Modeling video traffic using M/G/∞ input processes: A compromise between Markovian and LRD models

M. M. Krunz, A. M. Makowski

Research output: Contribution to journalArticlepeer-review

146 Scopus citations


Statistical evidence suggests that the autocorrelation function ρ (k) (k = 0, 1, ⋯) of a compressed-video sequence is better captured by ρ(k) = e-β√k than by ρ(k) = k = e-βlog k (long-range dependence) or ρ(k) = e-βk (Markovian). A video model with such a correlation structure is introduced based on the so-called M/G/∞ input processes. In essence, the M/G/∞ process is a stationary version of the busy-server process of a discrete-time M/G/∞ queue. By varying G, many forms of time dependence can be displayed, which makes the class of M/G/∞ input models a good candidate for modeling many types of correlated traffic in computer networks. For video traffic, we derive the appropriate G that gives the desired correlation function ρ(k) =e-β√ki . Though not Markovian, this model is shown to exhibit short-range dependence. Poisson variates of the M/G/∞ model are appropriately transformed to capture the marginal distribution of a video sequence. Using the performance of a real video stream as a reference, we study via simulations the queueing performance under three video models: our M/G/∞ model, the fractional ARIMA model [9] (which exhibits LRD), and the DAR(1) model (which exhibits a Markovian structure). Our results indicate that only the M/G/∞ model is capable of consistently providing acceptable predictions of the actual queueing performance. Furthermore, only script O sign(n) computations are required to generate an M/G/∞ trace of length n, compared to script O sign(n2) for an F-ARIMA trace.

Original languageEnglish (US)
Pages (from-to)733-748
Number of pages16
JournalIEEE Journal on Selected Areas in Communications
Issue number5
StatePublished - Jun 1998


  • Correlated variates
  • M/G/∞ process
  • Traffic modeling
  • VBR video

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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