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Queueing systems with batch Markovian arrival process (BMAP) have paramount applications in the domain of wireless communication. The BMAP has been used to model the superposition of video sources and to approximate the super-position of data, voice and video traffic. This article analyzes an infinite-buffer generally distributed batch-service queue with BMAP, general bulk service (a, b) rule and batch-size-dependent service time. In this proposed analysis, we mainly focus on deriving the bivariate vector generating function of queue and server content distribution together at departure epoch using supplementary variable technique. The mathematical procedure for the complete extraction of distribution at departure epoch has been discussed and using those extracted probabilities, we achieve the queue and server content distribution at arbitrary epoch. Finally, numerical illustrations have been carried out in order to make a deep insight to the readers which contains deterministic as well as phase-type service time distributions. [ABSTRACT FROM AUTHOR]

Background: The demands on Medical Education have greatly increased in the 21st century. For this very reason, there has been an unprecedented growth in the number of medical colleges in India. The teacher’s role is to facilitate rather than to direct, to coordinate as much as to communicate. Small group teaching offers students’ opportunity to discuss and refine their understanding of complex issues, to problem solve and apply their knowledge to new situations and to reflect on their attitudes and feelings. The study aims to assess the perception of undergraduate medical students regarding small group teaching, the perception of faculty regarding Small group teaching, compare the perception of students on small group teaching, with respect to their academic performance and attendance. Methodology: 93 faculty and 499 undergraduate MBBS students participated in the study and were given a self- administered semi-structured questionnaire. The perception of undergraduate students and teaching faculty on small group teaching was assessed using the 5-point Likert Scale. Independent t-test was applied to find difference in mean perception. Students were categorized based on their academic performance and on their attendance aggregate for the concluded semester. Results: In total, 404 students and 45 faculty members responded thus giving response rates of 80.9% and 48.4% respectively. The overall response rate was 75.8% Conclusion: The study found that both students and faculty members are favorable to the concept of SGT. They found it not only enhances the academic performance of students but also contributes to the personality development of students. Clinical correlations in all the subjects is well appreciated by students and faculty. Suggestions for improvement of SGT such as exam-oriented study, use of innovative and interactive aids can make SGT sessions more effective.

We consider a population model in which individuals arrive as per the batch Markovian arrival process. The population is influenced by catastrophes which occur according to Markovian arrival process and it eliminates each individual of the population in a sequential order with probability p until the one individual survives or the entire population is annihilated. We first obtain the steady-state vector generating function of the population size distribution at arbitrary epoch and then the distribution is extracted in term of roots of the associated characteristic equation. Further, we obtain the population size distribution at post-catastrophe and pre-arrival epochs. Finally, a few numerical results are given. [ABSTRACT FROM AUTHOR]