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

Søren Asmussen ()
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Søren Asmussen: Aarhus University, Department of Mathematics

Queueing Systems: Theory and Applications, 2025, vol. 109, issue 4, No 7, 23 pages

Abstract: Abstract 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.

Keywords: Canadization; Fixed point equation; Iteration; Lévy process; Markov additive process; Netput process; Phase-type distribution; Reflection; 60K25; 60-08; 60J28 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11134-025-09959-w

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