Simultaneous Embeddings Of Graphs As Median And Antimedian Subgraphs

The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. It is proved that for arbitrary graphs G and J and a positive integer r 2, there exists a connected graph H such that G is the antimedian and J the median subgraphs of H, respectively, and that dH(G, J) = r. When both G and J are connected, G and J can in addition be made convex subgraphs of H.

A Study of Some Centrality Measures in Graphs

Centrality is in fact one of the fundamental notions in graph theory which has established its close connection with various other areas like Social networks, Flow networks, Facility location problems etc. Even though a plethora of centrality measures have been introduced from time to time, according to the changing demands, the term is not well defined and we can only give some common qualities that a centrality measure is expected to have. Nodes with high centrality scores are often more likely to be very powerful, indispensable, influential, easy propagators of information, significant in maintaining the cohesion of the group and are easily susceptible to anything that disseminate in the network.

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

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability and with probability 1− leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability (< 1) and with probability 1 − leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

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 commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.