A clearing system with impatient passengers: asymptotics and estimation in a bus stop model

Offer Kella*, Wolfgang Stadje

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

At some location buses stop to pick up the passengers waiting there and leave immediately, empty or occupied. Passenger arrival times as well as bus arrival times form independent renewal processes. Every passenger is willing to wait for a random amount of time before leaving, and every bus takes away all waiting passengers. For this pickup model, we study the distributions of the number of waiting passengers and of the individual sojourn times. The sojourn times lead to a Markov chain embedded in the superposition of the two underlying renewal arrival processes, for which we study its convergence toward stationarity.

Original languageAmerican English
Pages (from-to)1-14
Number of pages14
JournalQueueing Systems
Volume80
Issue number1-2
DOIs
StatePublished - 1 Jun 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

  • Clearing system
  • Impatience
  • M/G/∞
  • Pickup problem
  • Rate of convergence
  • Strongly mixing

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