selected variables were determined and a set of fifty experiments programmed employing central composite design (CCD) of RSM for the final optimization. The response surface plots of biomass showed similar pattern with that of antagonistic activity, which indicated a strong correlation between the biomass and antagonism. The optimum concentration of the carbon sources, nitrogen sources, and growth factors for both biomass and antagonistic activity were glucose (17.4 g/L), lactose (17 g/L), sodium chloride (16.9 g/L), ammonium chloride (3.3 g/L), and mineral salts solution (18.3 mL/L). © KSBB

A Numerically efficient power optimization scheme for coded OFDM systems in achieving minimum frame error rate

Coded OFDM is a transmission technique that is used in many practical communication systems. In a coded OFDM system, source data are coded, interleaved and multiplexed for transmission over many frequency sub-channels. In a conventional coded OFDM system, the transmission power of each subcarrier is the same regardless of the channel condition. However, some subcarrier can suffer deep fading with multi-paths and the power allocated to the faded subcarrier is likely to be wasted. In this paper, we compute the FER and BER bounds of a coded OFDM system given as convex functions for a given channel coder, inter-leaver and channel response. The power optimization is shown to be a convex optimization problem that can be solved numerically with great efficiency. With the proposed power optimization scheme, near-optimum power allocation for a given coded OFDM system and channel response to minimize FER or BER under a constant transmission power constraint is obtained

Parallel Genetic Algorithm for Document Image Compression Optimization

This work proposes a parallel genetic algorithm for compressing scanned document images. A fitness function is designed with Hausdorff distance which determines the terminating condition. The algorithm helps to locate the text lines. A greater compression ratio has achieved with lesser distortion

The role of lower partial moments in stochastic modeling

Lower partial moments plays an important role in the analysis of risks and in income/poverty studies. In the present paper, we further investigate its importance in stochastic modeling and prove some characterization theorems arising out of it. We also identify its relationships with other important applied models such as weighted and equilibrium models. Finally, some applications of lower partial moments in poverty studies are also examined

Short-Term Load Forecast Of A Low Loadfactor Power System For Optimization Of Merit Order Dispatch Using Adaptive Learning Algorithm

Short term load forecasting is one of the key inputs to optimize the management of power system. Almost 60-65% of revenue expenditure of a distribution company is against power purchase. Cost of power depends on source of power. Hence any optimization strategy involves optimization in scheduling power from various sources. As the scheduling involves many technical and commercial considerations and constraints, the efficiency in scheduling depends on the accuracy of load forecast. Load forecasting is a topic much visited in research world and a number of papers using different techniques are already presented. The accuracy of forecast for the purpose of merit order dispatch decisions depends on the extent of the permissible variation in generation limits. For a system with low load factor, the peak and the off peak trough are prominent and the forecast should be able to identify these points to more accuracy rather than minimizing the error in the energy content. In this paper an attempt is made to apply Artificial Neural Network (ANN) with supervised learning based approach to make short term load forecasting for a power system with comparatively low load factor. Such power systems are usual in tropical areas with concentrated rainy season for a considerable period of the year

Reinforcement Learning Solution for Unit Commitment Problem Considering Minimum Start Up and Shut Down Times

Unit Commitment Problem (UCP) in power system refers to the problem of determining the on/ off status of generating units that minimize the operating cost during a given time horizon. Since various system and generation constraints are to be satisfied while finding the optimum schedule, UCP turns to be a constrained optimization problem in power system scheduling. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision making task and an efficient Reinforcement Learning solution is formulated considering minimum up time /down time constraints. The correctness and efficiency of the developed solutions are verified for standard test systems

Reinforcement Learning solution for Unit Commitment Problem through pursuit method

Unit commitment is an optimization task in electric power generation control sector. It involves scheduling the ON/OFF status of the generating units to meet the load demand with minimum generation cost satisfying the different constraints existing in the system. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision task and Reinforcement Learning solution is formulated through one efficient exploration strategy: Pursuit method. The correctness and efficiency of the developed solutions are verified for standard test systems

Optimization of parameters of chemical spray pyrolysis technique to get n and p-type layers of SnS

SnS thin films were prepared using automated chemical spray pyrolysis (CSP) technique. Single-phase, p-type, stoichiometric, SnS films with direct band gap of 1.33 eV and having very high absorption coefficient (N105/cm) were deposited at substrate temperature of 375 °C. The role of substrate temperature in determining the optoelectronic and structural properties of SnS films was established and concentration ratios of anionic and cationic precursor solutions were optimized. n-type SnS samples were also prepared using CSP technique at the same substrate temperature of 375 °C, which facilitates sequential deposition of SnS homojunction. A comprehensive analysis of both types of films was done using x-ray diffraction, energy dispersive x-ray analysis, scanning electron microscopy, atomic force microscopy, optical absorption and electrical measurements. Deposition temperatures required for growth of other binary sulfide phases of tin such as SnS2, Sn2S3 were also determined