Queueing Models with Vacations and Working Vacations

The thesis entitled “Queueing Models with Vacations and Working Vacations" consists of seven chapters including the introductory chapter. In chapters 2 to 7 we analyze different queueing models highlighting the role played by vacations and working vacations. The duration of vacation is exponentially distributed in all these models and multiple vacation policy is followed.In chapter 2 we discuss an M/M/2 queueing system with heterogeneous servers, one of which is always available while the other goes on vacation in the absence of customers waiting for service. Conditional stochastic decomposition of queue length is derived. An illustrative example is provided to study the effect of the input parameters on the system performance measures. Chapter 3 considers a similar setup as chapter 2. The model is analyzed in essentially the same way as in chapter 2 and a numerical example is provided to bring out the qualitative nature of the model. The MAP is a tractable class of point process which is in general nonrenewal. In spite of its versatility it is highly tractable as well. Phase type distributions are ideally suited for applying matrix analytic methods. In all the remaining chapters we assume the arrival process to be MAP and service process to be phase type. In chapter 4 we consider a MAP/PH/1 queue with working vacations. At a departure epoch, the server finding the system empty, takes a vacation. A customer arriving during a vacation will be served but at a lower rate.Chapter 5 discusses a MAP/PH/1 retrial queueing system with working vacations.In chapter 6 the setup of the model is similar to that of chapter 5. The signicant dierence in this model is that there is a nite buer for arrivals.Chapter 7 considers an MMAP(2)/PH/1 queueing model with a nite retrial group

On Multi- Server Queues With Consultation With Main Server

Queueing Theory is the mathematical study of queues or waiting lines. Queues abound in every day life - in computer networks, in tra c islands, in communication of electro-magnetic signals, in telephone exchange, in bank counters, in super market checkouts, in doctor's clinics, in petrol pumps, in o ces where paper works to be processed and many other places. Originated with the published work of A. K. Erlang in 1909 [16] on congestion in telephone tra c, Queueing Theory has grown tremendously in a century. Its wide range applications includes Operations Research, Computer Science, Telecommunications, Tra c Engineering, Reliability Theory, etc.

Stochastic Modelling Using Markov Chains

Department of Statistics, Cochin University of Science and Technology

On Queues with Interruptions and Repeat or Resumption of Service

This thesis entitled' On Queues with Interruptions and Repeat or Resumption of Service' introduces several new concepts into queues with service interruption. It is divided into Seven chapters including an introductory chapter. The following are keywords that we use in this thesis: Phase type (PH) distribution, Markovian Arrival Process (MAP), Geometric Distribution, Service Interruption, First in First out (FIFO), threshold random variable and Super threshold random variable. In the second chapter we introduce a new concept called the 'threshold random variable' which competes with interruption time to decide whether to repeat or resume the interrupted service after removal of interruptions. This notion generalizes the work reported so far in queues with service interruptions. In chapter 3 we introduce the concept of what is called 'Super threshold clock' (a random variable) which keeps track of the total interruption time of a customer during his service except when it is realized before completion of interruption in some cases to be discussed in this thesis and in other cases it exactly measures the duration of all interruptions put together. The Super threshold clock is OIl whenever the service is interrupted and is deactivated when service is rendered. Throughout this thesis the first in first out service discipline is followed except for priority queues.

Queues with Customer Induced Interruption

In this thesis we have introduced and studied the notion of self interruption of service by customers. Service interruption in queueing systems have been extensively discussed in literature (see, Krishnamoorthy, Pramod and Chakravarthy [38]) for the most recent survey. So far all work reported deal with cases in which service interruptions are generated by sources other than customers. However, there are situations where interruptions are due to the customers rather than the system. Such situations are especially arise at doctors clinic, banks, reservation counter etc. Our attempt is to quantify a few of such problems. Systematically we have proceed from single server queue (in Chapter 2) to multi-server queues (Chapter 3). In Chapte 4, we have studied a very general multiserver queueing model with service interruption and protection of service phases. We also introduced customer interruption in a retrial setup (in Chapter 5). All models (from Chapter 2 to Chapter 4) that were analyzed involve 'non-preemptive priority' for interrupted customers where as in the model discussed in Chapter 5 interruption of service by customers is not encouraged. So the interrupted customers cannot access the server as long as there are primary customers in the system. In Chapter 5 we have obtained an explicit expression for the stability condition of the system. In all models analyzed in this thesis, we have assumed that no more than one interruption is allowed for a customer while in service. Since the models are not analytically tractable, a large number of numerical illustrations were given in each chapter it illustrate the working of the systems. We can extend the models discussed in this thesis to several directions. For example some of the models can be analyzed with both server induced and customer induced interruptions the results for which are not available till date. Another possible extension of work is to the case where there is no bound on the number of interruptions a customer is permitted to have before service completion. More complex is the case where a customer is permitted to have a nite number (K ≥ 2) of We can extend the models discussed in this thesis to several directions.

