Queues with waiting time dependent service

R. Bekker, G. M. Koole, Bo Friis Nielsen, T. B. Nielsen

    Research output: Contribution to journalJournal articleResearchpeer-review


    Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline 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
    JournalQueueing Systems
    Issue number1
    Pages (from-to)61-78
    Publication statusPublished - 2011


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


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