Geiger Counter-Type Pólya–Eggenberger Distributions

Motivated by the paper of Dandekar (1955), a one-urn model with Polya–Eggenberger sampling scheme is developed, which yields a large number of discrete distributions, including the Dandekar's modified binomial distribution, as particular cases. The model is further modified to some new generalized distributions of order k. Some probable applications of these models were discussed in Dandekar (1955) and Feller (1968) in fields of fertility study and radioactivity. It also has applications in premium determination in insurance sector.     

Lattice paths combinatorics applied to transient queue length distribution of C2/M/1 queues and busy period analysis of bulk queues C2/M/1

This paper aims at deriving explicit transient queue length distribution for GI/M/1 system and busy period analysis of bulk queue GI^b/M/1 through lattice paths (LPs) combinatorics. The general interarrival time distribution is approximated by two-phase Cox distribution, C₂, that has Markovian property, enabling us to represent the processes by two-dimensional LPs. As distributions C₂ cover a wide class of distributions that have rational Laplace–Stieltjes transforms (LSTs) with square coefficient of variation lying in , the results obtained are applicable to a large class of real life situations. Some numerical results for the C₂^b/M/1 model are also given.     

Atmospheric Dispersion of Inflammable Substances for Estimating Vulnerable Zones in Hydrocarbon Industry

The present study utilizes an operational model as well as simple empirical relationships for estimating hazard zones due to fire, explosion, and toxic vapor cloud dispersion. The empirical relationships are based on giving appropriate weightage to each of the parameters on which the hazard in question (viz, fire, explosion, toxic vapour dispersion) is dependent. Results from these two approaches [i.e., an operational model FLAMCALC of U.K. Health and Safety Executive (HSE) and an empirical model named FIREX] have been compared with the data obtained from the Mexico City disaster in 1984. In general, results from the empirical approach and FLAMCALC are comparable to the observed effects.     

Estimation of Vulnerable Zones Due to Accidental Release of Toxic Materials Resulting in Dense Gas Clouds

Heavy gas dispersion models have been developed at IIT (hereinafter referred as IIT heavy gas models I and II) with a view to estimate vulnerable zones due to accidental (both instantaneous and continuous, respectively) release of dense toxic material in the atmosphere. The results obtained from IIT heavy gas models have been compared with those obtained from the DEGADIS model [Dense Gas Dispersion Model, developed by Havens and Spicer (1985) for the U.S. Coast Guard] as well as with the observed data collected during the Burro Series, Maplin Sands, and Thorney Island field trials. Both of these models include relevant features of dense gas dispersion, viz., gravity slumping, air entrainment, cloud heating, and transition to the passive phase, etc. The DEGADIS model has been considered for comparing the performance of IIT heavy gas models in this study because it incorporates most of the physical processes of dense gas dispersion in an elaborate manner, and has also been satisfactorily tested against field observations. The predictions from IIT heavy gas models indicate a fairly similar trend to the observed values from Thorney Island, Burro Series, and Maplin experiments with a tendency toward overprediction. There is a good agreement between the prediction of IIT Heavy Gas models I and II with those from DEGADIS, except for the simulations of IIT heavy gas model-I pertaining to very large release quantities under highly stable atmospheric conditions. In summary, the performance of IIT heavy gas models have been found to be reasonably good both with respect to the limited field data available and various simulations (selected on the basis of relevant storages in the industries and prevalent meteorological conditions performed with DEGADIS). However, there is a scope of improvement in the IIT heavy gas models (viz., better formulation for entrainment, modification of coefficients, transition criteria, etc.). Further, isotons (nomograms) have been prepared by using IIT heavy gas models for chlorine, which provide safe distance for various storage amounts for 24 meteorological scenarios prevalent in the entire year. These nomograms are prepared such that a nonspecialist can use them easily for control and management in case of an emergency requiring the evacuation of people in the affected region. These results can also be useful for siting and limiting the storage quantities.