ANALYSIS OF MARKOV-MODULATED INFINITE-SERVER QUEUES IN THE CENTRAL-LIMIT REGIME

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix Q = (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 (CLTs) for the number of customers in the system at time t >= 0, in the asymptotic regime in which the arrival rates lambda(i) are scaled by a factor N, and the transition rates qij by a factor N-alpha, with alpha is an element of 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/infinity queue, and in the CLT the centered process has to be normalized by root N; (ii) for alpha < 1, the centered process has to be normalized by N1-alpha/2, with the deviation matrix appearing in the expression for the variance.