2014-06-01
Tail asymptotics of a Markov-modulated infinite-server queue
Publication
Publication
Queueing Systems
,
Volume 78
-
Issue 4
p. 337-
357
This paper analyzes large deviation probabilities related to the number of customers in a Markov modulated infinite-server queue, with state-dependent arrival and service rates. Two specific scalings are studied: in the first, just the arrival rates are linearly scaled by $N$ (for large $N$), whereas in the second in addition the Markovian background process is sped up by a factor $N^{1+\epsilon}$, for some $\epsilon>0$. In both regimes, (transient and stationary) tail probabilities decay essentially exponentially, where the associated decay rate corresponds to that of the probability that the sample mean of i.i.d.\ Poisson random variables attains an atypical value.
| Additional Metadata | |
|---|---|
| Keywords | Queues, infinite-server systems, Markov modulation, large deviations |
| MSC | Queueing theory (msc 60K25) |
| THEME | Life Sciences (theme 5) |
| Publisher | Springer |
| Persistent URL | dx.doi.org/10.1007/s11134-014-9412-z |
| Journal | Queueing Systems |
| Project | Coarse grained stochastic methods for biochemical reactions |
| Citation |
Blom, J.G, de Turck, K, Kella, O, & Mandjes, M.R.H. (2014). Tail asymptotics of a Markov-modulated infinite-server queue. Queueing Systems, 78(4), 337–357. doi:10.1007/s11134-014-9412-z
|
