Queues with waiting time dependent service

Rene Bekker, Ger Koole, Bo Friis Nielsen, Thomas Bang Nielsen

    Research output: Contribution to journalJournal articleResearchpeer-review


    Motivated by service levels in terms of the waiting time distribution seen in e.g. call centers, we consider two models for systems with a service disciple that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting time process of the first customer in line, we derive steady-state waiting time distributions for both models. The results are illustrated with numerical examples.
    Original languageEnglish
    JournalMathematics of Operations Research
    Publication statusSubmitted - 2008


    • Queues
    • Overflow
    • Contact centers
    • Level crossing
    • Waiting-time distribution
    • Call centers
    • Adaptive service rate
    • Deterministic threshold


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