A state-dependent queueing system with asymptotic logarithmic distribution

作者：Giorno V; Nobile A G^*; Pirozzi E

来源：Journal of Mathematical Analysis and Applications, 2018, 458(2): 949-966.

DOI：10.1016/j.jmaa.2017.10.004

• Asymptotic behavior
• Stochastic orderings
• Stein's method
• First-passage time
• Busy period
• Catastrophes

A Markovian single-server queueing model with Poisson arrivals and state dependent service rates, characterized by a logarithmic steady-state distribution, is considered. The Laplace transforms of the transition probabilities and of the densities of the first-passage time to zero are explicitly evaluated. The performance measures are compared with those ones of the well-known M/M/1 queueing system. Finally, the effect of catastrophes is introduced in the model and the steady-state distribution, the asymptotic moments and the first-visit time density to zero state are determined.

• 出版日期2018-2-15