2018/10/16 by Landy Rabehasaina, Rabehasaina, Landy
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #Probability and Risk Models #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.1810.06894
We study a general k dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index α∈ (0,1). When the arrival rate is sped up by a factor nγ, the transition probabilities of the underlying Markov chain are divided by nγ and the service times are divided by n, we identify two regimes (''fast arrivals'', when γ>α, and ''equilibrium'', when γ=α) in which we prove that a properly rescaled process converges pointwise in distribution to some limiting process. In a third ''slow arrivals'' regime, γ