This paper analyzes renewal input state dependent queue with $N$- policy wherein the server takes exactly one vacation. Using the supplementary variable technique and recursive method, we derive the steady state system length distributions at various epochs. Various performance measures has been presented. Finally, some numerical  computations in the form of graphs are presented to show the par...

This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system len...

A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. Some performance measures are calculated. Some ...

This is an example of an observational study involving two variables of primary interest and several supplementary variables; these supplementary variables are ones that might affect the response variable and might also be correlated with the explanatory variable. The intent of the statistical analysis therefore is to produce the best possible description of the relationship between the two int...

Abstract: In this paper, we consider a single-server infinite(finite-) buffer bulk-service queues. The interarrival and service times are respectively, arbitrarily and exponentially distributed. The customers are served by a single server in accessible or non-accessible batches of maximum size ‘ b ’ with a minimum threshold value ‘ ’. We provide a recursive method, using the supplementary varia...

This paper considers the problem of estimating causal effects of a treatment on a response using supplementary variables. Under the assumption that a treatment is associated with a response through a univariate supplementary variable in the framework of linear regression models, Cox (1960) showed that the estimation accuracy of the regression coefficient of the treatment on the response in the ...

In the main paper, we have proposed a new representation for image shape: a dictionary of shape epitomes, which explicitly include hidden variables to encode shift and rotation. We have also applied this representation for semantic image labeling. In this supplementary material, we further show the versatility of shape epitomes by employing them for edge detection and local appearance modeling.

UNLABELLED The deluge of data emerging from high-throughput sequencing technologies poses large analytical challenges when testing for association to disease. We introduce a scalable framework for variable selection, implemented in C++ and OpenCL, that fits regularized regression across multiple Graphics Processing Units. Open source code and documentation can be found at a Google Code reposito...