Marginal and joint distribution of inter-departure times for a PH/PH/c queue

Ruth Sagron, Yoav Kerner

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce the Laplace–Stieltjes transform (LST) of the inter-departure time distribution in a PH/PH/c queue, and the two-dimensional joint LST of two consecutive inter-departure times to construct their correlation structure. We exploit the properties of phase-type (PH) random variables, as well as the steady-state distribution of the underlying continuous-time Markov chain in a PH/PH/c queue to construct these LSTs. We demonstrate our approach through numerical examples, while validating the results. Later, we analyze the correlation between two consecutive inter-departure times for various PH/PH/c queues. We observe that, if the fundamental elements of the queue have high (low) variability, then the correlation is positive (negative).

Original languageAmerican English
Article number102383
JournalPerformance Evaluation
Volume163
DOIs
StatePublished - 1 Jan 2024

Keywords

  • Correlation
  • Inter-departure time distribution
  • Laplace–Stieltjes transform
  • PH/PH/c queue
  • Phase-type distribution

All Science Journal Classification (ASJC) codes

  • Software
  • Modelling and Simulation
  • Hardware and Architecture
  • Computer Networks and Communications

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