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Search Results: 1 - 10 of 1728 matches for " Vidyadhar Kulkarni "
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Structural Properties of Optimal Scheduling Policies for Wireless Data Transmission  [PDF]
Nomesh Bolia, Vidyadhar Kulkarni
Int'l J. of Communications, Network and System Sciences (IJCNS) , 2012, DOI: 10.4236/ijcns.2012.510069
Abstract: We analyze a cell with a fixed number of users in a time period network. The base station schedules to serve at most one user in a given time period based on information about the available data rates and other parameter(s) for all the users in the cell. We consider infinitely backlogged queues and model the system as a Markov Decision Process (MDP) and prove the monotonicity of the optimal policy with respect to the \"starvation age\" and the available data rate. For this, we consider both the discounted as well as the long-run average criterion. The proofs of the monotonicity properties serve as good illustrations of analyzing MDPs with respect to their optimal solutions.
Introduction to matrix analytic methods in stochastic modeling, by G. Latouche and V. Ramaswamy
Vidyadhar G. Kulkarni
International Journal of Stochastic Analysis , 1999, DOI: 10.1155/s1048953399000362
Diffusion Models for Double-ended Queues with Renewal Arrival Processes
Xin Liu,Qi Gong,Vidyadhar G. Kulkarni
Mathematics , 2014,
Abstract: We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits.
A Stochastic Model of Order Book Dynamics using Bouncing Geometric Brownian Motions
Xin Liu,Qi Gong,Vidyadhar G. Kulkarni
Quantitative Finance , 2015,
Abstract: We consider a limit order book, where buyers and sellers register to trade a security at specific prices. The largest price the buyers on the book are willing to pay to buy the security is called the market bid price, and the smallest price the sellers on the book are willing to receive to sell the security is called the market ask price. Market ask price is always greater than the market bid price, and these prices move upwards and downwards due to new arrivals, market trades, and cancellations. When the two prices become equal, a trade occurs, and immediately after the trade, these prices bounce back, that is, the market bid price decreases and the market ask price increases. We model these two price processes as ``bouncing geometric Brownian motions (GBM)'': that is, the price processes evolve according to two independent GBMs between trading times. We show that, under this model, the inter-trading times follow an inverse Gaussian distribution, and the logarithmic returns between consecutive trading times follow a normal inverse Gaussian distribution. We show that the logarithmic trading price process is a renewal reward process, and that, under a suitable scaling, this renewal reward process converges to a standard Brownian motion. Finally, we develop a GBM asymptotic model for trading prices, and derive a simple and effective prediction formula. We illustrate the effectiveness of the prediction methods with an example using real stock price data.
The snowball effect of customer slowdown in critical many-server systems
Jori Selen,Ivo Adan,Vidyadhar Kulkarni,Johan van Leeuwaarden
Mathematics , 2015,
Abstract: Customer slowdown describes the phenomenon that a customer's service requirement increases with experienced delay. In healthcare settings, there is substantial empirical evidence for slowdown, particularly when a patient's delay exceeds a certain threshold. For such threshold slowdown situations, we design and analyze a many-server system that leads to a two-dimensional Markov process. Analysis of this system leads to insights into the potentially detrimental effects of slowdown, especially in heavy-traffic conditions. We quantify the consequences of underprovisioning due to neglecting slowdown, demonstrate the presence of a subtle bistable system behavior, and discuss in detail the snowball effect: A delayed customer has an increased service requirement, causing longer delays for other customers, who in turn due to slowdown might require longer service times.
Golden Research Thoughts , 2013, DOI: 10.9780/22315063
Abstract: There is gender inequality in education, health, nutrition, etc. The present paper focused on the female inequality in higher education. The statistics related to the enrolment of male and female students at different higher education courses are analyzed. It has found that there is marginal disparity between higher education of males and females. Hence, it is suggested to provide scholarships and fellowships to the female students, so as to get higher education
Golden Research Thoughts , 2013, DOI: 10.9780/22315063
Abstract: The Self-Help Groups are formed for the socio-economic empowerment of rural women. The government, NGOs and Banks are encouraging rural women to form Self-Help Groups by social welfare schemes and financial incentives. As such, financial progress of the Self-Help Groups is successful as revealed by the national level statistics. The paper provided statistics of the Self-Help Groups including self-employment, income generating activities, bank linkage, etc in different states.
Eruptive syringoma
Sardesai Vidyadhar,Gharpuray Mohan
Indian Journal of Dermatology, Venereology and Leprology , 1998,
Blind Non-parametric Statistics for Multichannel Detection Based on Statistical Covariances
Vidyadhar Upadhya,Devendra Jalihal
Mathematics , 2013,
Abstract: We consider the problem of detecting the presence of a spatially correlated multichannel signal corrupted by additive Gaussian noise (i.i.d across sensors). No prior knowledge is assumed about the system parameters such as the noise variance, number of sources and correlation among signals. It is well known that the GLRT statistics for this composite hypothesis testing problem are asymptotically optimal and sensitive to variation in system model or its parameter. To address these shortcomings we present a few non-parametric statistics which are functions of the elements of Bartlett decomposed sample covariance matrix. They are designed such that the detection performance is immune to the uncertainty in the knowledge of noise variance. The analysis presented verifies the invariability of threshold value and identifies a few specific scenarios where the proposed statistics have better performance compared to GLRT statistics. The sensitivity of the statistic to correlation among streams, number of sources and sample size at low signal to noise ratio are discussed.
On a Brownian motion with a hard membrane
Vidyadhar Mandrekar,Andrey Pilipenko
Mathematics , 2015,
Abstract: Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then changes a sign and behaves as a reflected Brownian motion on the negative half line until some stopping time, etc.
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