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<p>Markov-modulated queueing systems with continuous-valued netput process <i>Z</i> for the workload and discrete-valued <i>Z</i> for the queue length are considered. In the workload case, service times are assumed to be phase type; in the queue length case, both arrivals and services are allowed to be batched with batch sizes of discrete phase type. Using Erlangization, iterative algorithms for the Wiener–Hopf factors are developed and applied to computing the distributions of the workload/queue length at a finite point of time. Combining the Erlangization with Richardson extrapolation greatly reduces the number of Erlang stages needed for a given precision.</p>

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Wiener–Hopf factorization, Erlangization and transient solutions in some Markov-modulated queueing models

  • 期刊论文

  • 发表日期：

    2025年11月12日

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  • Søren Asmussen

摘要

Markov-modulated queueing systems with continuous-valued netput process Z for the workload and discrete-valued Z for the queue length are considered. In the workload case, service times are assumed to be phase type; in the queue length case, both arrivals and services are allowed to be batched with batch sizes of discrete phase type. Using Erlangization, iterative algorithms for the Wiener–Hopf factors are developed and applied to computing the distributions of the workload/queue length at a finite point of time. Combining the Erlangization with Richardson extrapolation greatly reduces the number of Erlang stages needed for a given precision.