Two stage \(\mathrm{M}^{[x]}/\mathrm{G}/1\) heterogeneous service, Bernoulli feed back, Bernoulli schedule server vacation random break down, setup time and restricted admissibility
type: Item
instance of: scholarly article
zbMATH Open document ID: 1314.60149
publication date: 2014-11-10T00:00:00Z
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K30
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 6367638
zbMATH Keywords: unreliable single server
zbMATH Keywords: Batch-Poisson arrivals
zbMATH Keywords: two stage services
zbMATH Keywords: Bernoulli feedback
zbMATH Keywords: Bernoulli vacation
zbMATH Keywords: restricted admissibility
zbMATH Keywords: steady state
zbMATH Keywords: transient analysis
zbMATH Keywords: transform methods
MaRDI profile type: Publication
author: G. Ayyappan
author: S. Shyamala
title: Two stage \(\mathrm{M}^{[x]}/\mathrm{G}/1\) heterogeneous service, Bernoulli feed back, Bernoulli schedule server vacation random break down, setup time and restricted admissibility
published in: Mathematical Sciences Research Journal
review text: An unreliable single server is investigated with Batch-Poisson arrivals, 2-stage services with general service time, Bernoulli feedback, and Bernoulli vacations after a customer's second stage of service is finished. The server's up-times and the repair times after breakdown are exponential. Admission of batches is regulated by a Bernoulli decision where the admission probability depends on whether the server is at vacation or not. A Markovian state description is constructed and, starting with an empty system, the transient state probabilities are derived in a complicated transform version. Assuming steady state conditions, transform expressions are given for the stationary distribution and some performance metrics are derived.
reviewed by: Hans Daduna
description: scientific article; zbMATH DE number 6367638