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.

Queueing Models with Vacations and Working Vacations

The objective of the study of \Queueing models with vacations and working vacations" was two fold; to minimize the server idle time and improve the e ciency of the service system. Keeping this in mind we considered queueing models in di erent set up in this thesis. Chapter 1 introduced the concepts and techniques used in the thesis and also provided a summary of the work done. In chapter 2 we considered an M=M=2 queueing model, where one of the two heterogeneous servers takes multiple vacations. We studied the performance of the system with the help of busy period analysis and computation of mean waiting time of a customer in the stationary regime. Conditional stochastic decomposition of queue length was derived. To improve the e ciency of this system we came up with a modi ed model in chapter 3. In this model the vacationing server attends the customers, during vacation at a slower service rate. Chapter 4 analyzed a working vacation queueing model in a more general set up. The introduction of N policy makes this MAP=PH=1 model di erent from all working vacation models available in the literature. A detailed analysis of performance of the model was provided with the help of computation of measures such as mean waiting time of a customer who gets service in normal mode and vacation mode.

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.