2008
DOI: 10.1017/s0269964809000084
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q-SERIES IN MARKOV CHAINS WITH BINOMIAL TRANSITIONS

Abstract: We consider a single-server Markovian queue with synchronized services and setup times. The customers arrive according to a Poisson process and are served simultaneously. The service times are independent and exponentially distributed. At a service completion epoch, every customer remains satisfied with probability p (independently of the others) and departs from the system; otherwise, he stays for a new service. Moreover, the server takes multiple vacations whenever the system is empty.Some of the transition … Show more

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Cited by 8 publications
(7 citation statements)
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“…The new feature of these models with synchronization is the existence of binomial type jumps at the abandonment epochs. Similar models with binomial type transitions have been recently studied by Economou (2004), Economou and Kapodistria (2006), Artalejo et al (2007) and Economou and Fakinos (2008).…”
Section: Introductionmentioning
confidence: 73%
“…The new feature of these models with synchronization is the existence of binomial type jumps at the abandonment epochs. Similar models with binomial type transitions have been recently studied by Economou (2004), Economou and Kapodistria (2006), Artalejo et al (2007) and Economou and Fakinos (2008).…”
Section: Introductionmentioning
confidence: 73%
“…Several other papers deal with the equilibrium analysis of birth models subject to binomial catastrophes (see, e.g. [2,5,20,22,23,24,25,38,40] and the references therein).…”
Section: Literature Overview and Motivationmentioning
confidence: 99%
“…In [22], for a different birth model still subject to binomial catastrophes, the authors discuss possible extensions of the existing methods in order to calculate the transient distribution of the system at hand. Several other papers deal with the equilibrium analysis of birth models subject to binomial catastrophes (see, e.g., [2,5,20,[22][23][24][25]38,40] and references therein).…”
Section: Literature Overview and Motivationmentioning
confidence: 99%
“…To the best of our knowledge, the functional equation 14below has never previously appeared in the literature. Yet it is possible to mark some analogies with the functional equation studied by Economou and Kapodistria (2009), Economou et al (2010),or Kapodistria (2011), the most important being that in both equations the right hand side exhibits the generating function computed in a convex combination in the parameter q. Adan et al (2009), Altman and Yechiali (2006), Neuts (1994), and Yechiali (2007) give other examples of chains with binomial transitions.…”
Section: Introductionmentioning
confidence: 99%