Name
Abstract | ||
|---|---|---|
In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the model parameters in terms of a functional central limit theorem. More specifically, relying on the martingale central limit theorem, this result is established, covering the situation in which the arrival rates are sped up by a factor $N$ and the transition rates of the background process by $N^\alpha$, for some $\alpha>0$. The results reveal an interesting dichotomy, with crucially different behavior for $\alpha>1$ and $\alpha<1$, respectively. The limiting Gaussian process, which is of the Ornstein-Uhlenbeck type, is explicitly identified, and it is shown to be in accordance with explicit results on the mean, variances and covariances of the number of jobs in the system. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s00186-016-0531-7 | Math. Meth. of OR |
Keywords | Field | DocType |
Queues,Infinite-server systems,Markov modulation,Central limit theorems | Discrete mathematics,Mathematical optimization,Central limit theorem,Markov chain,Martingale central limit theorem,Queue,Background process,Gaussian process,Asymptotic analysis,Scaling,Mathematics | Journal |
Volume | Issue | ISSN |
83 | 3 | 1432-2994 |
Citations | PageRank | References |
2 | 0.51 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joke G Blom | 1 | 161 | 23.43 |
| Koen De Turck | 2 | 98 | 19.83 |
| Michel Mandjes | 3 | 534 | 73.65 |