Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

2004 ◽  
Vol 41 (4) ◽  
pp. 1145-1156 ◽  
Author(s):  
Parijat Dube ◽  
Fabrice Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Closed Form ◽  
Lévy Processes ◽  
Busy Period ◽  
Exit Time ◽  
Levy Processes ◽  
Finite Capacity ◽  
Scale Functions ◽  
Period Distribution ◽  
Finite Capacity Queues ◽  
Time Theory

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

2004 ◽  
Vol 41 (04) ◽  
pp. 1145-1156 ◽  
Author(s):  
Parijat Dube ◽  
Fabrice Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Closed Form ◽  
Lévy Processes ◽  
Busy Period ◽  
Exit Time ◽  
Levy Processes ◽  
Finite Capacity ◽  
Scale Functions ◽  
Period Distribution ◽  
Finite Capacity Queues ◽  
Time Theory

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

scholarly journals Exit problems for general draw-down times of spectrally negative Lévy processes

2019 ◽  
Vol 56 (2) ◽  
pp. 441-457 ◽  
Author(s):  
Bo Li ◽  
Nhat Linh Vu ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Scale Functions ◽  
Dynamic Level ◽  
Running Maximum ◽  
Potential Measure ◽  
Exit Problems ◽  
Spectrally Negative Lévy Processes

AbstractFor spectrally negative Lévy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find expressions of the Laplace transforms for the two-sided exit problems involving the draw-down time. We also find the Laplace transforms for the hitting time and creeping time over the running-maximum related draw-down level, respectively, and obtain an expression for a draw-down associated potential measure. The results are expressed in terms of scale functions for the spectrally negative Lévy processes.

scholarly journals Lévy processes time-changed by the first-exit time of the inverse Gaussian subordinator

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2545-2552
Author(s):  
Farouk Mselmi
Keyword(s):  
Lévy Processes ◽  
Exponential Family ◽  
Exit Time ◽  
Levy Processes ◽  
Variance Function ◽  
Inverse Gaussian ◽  
Natural Exponential Family ◽  
First Exit Time

This paper deals with a characterization of the first-exit time of the inverse Gaussian subordinator in terms of natural exponential family. This leads us to characterize, by means its variance function, the class of L?vy processes time-changed by the first-exit time of the inverse Gaussian subordinator.

scholarly journals Correlating Lévy processes with self-decomposability: applications to energy markets

2021 ◽  
Author(s):  
Matteo Gardini ◽  
Piergiacomo Sabino ◽  
Emanuela Sasso
Keyword(s):  
Monte Carlo ◽  
Closed Form ◽  
Lévy Processes ◽  
Systematic Risk ◽  
Levy Processes ◽  
Energy Markets ◽  
Characteristic Functions ◽  
Stochastic Delay ◽  
Spread Options

AbstractBased on the concept of self-decomposability, we extend some recent multidimensional Lévy models built using multivariate subordination. Our aim is to construct multivariate Lévy processes that can model the propagation of the systematic risk in dependent markets with some stochastic delay instead of affecting all the markets at the same time. To this end, we extend some known approaches keeping their mathematical tractability, study the properties of the new processes, derive closed-form expressions for their characteristic functions and detail how Monte Carlo schemes can be implemented. We illustrate the applicability of our approach in the context of gas, power and emission markets focusing on the calibration and on the pricing of spread options written on different underlying commodities.

Transient and busy period analysis of the GIG/1 Queue as a Hilbert factorization problem

1991 ◽  
Vol 28 (4) ◽  
pp. 873-885 ◽  
Author(s):  
Dimitris J. Bertsimas ◽  
Julian Keilson ◽  
Daisuke Nakazato ◽  
Hongtao Zhang
Keyword(s):  
Closed Form ◽  
Waiting Time ◽  
Time Distribution ◽  
Busy Period ◽  
Laplace Transforms ◽  
Waiting Time Distribution ◽  
Period Analysis ◽  
Factorization Problem ◽  
Period Distribution ◽  
Lindley Process

In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI G/1 queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/1, R/G/1 queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two moments of the distributions involved.

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