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.

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

Information Discovery in Distributed Systems-A Novel Concept Based on Modelling of Information Elements

Sharing of information with those in need of it has always been an idealistic goal of networked environments. With the proliferation of computer networks, information is so widely distributed among systems, that it is imperative to have well-organized schemes for retrieval and also discovery. This thesis attempts to investigate the problems associated with such schemes and suggests a software architecture, which is aimed towards achieving a meaningful discovery. Usage of information elements as a modelling base for efficient information discovery in distributed systems is demonstrated with the aid of a novel conceptual entity called infotron.The investigations are focused on distributed systems and their associated problems. The study was directed towards identifying suitable software architecture and incorporating the same in an environment where information growth is phenomenal and a proper mechanism for carrying out information discovery becomes feasible. An empirical study undertaken with the aid of an election database of constituencies distributed geographically, provided the insights required. This is manifested in the Election Counting and Reporting Software (ECRS) System. ECRS system is a software system, which is essentially distributed in nature designed to prepare reports to district administrators about the election counting process and to generate other miscellaneous statutory reports.Most of the distributed systems of the nature of ECRS normally will possess a "fragile architecture" which would make them amenable to collapse, with the occurrence of minor faults. This is resolved with the help of the penta-tier architecture proposed, that contained five different technologies at different tiers of the architecture.The results of experiment conducted and its analysis show that such an architecture would help to maintain different components of the software intact in an impermeable manner from any internal or external faults. The architecture thus evolved needed a mechanism to support information processing and discovery. This necessitated the introduction of the noveI concept of infotrons. Further, when a computing machine has to perform any meaningful extraction of information, it is guided by what is termed an infotron dictionary.The other empirical study was to find out which of the two prominent markup languages namely HTML and XML, is best suited for the incorporation of infotrons. A comparative study of 200 documents in HTML and XML was undertaken. The result was in favor ofXML.The concept of infotron and that of infotron dictionary, which were developed, was applied to implement an Information Discovery System (IDS). IDS is essentially, a system, that starts with the infotron(s) supplied as clue(s), and results in brewing the information required to satisfy the need of the information discoverer by utilizing the documents available at its disposal (as information space). The various components of the system and their interaction follows the penta-tier architectural model and therefore can be considered fault-tolerant. IDS is generic in nature and therefore the characteristics and the specifications were drawn up accordingly. Many subsystems interacted with multiple infotron dictionaries that were maintained in the system.In order to demonstrate the working of the IDS and to discover the information without modification of a typical Library Information System (LIS), an Information Discovery in Library Information System (lDLIS) application was developed. IDLIS is essentially a wrapper for the LIS, which maintains all the databases of the library. The purpose was to demonstrate that the functionality of a legacy system could be enhanced with the augmentation of IDS leading to information discovery service. IDLIS demonstrates IDS in action. IDLIS proves that any legacy system could be augmented with IDS effectively to provide the additional functionality of information discovery service.Possible applications of IDS and scope for further research in the field are covered.

Studies On Classical And Retrial Inventory With Positive Service Time

Department of Mathematics, Cochin University of Science and Technology

Impact of Self-generation of Priorities and Non-preemptive Service in Single/Multiserver Queues

In this thesis we have studied a few models involving self-generation of priorities. Priority queues have been extensively discussed in literature. However, these are situations involving priority assigned to (or possessed by) customers at the time of their arrival. Nevertheless, customers generating into priority is a common phenomena. Such situations especially arise at a physicians clinic, aircrafts hovering over airport running out of fuel but waiting for clearance to land and in several communication systems. Quantification of these are very little seen in literature except for those cited in some of the work indicated in the introduction. Our attempt is to quantify a few of such problems. In doing so, we have also generalized the classical priority queues by introducing priority generation ( going to higher priorities and during waiting). Systematically we have proceeded from single server queue to multi server queue. We also introduced customers with repeated attempts (retrial) generating priorities. All models that were analyzed in this thesis involve nonpreemptive service. Since the models are not analytically tractable, a large number of numerical illustrations were produced in each chapter to get a feel about the working of the systems.

Stochastic Inventory with/without Service Time, Reneging and Retrial of Customers

This thesis Entitled Stochastic modelling and analysis.This thesis is divided into six chapters including this introductory chapter. In second chapter, we consider an (s,S) inventory model with service, reneging of customers and finite shortage of items.In the third chapter, we consider an (s,S) inventoiy system with retrial of customers. Arrival of customers forms a Poisson process with rate. When the inventory level depletes to s due to demands, an order for replenishment is placed.In Chapter 4, we analyze and compare three (s,S) inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. In chapter 5, we analyze and compare three production inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed.In chapter 6, we consider a PH /PH /l inventory model with reneging of customers and finite shortage of items.

Service quality and reliability assessment of mobile communication infrastructure

The service quality of any sector has two major aspects namely technical and functional. Technical quality can be attained by maintaining technical specification as decided by the organization. Functional quality refers to the manner which service is delivered to customer which can be assessed by the customer feed backs. A field survey was conducted based on the management tool SERVQUAL, by designing 28 constructs under 7 dimensions of service quality. Stratified sampling techniques were used to get 336 valid responses and the gap scores of expectations and perceptions are analyzed using statistical techniques to identify the weakest dimension. To assess the technical aspects of availability six months live outage data of base transceiver were collected. The statistical and exploratory techniques were used to model the network performance. The failure patterns have been modeled in competing risk models and probability distribution of service outage and restorations were parameterized. Since the availability of network is a function of the reliability and maintainability of the network elements, any service provider who wishes to keep up their service level agreements on availability should be aware of the variability of these elements and its effects on interactions. The availability variations were studied by designing a discrete time event simulation model with probabilistic input parameters. The probabilistic distribution parameters arrived from live data analysis was used to design experiments to define the availability domain of the network under consideration. The availability domain can be used as a reference for planning and implementing maintenance activities. A new metric is proposed which incorporates a consistency index along with key service parameters that can be used to compare the performance of different service providers. The developed tool can be used for reliability analysis of mobile communication systems and assumes greater significance in the wake of mobile portability facility. It is also possible to have a relative measure of the effectiveness of different service providers.

Discrete Time Inventory Models with/without Positive Service Time

In everyday life different flows of customers to avail some service facility or other at some service station are experienced. In some of these situations, congestion of items arriving for service, because an item cannot be serviced Immediately on arrival, is unavoidable. A queuing system can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service, leaving the system after being served. Examples Include shoppers waiting in front of checkout stands in a supermarket, Programs waiting to be processed by a digital computer, ships in the harbor Waiting to be unloaded, persons waiting at railway booking office etc. A queuing system is specified completely by the following characteristics: input or arrival pattern, service pattern, number of service channels, System capacity, queue discipline and number of service stages. The ultimate objective of solving queuing models is to determine the characteristics that measure the performance of the system