A queueing/inventory and an insurance risk model
| Autor: | R Rim Essifi, Onno Boxma, Augustus J. E. M. Janssen |
|---|---|
| Přispěvatelé: | Stochastic Operations Research, Mathematics and Computer Science |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Distribution (number theory) M/G/1 queue 90B22 Wiener-Hopf technique 01 natural sciences workload 010104 statistics & probability 47A68 Factorization 60K25 0502 economics and business FOS: Mathematics Applied mathematics ruin probability 0101 mathematics Algebraic number Cramér-Lundberg insurance risk model Mathematics Service (business) Queueing theory 050208 finance Actuarial science Cramér–Lundberg insurance risk model Applied Mathematics Probability (math.PR) 05 social sciences Workload Wiener–Hopf technique inventory 60K25 90B22 91B30 47A68 91B30 Constant (mathematics) Mathematics - Probability |
| Zdroj: | Advances in Applied Probability, 48(4), 1139-1160. University of Sheffield Adv. in Appl. Probab. 48, no. 4 (2016), 1139-1160 |
| ISSN: | 1475-6064 0001-8678 |
| DOI: | 10.1017/apr.2016.68 |
| Popis: | We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted as negative workload. At random times, with an intensity ω(x) when the inventory is at level x>0, the present inventory is removed, instantaneously reducing the inventory to 0. We study the steady-state distribution of the (positive and negative) workload levels for the cases ω(x) is constant and ω(x) = ax. The key tool is the Wiener–Hopf factorization technique. When ω(x) is constant, no specific assumptions will be made on the service requirement distribution. However, in the linear case, we need some algebraic hypotheses concerning the Laplace–Stieltjes transform of the service requirement distribution. Throughout the paper, we also study a closely related model arising from insurance risk theory. |
| Databáze: | OpenAIRE |
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