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On the joint distribution of tax payments and capital injections for a Lévy risk model

Albrecher H., Ivanovs J.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 2

219--227

We study the joint distribution of tax payments according to a loss-carry-forward scheme and capital injections in a Lévy risk model, and provide a transparent expression for the corresponding transform in terms of the scale function. This allows us to identify the net present value of capital injections in such a model, complementing the one for tax found in our paper [3]. We also apply the result to the situation when injections may be stopped at a constant rate, and in this case an explicit formula for the net present value of taxes and injections is given.

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Tikhonenko O., Kempa W. M.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 4

841--854

A queueing system of the M/G/n-type, n ≥ 1, with a bounded total volume is considered. It is assumed that the volumes of the arriving packets are generally distributed random variables. Moreover, the AQM-type mechanism is used to control the actual buffer state: each of the arriving packets is dropped with a probability depending on its volume and the occupied volume of the system at the pre-arrival epoch. The explicit formulae for the stationary queue-size distribution and the loss probability are found. Numerical examples illustrating theoretical formulae are given as well.