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.

Surface Circulation in the Tropical Indian Ocean Using Multi-Mission Altimeter Data

In the present study the availability of satellite altimeter sea level data with good spatial and temporal resolution is explored to describe and understand circulation of the tropical Indian Ocean. The derived geostrophic circulations showed large variability in all scales. The seasonal cycle described using monthly climatology generated using 12 years SSH data from 1993 to 2004 revealed several new aspects of tropical Indian Ocean circulation. The interannual variability presented in this study using monthly means of SSH data for 12 years have shown large year-to-year variability. The EOF analysis has shown the influence of several periodic signals in the annual and interannual scales where the relative strengths of the signals also varied from year to year. Since one of the reasons for this kind of variability in circulation is the presence of planetary waves. This study discussed the influence of such waves on circulation by presenting two cases one in the Arabian Sea and other in the Bay of Bengal.