20150701
Analysis of Markovmodulated infiniteserver queues in the centrallimit regime
Publication
Publication
Probability in the Engineering and Informational Sciences , Volume 29  Issue 3 p. 433 459
This paper focuses on an infiniteserver queue modulated by an independently evolving finitestate Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. {Both arrival rates and service rates are depending on the state of the background process.} The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time $t\ge 0$, in the asymptotic regime in which the arrival rates $\lambda_i$ are scaled by a factor $N$, and the transition rates $q_{ij}$ by a factor $N^\alpha$, with $\alpha \in \mathbb R^+$. The specific value of $\alpha$ has a crucial impact on the result: (i)~for $\alpha>1$ the system essentially behaves as an M/M/$\infty$ queue, and in the central limit theorem the centered process has to be normalized by $\sqrt{N}$; (ii)~for $\alpha<1$, the centered process has to be normalized by $N^{{1}\alpha/2}$, with the deviation matrix appearing in the expression for the variance.
Additional Metadata  

Life Sciences (theme 5)  
Cambridge U.P.  
Probability in the Engineering and Informational Sciences  
Organisation  Life Sciences and Health 
Blom, J.G, de Turck, K, & Mandjes, M.R.H. (2015). Analysis of Markovmodulated infiniteserver queues in the centrallimit regime. Probability in the Engineering and Informational Sciences, 29(3), 433–459.
