Value (Generating) Functions for the MX/G/1 Queue

Esa Hyytia, Rhonda Righter, Jorma Virtamo, Lauri Viitasaari

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

5 Citations (Scopus)


We analyze the MX/G/1 queue in the framework of Markov decision processes (MDPs). The service times become known upon arrival, and each job incurs a cost according to a given cost function. The value function is a central concept in MDP theory as it characterizes the value of the system's state with respect to future developments. We derive compact expressions for the generating functions for general families of value functions corresponding to often used cost structures defined in terms of waiting and sojourn times. Moreover, we consider systems with and without setup delays.

Original languageEnglish
Title of host publicationProceedings of the 29th International Teletraffic Congress, ITC 2017
Number of pages9
ISBN (Electronic)9780988304536
Publication statusPublished - 10 Oct 2017
MoE publication typeA4 Article in a conference publication
EventInternational Teletraffic Congress - Genoa, Italy
Duration: 4 Sep 20178 Sep 2017
Conference number: 29


ConferenceInternational Teletraffic Congress
Abbreviated titleITC
Internet address


  • Batch arrivals
  • Generating function
  • Laplace transform
  • LST
  • M/G/1
  • MDP
  • Value function

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  • Cite this

    Hyytia, E., Righter, R., Virtamo, J., & Viitasaari, L. (2017). Value (Generating) Functions for the MX/G/1 Queue. In Proceedings of the 29th International Teletraffic Congress, ITC 2017 (Vol. 1, pp. 232-240). [8064360] IEEE.