Search results for: R. Reynald Susainathan

Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

Abstract:

In this paper we study that the catastrophic events arrive independently at the service facility according to a Poisson process with rate λ. The nature of a catastrophic event is that upon its arrival at a service station, it destroys all the customers there waiting and in the service. We will derive the net profit associated with queuing system and obtain its probability of the busy period.

Keywords: queueing system, net-profit, busy period, catastrophical events

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

Abstract:

We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: stochastic integrals, single–server queue model, catastrophes, busy period

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Authors: Reni M. Sagayaraj, Anand Gnana S. Selvam, Reynald R. Susainathan

Abstract:

In this paper, we consider stochastic queueing models for Steady-state behavior of a multi-phase M/M/1 queue in random evolution subject to catastrophe failure. The arrival flow of customers is described by a marked Markovian arrival process. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. This model contains a repair state, when a catastrophe occurs the system is transferred to the failure state. The paper focuses on the steady-state equation, and observes that, the steady-state behavior of the underlying queueing model along with the average queue size is analyzed.

Keywords: M/G/1 queuing system, multi-phase, random evolution, steady-state equation, catastrophe failure

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

Abstract:

This study analyzed a queueing system with blocking and no waiting line. The customers arrive according to a Poisson process and the service times follow exponential distribution. There are two non-identical servers in the system. The queue discipline is FCFS, and the customers select the servers on fastest server first (FSF) basis. The service times are exponentially distributed with parameters μ1 and μ2 at servers I and II, respectively. Besides, the catastrophes occur in a Poisson manner with rate γ in the system. When server I is busy or blocked, the customer who arrives in the system leaves the system without being served. Such customers are called lost customers. The probability of losing a customer was computed for the system. The explicit time dependent probabilities of system size are obtained and a numerical example is presented in order to show the managerial insights of the model. Finally, the probability that arriving customer finds system busy and average number of server busy in steady state are obtained numerically.

Keywords: queueing system, blocking, poisson process, heterogeneous servers, queue discipline FCFS, busy period

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Authors: Reynald Contreras, Shaina Marie Bho, Kate Roan Dela Cruz, Marvin Dela Cruz

Abstract:

This study was conducted with the aim of determining the skill level of grade ten (Grade 10) students in writing a reflective essay in selected secondary schools of Valenzuela. This research used descriptive and qualitative-quantitative research methods to systematically and accurately describe the level of writing skills of students and used a convenient sampling technique in selecting forty (40) students in grade ten. (Grade 10) at Polo, Wawang Pulo, and Arkong Batong high schools with a total of one hundred and twenty (120) students to assess the written reflective essay using modified rubrics developed based on 6+1 writing traits by Ruth Culham. According to the findings of the study, students at Polo and Wawang Pulo National high schools have low levels of writing skills that need to be developed or are not proficient. Meanwhile, Arkong Bato National High School has achieved a high degree of writing proficiency. Based on the study's findings, the researchers devised a suggested curriculum mapping for the suggested activity or intervention activity that would aid in the development and cultivation of the writing skills of children in grade ten (Grade 10).

Keywords: writing skills, reflective essay, intervention activity, 6+1 writing traits, modified rubrics

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