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Chowdhury S.,Army Institute of Management | Mukherjee S.P.,University of Calcutta
OPSEARCH | Year: 2011

Estimation of waiting time distribution in the form of its right tail area, known as exceedance probability is carried out in an M/M/1/FCFS/∞/∞ queue with the help of data consists of non zero waiting time of randomly chosen customer from n independent queues and number of queues with zero waiting time. In the first section, MLE of rate parameters and exceedance probability are obtained and their large sample behaviour is studied. Next section, Bayes estimators of the same parametric function along with the minimum Bayes risks have been derived under squared error loss using McKay's Bivariate Gamma as prior and also independent Gamma as prior with the prior for arrival rate being truncated between 0 and μ. Some numerical calculations are shown in the last section. © Operational Research Society of India 2011. Source

Banerjee S.,Polytechnic University of Turin | Mukhopadhyay S.,Army Institute of Management
Communications in Computer and Information Science | Year: 2011

The Optical chaotic systems, with infinite dimensionality, have gained a lot of attention for communication and cryptographic purposes. The semiconductor devices act as a cryptosystem with high bandwidth. We explore the synchronization phenomenon between two spatio-temporal chaotic semi conductor lasers with bi-directional coupling. The coupling facilitates two way simultaneous communication. The ease of modular implementation of optical feedback together with the randomness and ergodic properties of the infinite dimensional systems produces completely randomized chaotic time series. Such a system is an ideal candidate for cryptographic purposes of large streams of data such as a digital image. The system renders enough confusion and diffusion properties to the transmitted gray scaled image rendering the statistically disordered cipher image totally incoherent from the original message. Simulation result and statistical tests demonstrate the merit of the system in achieving robust and secure cryptography with deterministic chaos aiding in the correct recovery of the encoded image. © Springer-Verlag 2011. Source

Banerjee S.,Polytechnic University of Turin | Rondoni L.,Polytechnic University of Turin | Rondoni L.,National Institute of Nuclear Physics, Italy | Mukhopadhyay S.,Army Institute of Management
Optics Communications | Year: 2011

This work aims to demonstrate the effect of synchronization phenomena in chaotic laser systems described by modified Lang-Kobayashi's (L-K) delay differential equations. The synchronized system considered for numerical simulations and for cryptography consists of identical semiconductor lasers operating in single longitudinal mode. The two lasers are bidirectionally coupled by linear optical feedback. As this is essential in simultaneous transmission of messages, we have applied the corresponding coupled chaotic dynamics to secure communications. An investigation of the system together with a novel scheme for digital cryptography and visual recurrence analysis (VRA) of the chaotic time series are presented. Extended statistical tests with the proposed two phase scheme demonstrate the efficiency of these infinite dimensional systems in being tolerant to different types of statistical attacks. The result emphasizes the merits of the uncertainty and high dimensionality of optical chaos system in duplex high speed secure communications. © 2011 Elsevier B.V. Source

Guhathakurta K.,Army Institute of Management | Bhattacharya B.,Jadavpur University | Chowdhury A.R.,Jadavpur University
Physica A: Statistical Mechanics and its Applications | Year: 2010

Recurrence Plots are graphical tools based on Phase Space Reconstruction. Recurrence Quantification Analysis (RQA) is a statistical quantification of RPs. RP and RQA are good at working with non-stationarity and noisy data, in detecting changes in data behavior, in particular in detecting breaks, like a phase transition and in informing about other dynamic properties of a time series. Endogenous Stock Market Crashes have been modeled as phase changes in recent times. Motivated by this, we have used RP and RQA techniques for detecting critical regimes preceding an endogenous crash seen as a phase transition and hence give an estimation of the initial bubble time. We have used a new method for computing RQA measures with confidence intervals. We have also used the techniques on a known exogenous crash to see if the RP reveals a different story or not. The analysis is made on Nifty, Hong Kong AOI and Dow Jones Industrial Average, taken over a time span of about 3 years for the endogenous crashes. Then the RPs of all time series have been observed, compared and discussed. All the time series have been first transformed into the classical momentum divided by the maximum Xmax of the time series over the time window which is considered in the specific analysis. RPs have been plotted for each time series, and RQA variables have been computed on different epochs. Our studies reveal that, in the case of an endogenous crash, we have been able to identify the bubble, while in the case of exogenous crashes the plots do not show any such pattern, thus helping us in identifying such crashes. © 2010 Elsevier B.V. All rights reserved. Source

Chowdhury S.,Army Institute of Management | Mukherjee A.,Indian Institute of Technology Madras | Chakraborti S.,University of Alabama
Quality and Reliability Engineering International | Year: 2014

While the assumption of normality is required for the validity of most of the available control charts for joint monitoring of unknown location and scale parameters, we propose and study a distribution-free Shewhart-type chart based on the Cucconi statistic, called the Shewhart-Cucconi (SC) chart. We also propose a follow-up diagnostic procedure useful to determine the type of shift the process may have undergone when the chart signals an out-of-control process. Control limits for the SC chart are tabulated for some typical nominal in-control (IC) average run length (ARL) values; a large sample approximation to the control limit is provided which can be useful in practice. Performance of the SC chart is examined in a simulation study on the basis of the ARL, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparisons with a competing distribution-free chart, known as the Shewhart-Lepage chart (see Mukherjee and Chakraborti) show that the SC chart performs just as well or better. The effect of estimation of parameters on the IC performance of the SC chart is studied by examining the influence of the size of the reference (Phase-I) sample. A numerical example is given for illustration. Summary and conclusions are offered. Copyright © 2013 John Wiley & Sons, Ltd. Source

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