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

Stochastic processes and their applications time dependent solutions for some queueing and inventory models

The objective of this thesis is to study the time dependent behaviour of some complex queueing and inventory models. It contains a detailed analysis of the basic stochastic processes underlying these models. In the theory of queues, analysis of time dependent behaviour is an area.very little developed compared to steady state theory. Tine dependence seems certainly worth studying from an application point of view but unfortunately, the analytic difficulties are considerable. Glosod form solutions are complicated even for such simple models as M/M /1. Outside M/>M/1, time dependent solutions have been found only in special cases and involve most often double transforms which provide very little insight into the behaviour of the queueing systems themselves. In inventory theory also There is not much results available giving the time dependent solution of the system size probabilities. Our emphasis is on explicit results free from all types of transforms and the method used may be of special interest to a wide variety of problems having regenerative structure.

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.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

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.

Managing Rentals with Usage-Based Loss

Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different \recirculation" rules | i.e., which rental unit to choose to meet each demand | we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens. We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic. Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

Examining the predictive value of combining the theory of planned behaviour and the volunteer functions inventory

The functions of the volunteer functions inventory were combined with the constructs of the theory of planned behaviour (i.e., attitudes, subjective norms, and perceived behavioural control) to establish whether a stronger, single explanatory model prevailed. Undertaken in the context of episodic, skilled volunteering by individuals who were retired or approaching retirement (N = 186), the research advances on prior studies which either examined the predictive capacity of each model independently or compared their explanatory value. Using hierarchical regression analysis, the functions of the volunteer functions inventory (when controlling for demographic variables) explained an additional 7.0% of variability in individuals’ willingness to volunteer over and above that accounted for by the theory of planned behaviour. Significant predictors in the final model included attitudes, subjective norms and perceived behavioural control from the theory of planned behaviour and the understanding function from the volunteer functions inventory. It is proposed that the items comprising the understanding function may represent a deeper psychological construct (e.g., self-actualisation) not accounted for by the theory of planned behaviour. The findings highlight the potential benefit of combining these two prominent models in terms of improving understanding of volunteerism and providing a single parsimonious model for raising rates of this important behaviour.

The applicability of Bowen's family theory to the Malay population

The changes of economic status in Malaysia have lead to many psychosocial problems especially among the young people. Counselling and psychotherapy have been seen as one of the solutions that are practiced in Western Culture. Most counselling theorists believe that their theory is universal however there is limited research to prove it. This paper will describe an ongoing study conducted in Malaysia about the applicability of one Western counselling Theory, Bowen’s family theory the Differentiation of self levels in the family allow a person to both leave the family’s boundaries in search of uniqueness and continually return to the family in order to further establish a sense of belonging. In addition Bowen believed that this comprised of four measures: Differentiation of Self (DSI), Family Inventory of Live Event (ILE), Depression Anxiety and Stress Scale (DASS) and Connor-Davidson Resilience Scale (CD-RISC). Preliminary findings are discussed and the implication in enhancing the quality of teaching family counselling in universities explored.

The application of Bowen’s family system theory (BFST) to the Malay population in Malaysia

