Instability of SRPT, SERPT and SJF multiclass queueing networks

Łukasz Kruk () and Tymoteusz Chojecki ()
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Łukasz Kruk: Maria Curie- Skłodowska University
Tymoteusz Chojecki: Maria Curie- Skłodowska University

Queueing Systems: Theory and Applications, 2022, vol. 101, issue 1, No 2, 57-92

Abstract: Abstract We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol. Both of them are reentrant lines with two servers and eight customer classes. The customer service times in our first system are deterministic, yielding an example of an unstable shortest remaining expected processing time (SERPT) network. In the second one, the service times in one customer class are randomized. Both our examples show also system instability under the shortest job first (SJF) discipline. A simulation study of robustness of our results with respect to changes in the customer interarrival and service times is also provided. Our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and in fact cause instability effects. This is in sharp contrast with their satisfactory performance for single-server queues.

Keywords: Instability; Multiclass queueing networks; Simulation; Size-based scheduling; SJF; SRPT; 60K25; 60K20; 68M20; 90B22; 90B36 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11134-021-09733-8

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