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.

Existence results for partial neutral functional differential equations with state-dependent delay

In this paper we study the existence of mild solutions for a class of first order abstract partial neutral differential equations with state-dependent delay. (C) 2008 Elsevier Ltd. All rights reserved.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

The Maximal Number of Particles in a Branching Process with State-Dependent Immigration

AMS subject classification: 60J80, 60J15.

Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

2000 Mathematics Subject Classification: 35K55, 35K60.

Similarity solutions of a Becker-Döring system with time-dependent monomer input

We formulate the Becker-Döring equations for cluster growth in the presence of a time-dependent source of monomer input. In the case of size-independent aggregation and ragmentation rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found.

Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

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.

Time-dependent or state-dependent pricing? Evidence from a large devaluation episode

State-dependent and time-dependent price setting models yield distinct implications for how frequency and magnitude of price changes react to shocks. This note studies pricing behavior in Brazil following the large devaluation of the Brazilian Real in 1999 to distinguish between models. The results are consistent with state-dependent pricing

A general multiserver state-dependent queueing system

The work studies a general multiserver queue in which the service time of an arriving customer and the next interarrival period may depend on both the current waiting time and the server assigned to the arriving customer. Stability of the system is proved under general assumptions on the predetermined distributions describing the model. The proof exploits a combination of the Markov property of the workload process with a regenerative property of the process. The key idea leading to stability is a characterization of the limit behavior of the forward renewal process generated by regenerations. Extensions of the basic model are also studied.

Spinal cord injury: assessment of autonomic state-dependent control of cardiovascular system and body core temperature

Spinal cord injury (SCI) results not only in paralysis; but it is also associated with a range of autonomic dysregulation that can interfere with cardiovascular, bladder, bowel, temperature, and sexual function. The entity of the autonomic dysfunction is related to the level and severity of injury to descending autonomic (sympathetic) pathways. For many years there was limited awareness of these issues and the attention given to them by the scientific and medical community was scarce. Yet, even if a new system to document the impact of SCI on autonomic function has recently been proposed, the current standard of assessment of SCI (American Spinal Injury Association (ASIA) examination) evaluates motor and sensory pathways, but not severity of injury to autonomic pathways. Beside the severe impact on quality of life, autonomic dysfunction in persons with SCI is associated with increased risk of cardiovascular disease and mortality. Therefore, obtaining information regarding autonomic function in persons with SCI is pivotal and clinical examinations and laboratory evaluations to detect the presence of autonomic dysfunction and quantitate its severity are mandatory. Furthermore, previous studies demonstrated that there is an intimate relationship between the autonomic nervous system and sleep from anatomical, physiological, and neurochemical points of view. Although, even if previous epidemiological studies demonstrated that sleep problems are common in spinal cord injury (SCI), so far only limited polysomnographic (PSG) data are available. Finally, until now, circadian and state dependent autonomic regulation of blood pressure (BP), heart rate (HR) and body core temperature (BcT) were never assessed in SCI patients. Aim of the current study was to establish the association between the autonomic control of the cardiovascular function and thermoregulation, sleep parameters and increased cardiovascular risk in SCI patients.

Contribution of cholinergic systems to state-dependent modulation of respiratory control

Respiration is altered during different stages of the sleep-wake cycle. We review the contribution of cholinergic systems to this alteration, with particular reference to the role of muscarinic acetylcholine receptors (MAchRs) during rapid eye movement (REM) sleep. Available evidence demonstrates that MAchRs have potent excitatory effects on medullary respiratory neurones and respiratory motoneurones, and are likely to contribute to changes in central chemosensitive drive to the respiratory control system. These effects are likely to be most prominent during REM sleep, when cholinergic brainstem neurones show peak activity levels. It is possible that MAchR dysfunction is involved in sleep-disordered breathing, Such as obstructive sleep apnea. (C) 2002 Elsevier Science B.V. All rights reserved.

Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model

In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by DIETERICH and KILGORE (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D-c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.