Climatology of dry and wet spell over Vidarbha region during monsoon months

In this investigation 10-day period-wise simple probability, 10-day period-wise probability of consecutive dry and wet spells of different lengths, and month-wise different parameters, and properties of Markov Chain Model over Vidarbha region during south-west monsoon months have been studied. For this purpose, daily rainfall data (1 June – 30 September) of 11 stations covering all the districts of Vidarbha for the period 1960-90 have been utilized. The study reveals that over Vidarbha during monsoon season (June - September) probability of a day being wet and probability of consecutive wet spell of different lengths are by and large high during the last and first 10-day periods of July and August respectively when the monsoon is at its peak. During the first two 10-day periods in June and last two 10-day periods in September, the probabilities of a dry day and that of consecutive dry spell of different lengths and quite high. During July and August a maximum of 12-14 wet days are expected and wet spell, on an average, lasts for 2 days. Stationary probability of the occurrence of wet day (pi2) is found to be maximum during July making it the most humid month in the monsoon season.

Statistical Mechanics of Unconfined Systems: Challenges and Lessons

Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space of an unconfined ideal gas in an anti-de Sitter background. Notwithstanding the gas’ freedom to move in an infinite volume, we establish necessary conditions for the stationary probability distribution solving a general maximum entropy problem to be normalizable and obtain the resulting probability for a particular choice of constraints. As a part of our analysis, we develop a novel method for identifying dynamical constraints based on local measurements. With no appeal to a priori information about globally defined conserved quantities, it is therefore applicable to a much wider range of problems.

Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the system is called an impulse customer. Suppose the customer enters into the system to buy the product with a plan is called ordinary customer. The system consists of a pool of finite waiting areas of size N and maximum S items in the inventory. The ordinary customer can move to the pooled place if they find that the inventory is empty under the Bernoulli schedule. In such a situation, impulse customers are not allowed to enter into the pooled place. Additionally, the pooled customers buy the product whenever they find positive inventory. If the inventory level falls to s, the replenishment of Q items is to be replaced immediately under the (s, Q) ordering principle. Both arrival streams occur according to the independent Markovian arrival process (MAP), and lead time follows an exponential distribution. In addition, the system allows the cancellation of the purchased item only when there exist fewer than S items in the inventory. Here, the time between two successive cancellations of the purchased item is assumed to be exponentially distributed. The Gaver algorithm is used to obtain the stationary probability vector of the system in the steady-state. Further, the necessary numerical interpretations are investigated to enhance the proposed model.

Quasi-stationary probability distribution for the SIR epidemic model

In this paper, we propose two new approximations to the joint quasi-stationary distribution (QSD) of the number susceptible and infected individuals in the Susceptible-Infected-Recovered (SIR) stochastic epidemic model and we derive the marginal QSD of the infected individuals. These two approximations depend on the basic reproduction number [Formula: see text] and give a positive probability of the QSD to all the transient states. Numerical comparisons are presented to check the accuracy of these approximations.

Analysis of M/G/1 Feedback Queue under Steady State When Catastrophes Occur

In this paper we analyse the M/G/1 feedback queue under steady states conditionswhen catastrophe occur. The stationary probability of ‘n’ and zero customers sins the system are derived. The asymptotic behaviour of the model and the averages queues lengthare also obtained. The numerical example are provided to test the feasibility of the model.

Non-Maxwellian distribution in linear systems and its applications

Bimodality is a typical behavior of bistable nonlinear stochastic differential equations. In this work, we find an exact result for calculating the dynamical and stationary probability distribution function in a simple linear system driven by an asymmetric Markovian dichotomous noise. The results show that asymmetric dichotomous noise leads to a unimodal-bimodal distribution transition, exhibiting eight different non-Maxwellian stationary probability distribution profiles in the parameter space. The noise-induced transitions depend on the correlation time, which characterizes the asymmetric dichotomous noise. The calculations are performed using a linear configuration; but applications to other systems governed by nonlinear equations such as single species population growth models are discussed. In the proper limits, the symmetric case, including the Gaussian white noise limit, is recovered. Numerical simulations show good agreement with analytical results. Finally, a possible experimental setup is proposed.