TY - JOUR
T1 - A Lévy input model with additional state-dependent services
AU - Palmowski, Z.B.
AU - Vlasiou, M.
PY - 2011
Y1 - 2011
N2 - We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers $\{e^{(i)}_q\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y(t)$ which is reflected at 0. When the exponential clock $e^{(i)}_q$ ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to $F_i(Y(e^{(i)}_q))$ at epoch $e^{(1)}_q + ... + e^{(i)}_q$ for some random nonnegative i.i.d. functionals $F_i$. In particular, we focus on the case when $F_i(y)=(B_i - y)^+$, where ${\{B_i\}}_{i=1,2,...}$ are i.i.d. nonnegative random variables. We analyse the steady-state workload distribution for this model.
AB - We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers $\{e^{(i)}_q\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y(t)$ which is reflected at 0. When the exponential clock $e^{(i)}_q$ ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to $F_i(Y(e^{(i)}_q))$ at epoch $e^{(1)}_q + ... + e^{(i)}_q$ for some random nonnegative i.i.d. functionals $F_i$. In particular, we focus on the case when $F_i(y)=(B_i - y)^+$, where ${\{B_i\}}_{i=1,2,...}$ are i.i.d. nonnegative random variables. We analyse the steady-state workload distribution for this model.
U2 - 10.1016/j.spa.2011.03.010
DO - 10.1016/j.spa.2011.03.010
M3 - Article
SN - 0304-4149
VL - 121
SP - 1546
EP - 1564
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 7
ER -