Parallel algorithms for fitting Markov arrival processes

Mindaugas Bražėnas, Gábor Horváth, M. Telek

Research output: Contribution to journalArticle

3 Citations (Scopus)


The fitting of Markov arrival processes (MAPs) with the expectation–maximization (EM) algorithm is a computationally demanding task. There are attempts in the literature to reduce the computational complexity by introducing special MAP structures instead of the general representation. Another possibility to improve the efficiency of MAP fitting is to reformulate the inherently serial classical EM algorithm to exploit modern, massively parallel hardware architectures. In this paper we present three different EM-based fitting procedures that can take advantage of the parallel hardware (like Graphics Processing Units, GPUs) and apply a special MAP structure, the Erlang distributed-continuous-time hidden Markov chain (ER-CHMM) structure for reducing the computational complexity. All the proposed parallel algorithms have their strengths: the first one traverses the samples only once per iteration, the second one is memory efficient (far more than the classical serial algorithm), and the third one has exceptionally low execution times. These procedures are compared with the standard serial forward–backward procedure for performance comparison. The new algorithms are orders of magnitudes faster than the standard serial procedure, while (depending on the variant) using less memory.

Original languageEnglish
Pages (from-to)50-67
Number of pages18
JournalPerformance Evaluation
Publication statusPublished - Jul 1 2018



  • EM algorithm
  • GPU
  • Markov arrival process
  • Parallel computation
  • Traffic model fitting

ASJC Scopus subject areas

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

Cite this