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.

Phase Transitions of Trace Metals in the Aquatic Environment of Kuttanad, Kerala

This thesis is a modest attempt in assessing the trace metal levels and their behavior in the aquatic environment of Kuttanad, an aquatic system that is severely affected by man’s intervention on natural processes, by study seriously evaluating the levels of trace metals in dissolved and particulate phases and also in the different chemical fractions of the sediments. Understanding of the distributions, variations and transfer processes of trace metals in different environmental phases in the backwaters of Kuttanad is vital for the assessment of the water pollution problems and study the ecology of the area which contributes 20% of the rice production in the State of Kerala. Kuttand is a low-lying, shallow bay formed as a result of geological uplift. The major economic activity is agriculture involving 40% of the population. About 1.5% of the people are engaged in aquaculture. The trace metal distribution in the Kuttand backwaters is considerably influenced by the tropical features of the location and by human activities including agricultural activities and construction of salinity barrier. In this study an attempt is made to differentiate the metals in the sediment into exchangeable, reducible and resistant fractions in the sediments.

Liquid-phase Friedel-Crafts acylation using NixMn(l-x)Fe2O4 spinel catalysts

The liquid-phase Friedel-Crafts acylation of toluene using benzoyl chloride as benzoylating agent has heen carried out over Nix, Mn(l-x)Fe2 O4 (x=O, 0.2, 0.4, 0.6, 0.8 and 1.0) type systems under different reaction conditions. It is observed that the systems with high 'x' values are effective for the conversion of BOC and the selective formation of 4-MBP. Selectivity for 4-MBP over MnFe2O4 is more than 90% under the optimized reaction conditions. Sites of moderate acidity is effective in calalyzing the benzoylation reaction.

Catalytic activity of some of the perovskite-type mixed oxides (ABO3) consisting of rare earth and 3d transition metals

The catalytic activity of some of the ABO3 (A = La, Pr and Sm, B= Cr, Mn, Fe, Co and Ni) perovskite-type oxides for the liquid phase reduction of ketone and oxidation of alcohol in 2-propanol medium has been studied. The data have been correlated with the surface electron donor properties of these oxides. The surface electron donor properties have been determined from the adsorption of electron acceptors of varying electron affinities on the oxide surface.

Photoacoustic studies on n-type InP

We discuss an open photoacoustic cell study on sulfer-doped n-type InP wafer. The thermal diffusivity of the sample is evaluated from the phase data associated with the photoacoustic signal as a function of the modulation frequency under heat transmission configuration. Analysis is made on the basis of the Rosencwaig-Gersho theory and the results are compared with those from earlier reported photoacoustic studies of semiconductors. Our investigation clearly indicates that the instantaneous thermalization process is the major heat diffusion mechanism responsible for the photoacoustic signal generation in an InP sample.

Bivarite burr distributions

The present work is organized into six chapters. Bivariate extension of Burr system is the subject matter of Chapter II. The author proposes to introduce a general structure for the family in two dimensions and present some properties of such a system. Also in Chapter II some new distributions, which are bivariate extension of univariate distributions in Burr (1942) is presented.. In Chapter III, concentrates on characterization problems of different forms of bivariate Burr system. A detailed study of the distributional properties of each member of the Burr system has not been undertaken in literature. With this aim in mind in Chapter IV is discussed with two forms of bivariate Burr III distribution. In Chapter V the author Considers the type XII, type II and type IX distributions. Present work concludes with Chapter VI by pointing out the multivariate extension for Burr system. Also in this chapter the concept of multivariate reversed hazard rates as scalar and vector quantity is introduced.

Electrical properties and phase transitions insome ammonium containing ferroelectrics

The thesis aims to present the results of the experimental investigations on the electrical properties like electrical conductivity, dielectric constant and ionic thermo~ currents in certain ammonium containing ferroelectric crystals viz. LiNH4SO4, (NH4)2SO4 and (NH4)5H(SO4)2. Special attention has been paid in revealing the mechanisms of electrical conduction in the various phases of these crystals and those asso~ ciated with the different phase transitions occurring in them, by making studies on doped, quenched and deuterated crystals. The report on the observation of two new phase transitions in (NH4) S O2 and of a similar one in ( NH4 ) H (2SO4 ) are included. The relaxation mechanisms of the impurity-vacancy complexes and the space charge phenomena in pure and doped crystals of LiNH4SO4 and (NH4)2SO4 and the observation of a new type of ionic thermo-current viz. Protonic Thermo-Current (PTC) in these crystals are also presented here.

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