8 resultados para Poisson Arrivals

em Cochin University of Science


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The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

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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

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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.

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Certain organic crystals are found to possess high non- linear optical coefficients,often one to two orders of magnitude higher than those of the well known inorganic non-linear optical materials.Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique using N,N-dimethyl formamide as the solvent.All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique.The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness,Young's modulus and linear compressibility surfaces along symmetry planes.The volume compressibility, bulk modulus and relevant Poisson's ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.

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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

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In this thesis, certain continuous time inventory problems with positive service time under local purchase guided by N/T-policy are analysed. In most of the cases analysed, we arrive at stochastic decomposition of system states, that is, the joint distribution of the system states is obtained as the product of marginal distributions of the components. The thesis is divided into ve chapters

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The inferences obtained from the study are presented in coherent area-specific levels so as to understand the ecotourism and its sub-sector areas for the researchers and policy makers about the issues, importances and potentialities of the sector. An analysis of the tourism sector in Kerala has shown tremendous growth both in terms of tourist arrivals and in terms of revenue generation from direct and indirect sources. The foreign tourist visitors in Kerala in 2014 was 9,23,336 which shows 7.60 percent increase from the last year and the domestic tourist visitors were 1,16,95,411 which again shows 7.71 percent increase, is a clear evidence of its potential. In 2014 the industry contributed revenue of 24885.44 crores from direct and indirect sources giving rise to an increase of 12.11 percent from the last year. A dichotomy of tourists and ecotourists shows that tourists in the ecotourism destinations come to 42.6 percent of the total, shows the scope, significance and its potential. Correlation of zone-wise tourist arrivals based on the ecotourism destinations highlights the fact that with only 19 of the 64 destinations that come in the central zone are the most preferred centres (around 54 percent) for the domestic as well as foreign tourists. The north zone encompassing 6 districts with rich biodiversity shows that the tourists‟ arrival patterns exhibit less promising results. Though the north zone has 31 ecotourism destinations of the state receives only 6.19 percent of the foreign visitors. The ecotourism activities in the state are primarily managed by the Eco-Development Committees (EDCs) and the Vana Samrakshana Samithies (VSS) under the Forest Development Agency of Kerala. Social class-wise categorization of membership shows that 13142 families have membership in 190 EDCs with SC (28 percent), ST (33 percent) and other marginalised communities (39 percent). But this in the VSS shows that 400 VSS have 59085 members actively engaged in ecotourism activities and social category of the VSS makes clear that majority are from the other marginalized fringe households with 62 percent where as the participation of SC is 12 percent and ST is 26 percent. An evaluation of the socio-economic and demographic matrix of the community members involved in ecotourism activities brings out region specific differences. About 75.70 percent of the respondents are males and the rest are females. Majority of the respondents (about 60 percent) are in the age group of 20 to 40 years, followed by the age group of 40-50 (20 percent). The average age of respondents in the three zones is between 35 and 37 years. The majority of the respondents are married, a few are unmarried. Average family size is 4-5 members and differences are identified among zones. Average number of adults per household is 3 and child per household is 2. Majority have an education of 10th class and below i.e. about 60 percent of the sample have only basic school education like primary, secondary and high school (i.e. up to SSLC but not passed) level. About 18 percent are SSLC passed, 10 percent are undergraduates whereas 6 percent constitute respondents having qualification of graduation and above. Majority of the „graduates and above‟ are from south and central zone. Inter-zone differences in educational profile are also identified with lesser number of „graduates and above‟ are identified in the north zone compared to the other two zones. Investigating into the income and livelihood options of the respondents gives insight about the prominence of ecotourism as an employment and livelihood option for the community members, as more than 90 percent of the respondents have cited tourism sector as their main employment option. Most (49.30 percent) of respondents get 100 percent income from tourism related activities, followed by 37.30 percent of community members have income between 75-99 percent from tourism whereas the rest (13 percent) have less than 74 percent of their income from tourism and there exists difference between zones and percentage of income. Financial habit shows that about 49.7 percent hold active bank accounts, 61 percent have savings behaviour and 73.8 percent have indebtedness. Analysis about the ownership of house brings to light that 37 percent of respondents live in their own house followed by 25.7 percent in government funded/provided house and 21 percent in their parent‟s house and 3.5 percent in rented house. About 12 percent of the respondents have other kinds of accommodation facilities such as staff quarters, etc. But in the case of north zone majority i.e. 52 percent primarily depend on the government funded house indicating the effectiveness of government housing programme. Standard of living measured in SLI frameworks shows that majority of the respondents have medium SLI values (42.3 percent); the remaining 47.7 percent have low SLI and 10 percent have high SLI. The community members have been benefitted immensely from forest and its resources. Since the ecotourism destinations are located amidst the wildlife settings, majority of them depend on forest for their livelihood. The information on the tourist‟s demographic characteristics like age, sex, educational qualification and annual income show that the age category of domestic and foreign tourists falls below the age group of less than 35 years (about 65 percent), whereas only 16 percent of tourists are aged above 46 years. The age group below 25 years consists of more international tourists (31.3 percent) compared to the proportion of domestic tourists (12.5 percent). Male-female ratio shows that the males constitute 56 percent of the sample and females with 44 percent. The factors determining the impact of ecotourism programmes in the community was evaluated with the aid of a factor analysis with 12 selected statements. The worries and concerns of the community members about the impact of ecotourism on the environment are well understood from this analysis. It can be drawn that environment protection and the role of ecotourism in improving the income and livelihood options of the local communities is the most important factor concerning the community members.