Analysis of stochastic fluid queues driven by local-time processes

Panagiotis Takis Konstantopoulos, Andreas E. Kyprianou, Paavo Salminen, Marina Sirviö

Research output: Contribution to journalArticle

Abstract

We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a reflected Lévy process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically(but not necessarily) singular with respect to the Lebesgue measure, a situation which, in view of the nonsmooth or bursty nature of several types of Internet traffic, is nowadays quite realistic. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period, and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a Lévy process (a subordinator). hence making the theory of Lévy processes applicable. Another important ingredient in our approach the use of Palm calculus for stationary random point processes and measures. © Applied Probability Trust 2008.

Original languageEnglish
Pages (from-to)1072-1103
Number of pages32
JournalAdvances in Applied Probability
Volume40
Issue number4
DOIs
Publication statusPublished - 2008

Fingerprint

Fluid Queue
Local Time
Applied Probability
Subordinator
Busy Period
Internet Traffic
Point Process
Random process
Lebesgue Measure
Rate Constant
Stochastic Systems
Stability Condition
Markov Process
Buffer
Calculus
Time Scales
Server
Model

Keywords

  • Fluid queue
  • Inspection paradox
  • Lévy process
  • Local time
  • Palm calculus
  • Performance analysis
  • Skorokhod reflection

Cite this

Konstantopoulos, P. T., Kyprianou, A. E., Salminen, P., & Sirviö, M. (2008). Analysis of stochastic fluid queues driven by local-time processes. Advances in Applied Probability, 40(4), 1072-1103. https://doi.org/10.1239/aap/1231340165
Konstantopoulos, Panagiotis Takis ; Kyprianou, Andreas E. ; Salminen, Paavo ; Sirviö, Marina. / Analysis of stochastic fluid queues driven by local-time processes. In: Advances in Applied Probability. 2008 ; Vol. 40, No. 4. pp. 1072-1103.
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Konstantopoulos, PT, Kyprianou, AE, Salminen, P & Sirviö, M 2008, 'Analysis of stochastic fluid queues driven by local-time processes', Advances in Applied Probability, vol. 40, no. 4, pp. 1072-1103. https://doi.org/10.1239/aap/1231340165

Analysis of stochastic fluid queues driven by local-time processes. / Konstantopoulos, Panagiotis Takis; Kyprianou, Andreas E.; Salminen, Paavo; Sirviö, Marina.

In: Advances in Applied Probability, Vol. 40, No. 4, 2008, p. 1072-1103.

Research output: Contribution to journalArticle

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