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.

The Steady-State and Transient Characteristic Analysis of Thermal Fixing a Photorefractive Hologram Grating in Lithium Niobate

The transient interaction between a refraction index grating and light beams during simultaneous writing and thermal fixing of a photorefractive hologram is investigated. With a diffusion- and photovoltaic-dominated carrier transport mechanism and carrier thermal activation (temperature dependent) considered in Fe:LiNbO3 crystal, from the standpoint of field-material coupling, the theoretical thermal fixing time and the space-charge field buildup, spatial distribution, and temperature dependence are given numerically by combining the band transport model with mobile ions with the coupled-wave equation

Excitation wavelength dependent fluorescence behaviour of nano colloids of ZnO

In this paper, the fluorescence behaviour of nano colloids of ZnO has been studied as a function of the excitation wavelength. We have found that excitation at the tail of the absorption band gives rise to an emission that shifts with the change of the excitation wavelength. The excitation wavelength dependent shift of the fluorescence maximum is measured to be between 60 and 100 nm. This kind of excitation wavelength dependent fluorescence behaviour, which may appear to be in violation of Kasha’s rule of excitation wavelength independence of the emission spectrum, has been observed for nano ZnO colloids prepared by two different chemical routes and different capping agents. It is shown that the existence of a distribution of energetically different molecules in the ground state coupled with a low rate of the excited state relaxation processes, namely, solvation and energy transfer, are responsible for the excitation wavelength dependent fluorescence behaviour of the systems.

Excitation wavelength dependent fluorescence behaviour of nano colloids of ZnO

In this paper, the fluorescence behaviour of nano colloids of ZnO has been studied as a function of the excitation wavelength. We have found that excitation at the tail of the absorption band gives rise to an emission that shifts with the change of the excitation wavelength. The excitation wavelength dependent shift of the fluorescence maximum is measured to be between 60 and 100 nm. This kind of excitation wavelength dependent fluorescence behaviour, which may appear to be in violation of Kasha’s rule of excitation wavelength independence of the emission spectrum, has been observed for nano ZnO colloids prepared by two different chemical routes and different capping agents. It is shown that the existence of a distribution of energetically different molecules in the ground state coupled with a low rate of the excited state relaxation processes, namely, solvation and energy transfer, are responsible for the excitation wavelength dependent fluorescence behaviour of the systems.

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.