@inproceedings{e86d9089ba9d45f2992ce03ff6d4273b,
title = "Value (Generating) Functions for the MX/G/1 Queue",
abstract = "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.",
keywords = "Batch arrivals, Generating function, LST, Laplace transform, M/G/1, MDP, Value function",
author = "Esa Hyytia and Rhonda Righter and Jorma Virtamo and Lauri Viitasaari",
note = "Funding Information: This work was supported by the Academy of Finland in the FQ4BD and TOP-Energy projects (grant nos. 296206 and 268992). We thank the anonymous referees and our shepherd, Mark Squillante, for helping to improve the paper. Publisher Copyright: {\textcopyright} 2017 ITC Press.; 29th International Teletraffic Congress, ITC 2017 ; Conference date: 04-09-2017 Through 08-09-2017",
year = "2017",
month = oct,
day = "10",
doi = "10.23919/ITC.2017.8064360",
language = "English",
series = "Proceedings of the 29th International Teletraffic Congress, ITC 2017",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "232--240",
editor = "Raffaele Bolla and Florin Ciucu",
booktitle = "Proceedings of the 29th International Teletraffic Congress, ITC 2017",
address = "United States",
}