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- Title
An exact root-free method for the expected queue length for a class of discrete-time queueing systems.
- Authors
Oblakova, A.; Al Hanbali, A.; Boucherie, R. J.; van Ommeren, J. C. W.; Zijm, W. H. M.
- Abstract
For a class of discrete-time queueing systems, we present a new exact method of computing both the expectation and the distribution of the queue length. This class of systems includes the bulk-service queue and the fixed-cycle traffic-light (FCTL) queue, which is a basic model in traffic-control research and can be seen as a non-exhaustive time-limited polling system. Our method avoids finding the roots of the characteristic equation, which enhances both the reliability and the speed of the computations compared to the classical root-finding approach. We represent the queue-length expectation in an exact closed-form expression using a contour integral. We also introduce several realistic modifications of the FCTL model. For the FCTL model for a turning flow, we prove a decomposition result. This allows us to derive a bound on the difference between the bulk-service and FCTL expected queue lengths, which turns out to be small in most of the realistic cases.
- Subjects
DISCRETE-time systems
- Publication
Queueing Systems, 2019, Vol 92, Issue 3/4, p257
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-019-09614-1