A Lévy input model with additional state-dependent services

Abstract

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers $\{e_q^{(i)}{\}}_{i=1,2,...}$ according to a spectrally positive Lévy process $Y(t)$ which is reflected at 0. When the exponential clock $e_q^{(i)}$ ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to $F_i(Y(e_q^{(i)}))$ at epoch $e_q^{(1)}+...+e_q^{(i)}$ 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.

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• Ruin Probabilities and Overshoots for General Levy Insurance Risk Processes
• On queues with service and interarrival times depending on waiting times
• A non-increasing Lindley-type equation
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Cited by in corpus (3)

• An M/M/c queue with queueing-time dependent service rates
• A Lévy input fluid queue with input and workload regulation
• On Future Drawdowns of Lévy processes