An application of Markovian arrival process (MAP) to modeling superposed ATM cell streams

Sang H. Kang, Yong Han Kim, Dan K. Sung, Bong D. Choi

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


First, we propose a new modeling method for superposed ATM traffic by the MMPP(2), which is a special case of the MAP(2). In this new method, we measure the mean and autocorrelation of cell interarrival times, and the histogram of the number of arrivals during measurement windows of fixed size. The MMPP(2) has interarrival times with the second-order hyper-exponential distribution with coefficient of variation cv > 1. However, superposed traffic is often observed to have cv < 1. To cover this situation, we extend the MMPP(2) to a MAP(3) by adding a new state with inter-state transition accompanied by an arrival. For the MAP(3) model, we take into account the second moment of the interarrival times. From numerical examples, we observe that both the proposed MMPP(2) and MAP(3) yields very good estimation of the cell loss ratio (CLR) for usual superpositions of voice and/or VBR video sources. However, when we have superpositions from CBR video sources together with other VBR sources, cv is much less than 1, and the MAP(3) outperform the MMPP(2), as expected. The proposed MAP(3) well characterizes the cell scale component as well as the burst scale component of superposed traffic streams.

Original languageEnglish
Pages (from-to)633-642
Number of pages10
JournalIEEE Transactions on Communications
Issue number4
StatePublished - Apr 2002


  • ATM cell stream
  • Cell loss ratio (CLR)
  • Markovian arrival process (MAP)
  • Traffic modeling


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