Technical note: The MAPt/Pht/∞ queueing system and multiclass [MAPt/Pht/∞]K queueing network

Ira Gerhardt, Barry L. Nelson, Michael R. Taaffe

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper we demonstrate how a key adjustment to known numerically exact methods for evaluating time-dependent moments of the number of entities in the Pht/Pht/∞ queueing system and [Pht/Pht/∞]K queueing network may be implemented to capture the effect of autocorrelation that may be present in arrivals to the more general MAPt/Pht/∞ queueing system and multiclass [MAPt/Pht/∞]K queueing network. The MAPt is more general than the Pht arrival process in that it allows for stationary nonrenewal point processes, as well as the time-dependent generalization of nonrenewal point processes. Modeling real-world systems with bursty arrival processes such as those in telecommunications and transportation, for example, necessitate the use of nonrenewal processes. Finally, we show that the covariance of the number of entities at different nodes and times may be described by a single closed differential equation.

Original languageEnglish (US)
Pages (from-to)367-376
Number of pages10
JournalINFORMS Journal on Computing
Issue number2
StatePublished - Mar 1 2017


  • Algorithms
  • Infinite server
  • MAPs
  • Nonstationary processes
  • Phase-type distribution
  • Queueing
  • Queueing networks
  • Queues
  • Time-dependent
  • Transient

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research


Dive into the research topics of 'Technical note: The MAPt/Pht/∞ queueing system and multiclass [MAPt/Pht/∞]K queueing network'. Together they form a unique fingerprint.

Cite this