Quantization error in stereo imaging systems

In this paper a stochastic analysis of the quantization error in a stereo imaging system has been presented. Further the probability density function of the range estimation error and the expected value of the range error magnitude are derived in terms of various design parameters. Further the relative range error is proposed

Two substitutable perishable product disaster inventory systems

A disaster inventory system is considered in which two substitutable items are stored for disaster management. In the event of disaster management, a particular product may become stock-out and the situation warrants that a demand for the particular product during its stock-out period may be substituted with another available similar product in the inventory. From the utility point of view, continuous review inventory models are quite appro-priate in disaster inventory management. In this paper, a continuous review two substitutable perishable product disaster inventory model is proposed and analyzed. Since the inventory is maintained for disaster management, an adjustable joint reordering policy for replenishment is adopted. There is no lead time and the replenishment is instantaneous. For this model, some measures of system performance are obtained. The stationary behavior of the model is also considered. Numerical examples are also provided to illustrate the results obtained.http://link.springer.com/journal/10479hb2016Industrial and Systems Engineerin

A stochastic point process model of the incubation period of a HIV infected individual

The inability to get people to regularly test and know their HIV status has caused the widespread unavailability of correct and comprehensive data on HIV infection especially the time at which an individual was first infected. Hence, mathematical scientists have relied extensively on inference obtained from small samples to estimate the HIV incubation and seroconversion times. We set out to obtain in this paper, (i) the distribution functions of the HIV incubation period and seroconversion time by considering the stochastic behaviours of the members of the population under discussion, and (ii) the method of estimation that gives the best parameter estimate by building on previous work of Lui et al. (1988) and Medley et al. (1988). We obtained a one-parameter family distribution for the incubation period and a two-parameter family distribution for the seroconversion time. Data on homosexual individuals were used since we built on past work of Lui et al. (1988). Also AIDS incidence projection was done using the backcalculation method. However, the shortfall of the back-calculation method was not addressed in this paper as this is meant for further research.Thanks to NRF for funding this project.http://www.sastat.org.za/journal.ht

A Temporo-Spatial Stochastic Model for Optimal Positioning of Humanitarian Inventories for Disaster Relief Management

A temporo-spatial stochastic model is formulated for analysing the problem of positioning of humanitarian relief centres for optimum disaster-relief management. Disasters occur in a line segment region of the real line according to a Poisson process. Two relief centres are positioned at two different points of the line segment for providing humanitarian relief to the disaster sites. The stationary mean rate of relief rendered by the two inventories is obtained. By optimizing the mean rate, the optimum positions of the two relief centres are obtained

Modelling T4 cell count as a marker of HIV progression in the absence of any defence mechanism

The T4 cell count, which is considered one of the markers of disease progression in an HIV infected individual, is modelled in this paper. The World Health Organisation has recently advocated that countries encourage HIV infected individuals to commence antiretroviral treatments once their T4 cell count drops below 350 cells per ml of blood (this threshold was formerly 200 cells per ml of blood). This recommendation is made because when the T4 cell count is low, the T4 cells are unable to mount an effective immune response against antigens and any such foreign matters in the body, and consequently the individual becomes susceptible to opportunistic infections and lymphomas. A stochastic catastrophe model is developed in this paper to obtain the mean, variance and covariance of the uninfected, infected and lysed T4 cells. The amount of toxin produced in an HIV infected person from the time of infection to a later time may also be obtained from the model. Numerical illustrations of the correlation structures between uninfected and infected T4 cells, and between the infected and lysed T4 cells are also presented

An environment-dependent branching process

A mathematical model of a biological population, taking into account the effect of environmental in uences both on the life-time distribution and on the reproductive capacity of the individuals of the population, is considered and analyzed. It is assumed that the environment stays in level 0 and in level 1 alternately for random lengths of time. The sojourn-times of the environment in the levels 0 and 1 form an alternating renewal process and the probability density function (p.d.f.) of the stay-in times of the environment in level i is i = 0, 1. Further, assuming that the p.d.f. of the life-time of an individual of the population when the population is in level i,i = 0,1, is an explicit expression for the time-dependent mean size of the population is obtained. The particular case corresponding to the environment independent population is deduced and two other particular cases, corresponding to partial interaction of the environment, are analysed. The coef cient of variation of the population size is also obtained and a numerical illustration is provided to highlight the impact of environment on the population size

A two-stage mutation stochastic model of carcinogenesis driven by a two level random environment

In this paper, we present a two-stage stochastic model of carcinogenesis in a two level random environment. The random environment switches between two levels, say, 1 and 2 alternately. When the environment is in level 1, a normal cell either divides into two normal cells or dies; and an intermediate cell divides into two intermediate cells or dies. When the environment is in level 2, a normal cell either divides into two intermediate cells or divides into one normal cell and one intermediate cell or divides into two normal cells or dies; and an intermediate cell either divides into two malignant cells or divides into one intermediate cell and one malignant cell or divides into two intermediate cells or dies. It is assumed that, once a malignant cell is produced, it generates a malignant tumor with probability 1. We obtain the mean numbers of normal, intermediate and malignant cells.http://www.ijmems.inpm2020Industrial and Systems Engineerin

A two-stage mutation stochastic model of carcinogenesis driven by a three level environmental process

A two-mutation model of carcinogenesis which evolves under the influence of three level random environment on the production process is formulated and analyzed. A random environment occupies one of the levels 1, 2 and 3 at any time according to a Markov process. When the environment is in level 1, a normal cell either divides into two normal cells or dies; and an intermediate cell divides into two intermediate cells or dies. When the environment is in level 2, a normal cell either divides into one normal cell and one intermediate cell or dies and an intermediate cell either divides into one intermediate cell and one malignant cell or dies. When the environment is in level 3, a normal cell either divides into two intermediate cells or dies and an intermediate cell either divides into two malignant cells or dies. It is assumed that, once a malignant cell is produced, it generates a malignant tumor with probability 1. We obtain the mean numbers of normal, intermediate and malignant cells at any time.https://www.ijmems.inpm2021Industrial and Systems Engineerin

Transient Analysis of a Non-Preemptive Priority Queueing System

A single server queueing system is considered in which two types of customers arrive according to independent Poisson processes. Customers of type 1 are of priority nature and the other customers of type 2 are of non-priority. Type 1 customers have nonpreemptive priority over type 2 customers. Assuming that service times for both types of customers have exponential distribution with mean 1/m, we obtain explicit expressions for the transient solution for the state probability distribution. We deduce the steady-state joint distribution of the number of customers of type 1 and customers of type 2 and also obtain performance measures of the system