S. P. Mukherjee

Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue

In this article, maximum likelihood estimator (MLE) as well as Bayes estimator of traffic intensity (ρ) in an M/M/1/∞ queueing model in equilibrium based on number of customers present in the queue at successive departure epochs have been worked out. Estimates of some functions of ρ which provide measures of effectiveness of the queue have also been derived. A comprehensive simulation study starting with the transition probability matrix has been carried out in the last section.

Stochastic dominance of higher orders and its implications

Higher order stochastic dominance has been considered from a reliability theoretic point of view and related to moment inequalities among life distributions. A generalization of HNBUE/ HNWUE class of distributions has been conceived and its relationship with higher order stochastic dominance has been studied.

Bayes estimation in M/M/1 queues with bivariate prior

Abstract Bayes estimator of different queueing performance measures are derived in steady state by recording system size from each of n iid M/M/1 queues. The Bayes estimators are obtained under both squared error loss function and precautionary loss function with a bivariate distribution beta stacy as prior, with natural restriction 0 < λ < µ where λ and µ are arrival rate and service rate respectively. A comprehensive simulation results are also shown at the last section.

Bayes Estimation of Measures of Effectiveness in an M/M/1 Queueing Model

Abtsrcat In this paper, Bayes estimators of trafic intensity (ρ) and other measures of effectiveness are worked out under squared error loss function (SELF) and entropy loss function (ELF) with Beta distribution as prior. Number of customers present in each of n iid M/M/1 queueing systems are considered as data. A comprehensive simulation study has been carried out in the last section.

Measurement of occupational mobility using semi-markov models

As proposed by Bartholomew (1967), occupational mobility should better be represented by semi-Markov processes. In the present paper attempts have been made to develop some new measures of occupational mobility in terms of serai-Markov processes and their values have been studied in the three extreme situations of interest.

Closure under Convolution of Dominance Relations

The closure of likelihood ratio (LR), failure rate (FR) and mean remaining life (MRL) orderings under convolution of distributions have been established in a restricted set up.

Estimation of Weibull Parameters Using Fractional Moments

For a two-parameter Weibull distribution, moment estimators of the parameters have been developed by choosing orders of two moments (allowing fractions) so that the overall relative efficiency of the moment estimators compared with the maximum likelihood estimators is maximized . Some calculations in support of the superiority of fractional moments over integer moments in this connection have also been presented.

An Inventory Problem Revisited

In this paper, we propose a new solution to a point demand inventory problem that minimises the mode of the distribution of total cost, Some analytic results are given for the case of gamma and beta distributed demand.

Ridge estimation of restricted parameters in production techniques

The problem of determining ridge estimates of the regression parameters in a two-input production function model,constrained to be non-negative,has been formulated as an exercise in quadratic programming. Relevant Kuhn-Tucker conditions have been derived and a small simulation studv has been carried out.

Static Inventory Model with Unknown Proportion of Defectives in the Supplied Lot

A static inventory model where lots received (against orders) are accepted through a curtailed single sampling inspection plan has been considered. Since the proportion of non-defective units in a lot is not likely to be known in advance, a probability Jaw has been assumed for the same. The optimal order quantity has been obtained by maximizing the expected net profit, taking into account selling price, purchase cost, carrying cost, shortage cost, salvage cost and inspcctioo cost.