The rapid economic development and social changes in Malaysia recently have led to many psychosocial problems in young people, such as drug addiction, child sexual abuse and mental illness. The Malaysian government is beginning to focus more attention on its social welfare and human service needs in order to alleviate these psychosocial problems. Although counselling is accepted and widespread in Malaysia, the practice of family therapy is not as accepted as it is still a widely held belief that family problems need to be kept within the family. However, changes are imminent and thus the theoretical basis of family therapy needs to be culturally relevant. Bowen‟s Family Systems Theory (BFST) is already one of the major theories taught to tertiary counselling students in Malaysian universities. The main tenet of Bowen‟s theory is that the family as a system may be unstable unless each member of the family is well differentiated. High differentiation levels in the family allow a person to both leave the family‟s boundaries in search of uniqueness and to continually return to the family fold in order to establish a more mature sense of belonging. The difficulty, however, is that while Bowen has claimed that his theory is universal nearly all of the research confirming the theory has been conducted in the United States of America. The only known study outside America, however, did show that Bowen‟s theory applied to a Filipino population but, one of the theory‟s propositions that differentiation is intergenerational was not supported in this non-American sample. The American sample that was compared to the Malay sample was taken from Skowron and Friedlander‟s (1998) study. One hundred and twenty-seven faculty staff in an American university completed the Differentiation of Self Inventory (DSI) to measure level of differentiation of self. This thesis therefore, set out to determine whether Bowen‟s theory applied to another non-American sample, the Malaysian community. The research also investigated if the intergenerational effect was present in the Malaysian sample as well as explored the role of socio-economic status on Bowen‟s theory of differentiation and gender effect. Three hundred and seventy-four families completed four measures to examine these research questions: the Differentiation of Self Inventory (DSI), the Family Inventory of Life Event (FILE), the Depression Anxiety and Stress Scale (DASS) and the Connor-Davidson Resilience Scale (CD-RISC). The results of the study showed that differentiation of self is a valid construct for the Malay population. However, all four subscales of the Differentiation of Self Inventory (DSI); emotional reactivity (ER), emotional cut-off (EC), fusion with other (FO) and I position (IP), showed significant differences compared to the American sample from Skowron and Friedlander‟s (1998) study. The Malay sample scored higher in emotional reaction (ER), fusion with other (FO), but lower on emotional cut-off (EC) and I position (IP) than the American sample. The intergenerational effect was found in the Malay population as the parent‟s level of differentiation correlated with their children‟s level of differentiation. It was found that stress as measured by the Family Inventory of Life Event (FILE) and as measured by the Depression Anxiety and Stress Scale (DASS) were not correlated with the level of differentiation of self in parents. However, gender had a significant effect in predicting the level of differentiation among parents in Malay population with females scores higher on emotional reactivity (ER) and fusion with other (FO) than males. An additional finding was that resilience can be predicted from the level of differentiation of self in children in the Malay sample. There was also a positive correlation between the level of differentiation of self in parents and resilience in their children. Findings from this study indicate that the concept of differentiation of self is applicable to a Malay sample; however, the implementation of the theory should be applied with cultural sensitivity.

The impact of anxiety on processing efficiency : implications for the attentional control theory

The Attentional Control Theory (ACT) proposes that high-anxious individuals maintain performance effectiveness (accuracy) at the expense of processing efficiency (response time), in particular, the two central executive functions of inhibition and shifting. In contrast, research has generally failed to consider the third executive function which relates to the function of updating. In the current study, seventy-five participants completed the Parametric Go/No-Go and n-back tasks, as well as the State-Trait Anxiety Inventory in order to explore the effects of anxiety on attention. Results indicated that anxiety lead to decay in processing efficiency, but not in performance effectiveness, across all three Central Executive functions (inhibition, set-shifting and updating). Interestingly, participants with high levels of trait anxiety also exhibited impaired performance effectiveness on the n-back task designed to measure the updating function. Findings are discussed in relation to developing a new model of ACT that also includes the role of preattentive processes and dual-task coordination when exploring the effects of anxiety on task performance.

Driven by distraction: Investigating the effects of anxiety on driving performance using the Attentional Control Theory

This study investigates the effects of trait anxiety on self-reported driving behaviours through its negative impacts on Central Executive functions. Following a self-report study that found trait anxiety to be significantly related to driving behaviours, the present study extended the predictions of Eysenck and Calvo’s Attentional Control Theory, proposing that anxiety affects driving behaviours, in particular driving lapses, through its impact across the Central Executive. Seventy-five Australian drivers participated in the study, completing the Parametric Go/No-Go and n-back tasks, as well as the State-Trait Anxiety Inventory and the Driving Behaviour Questionnaire. While both trait anxiety and processing efficiency of the Central Executive was found to significantly predict driving lapses, trait anxiety remained a strong predictor of driving lapses after processing efficiency was controlled for. It is concluded that while processing efficiency of the central Executive is a key determinant of driving lapses, another Central Executive function that is closer to the driving lapses in the trait anxiety – driving lapses relationship may be needed. Suggestions regarding how to improve future trait anxiety – driving behaviours research are discussed.

Markov random fields and spatial smoothing in improving of forest inventory estimates

Markov random fields (MRF) are popular in image processing applications to describe spatial dependencies between image units. Here, we take a look at the theory and the models of MRFs with an application to improve forest inventory estimates. Typically, autocorrelation between study units is a nuisance in statistical inference, but we take an advantage of the dependencies to smooth noisy measurements by borrowing information from the neighbouring units. We build a stochastic spatial model, which we estimate with a Markov chain Monte Carlo simulation method. The smooth values are validated against another data set increasing our confidence that the estimates are more accurate than the originals.

Strategies that students use to trace code: an analysis based in grounded theory

Fitzgerald, S., Simon, B., and Thomas, L. 2005. Strategies that students use to trace code: an analysis based in grounded theory. In Proceedings of the First international Workshop on Computing Education Research (Seattle, WA, USA, October 01 - 02, 2005). ICER '05. ACM, New York, NY, 69-80