On Implementing Joins, Aggregates and Universal Quantifier in Temporal Databases using SQL Standards

A feasible way of implementing a temporal database is by mapping temporal data model onto a conventional data model followed by a commercial database management system. Even though extensions were proposed to standard SQL for supporting temporal databases, such proposals have not yet come across standardization processes. This paper attempts to implement database operators such as aggregates and universal quantifier for temporal databases, implemented on top of relational database systems, using currently available SQL standards.

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.

Analysis of Some Queueing Models Related To N-Policy: Operations Research

This study is about the analysis of some queueing models related to N-policy.The optimal value the queue size has to attain in order to turn on a single server, assuming that the policy is to turn on a single server when the queue size reaches a certain number, N, and turn him off when the system is empty.The operating policy is the usual N-policy, but with random N and in model 2, a system similar to the one described here.This study analyses “ Tandem queue with two servers”.Here assume that the first server is a specialized one.In a queueing system,under N-policy ,the server will be on vacation until N units accumulate for the first time after becoming idle.A modified version of the N-policy for an M│M│1 queueing system is considered here.The novel feature of this model is that a busy service unit prevents the access of new customers to servers further down the line.It is deals with a queueing model consisting of two servers connected in series with a finite intermediate waiting room of capacity k.Here assume that server I is a specialized server.For this model ,the steady state probability vector and the stability condition are obtained using matrix – geometric method.

T-Policy in Reliability and Inventory

In this thesis T-policy is implemented to the inventory system with random lead time and also repair in the reliability of k-out-of-n system. Inventory system may be considered as the system of keeping records of the amounts of commodities in stock. Reliability is defined as the ability of an entity to perform a required function under given conditions for a given time interval. It is measured by the probability that an entity E can perform a required function under given conditions for the time interval. In this thesis considered k-out-of-n system with repair and two modes of service under T-policy. In this case first server is available always and second server is activated on elapse of T time units. The lead time is exponentially distributed with parameter  and T is exponentially distributed with parameter  from the epoch at which it was inactivated after completion of repair of all failed units in the previous cycle, or the moment n-k failed units accumulate. The repaired units are assumed to be as good as new. In this study , three different situations, ie; cold system, warm system and hot system. A k-out-of-n system is called cold, warm or hot according as the functional units do not fail, fail at a lower rate or fail at the same rate when system is shown as that when it is up.

Retrial Queues with Orbital Search

Queueing system in which arriving customers who find all servers and waiting positions (if any) occupied many retry for service after a period of time are retrial queues or queues with repeated attempts. This study deals with two objectives one is to introduce orbital search in retrial queueing models which allows to minimize the idle time of the server. If the holding costs and cost of using the search of customers will be introduced, the results we obtained can be used for the optimal tuning of the parameters of the search mechanism. The second one is to provide insight of the link between the corresponding retrial queue and the classical queue. At the end we observe that when the search probability Pj = 1 for all j, the model reduces to the classical queue and when Pj = 0 for all j, the model becomes the retrial queue. It discusses the performance evaluation of single-server retrial queue. It was determined by using Poisson process. Then it discuss the structure of the busy period and its analysis interms of Laplace transforms and also provides a direct method of evaluation for the first and second moments of the busy period. Then it discusses the M/ PH/1 retrial queue with disaster to the unit in service and orbital search, and a multi-server retrial queueing model (MAP/M/c) with search of customers from the orbit. MAP is convenient tool to model both renewal and non-renewal arrivals. Finally the present model deals with back and forth movement between classical queue and retrial queue. In this model when orbit size increases, retrial rate also correspondingly increases thereby reducing the idle time of the server between services

Queues with retrial/self-generation of priorities /postponement of work and some related reliability problems

Application of Queueing theory in areas like Computer networking, ATM facilities, Telecommunications and to many other numerous situation made people study Queueing models extensively and it has become an ever expanding branch of applied probability. The thesis discusses Reliability of a ‘k-out-of-n system’ where the server also attends external customers when there are no failed components (main customers), under a retrial policy, which can be explained in detail. It explains the reliability of a ‘K-out-of-n-system’ where the server also attends external customers and studies a multi-server infinite capacity Queueing system where each customer arrives as ordinary but can generate into priority customer which waiting in the queue. The study gives details on a finite capacity multi-server queueing system with self-generation of priority customers and also on a single server infinite capacity retrial Queue where the customer in the orbit can generate into a priority customer and leaves the system if the server is already busy with a priority generated customer; else he is taken for service immediately. Arrival process is according to a MAP and service times follow MSP.

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.

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.

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.

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

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.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Queueing Theory And Other Applications Of Stochastic Processes Queueing And Inventory Models With Rest Periods

In this thesis we study the effect of rest periods in queueing systems without exhaustive service and inventory systems with rest to the server. Most of the works in the vacation models deal with exhaustive service. Recently some results have appeared for the systems without exhaustive service.

Probability Theory. Stochastic Processes And Their Applications Probabilistic Analysis Of Some Queueing And Inventory Models

In this thesis we attempt to make a probabilistic analysis of some physically realizable, though complex, storage and queueing models. It is essentially a mathematical study of the stochastic processes underlying these models. Our aim is to have an improved understanding of the behaviour of such models, that may widen their applicability. Different inventory systems with randon1 lead times, vacation to the server, bulk demands, varying ordering levels, etc. are considered. Also we study some finite and infinite capacity queueing systems with bulk service and vacation to the server and obtain the transient solution in certain cases. Each chapter in the thesis is provided with self introduction and some important references