We consider an $M^x/G/1$ queueing system with Bernoulli vacation schedule under multiple vacation policy. where after each vacation completion or service completion the server takes sequence of vacations until a batch of new customer arrive. This generalizes both $M^x/G/1$ queueing system with multiple vacation as well as M/G/1 Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further attempts have been made to unify the results of related batch arrival vacation models.

We use the hierarchical Bayesian approach to describe the transition probabilities of a binary nonhomogeneous Markov chain. The Markov chain is used for describing the transition behavior of emotionally disturbed children in a treatment program. The effects of covariates on transition probabilities are assessed using a logit link function. To describe the time evolution of transition probabilities, we consider two modeling strategies. The first strategy is based on the concept of exchangeabiligy, whereas the second one is based on a first order Markov property. The deviance information criterion (DIC) measure is used to compare models with two different time dependent structures. The inferences are made using the Markov chain Monte Carlo technique. The developed methodology is applied to some real data.

This paper considers the problem of designing logical tunnels in virtual private networks considering QoS guarantee which restricts the number of tunnel hops for each traffic routing. The previous researches focused on the design of logical tunnel itself and Steiner-tree based solution algorithms were proposed. However, we show that for some objective settings it is not sufficient and is necessary to consider both physical and logical connectivity at the same time. Thereupon, the concept of the layered network is applied to the logical tunnel design problem in virtual private networks. The layered network approach considers the design of logical tunnel as well as its physical routing and we propose a modified branch-and-price algorithm which is known to solve layered network design problems effectively. To show the performance of the proposed algorithm, computational experiments have been done and the results show that the proposed algorithm solves the given problem efficiently and effectively.

To generate a multicast routing tree guaranteeing the quality of service (QoS), we consider the hop constrained Steiner tree problem and propose a new mathematical formulation for it, which contains fewer constraints than a known formulation. An efficient procedure is also proposed to solve the problem. Preliminary tests show that the procedure reduces the computing time significantly.

Collaborative filtering, among other recommender systems, has been known as the most successful recommendation technique. However, it requires the user-item rating data, which may not be easily available. As an alternative, some collaborative filtering algorithms have been developed recently by utilizing the market basket data in the form of the binary user-item matrix. Viewing the recommendation scheme as a two-class classification problem, we proposed a new collaborative filtering scheme using a regularized discriminant analysis applied to the binary user-item data. The proposed discriminant model was built in terms of the major principal components and was used for predicting the probability of purchasing a particular item by an active user. The proposed scheme was illustrated with two modified real data sets and its performance was compared with the existing user-based approach in terms of the recommendation precision.

In a hierarchical road network, all roads can be classified according to their attributes such as speed limit, number of lanes, etc. By splitting the whole road network into the subnetworks of the highlevel and low-level roads, we can reduce the size of the network to be calculated at once, and find a path in the way that drivers usually adopt when searching out a travel route. To exploit the hierarchical property of road networks, we define a convenient path and propose an algorithm for finding convenient paths. We introduce a parameter indicating the driver's tolerance to the difference between the length of a convenient path and that of a shortest convenient path. From this parameter, we can determine how far we have to search for the entering and exiting gateway. We also propose some techniques for reducing the number of pairs of entries and exits to be searched in a road network. A result of the computational experiment on a real road network is given to show the efficiency of the proposed algorithm.