An exact root-free method for the expected queue length for a class of discrete-time queueing systems

A. Oblakova (), A. Al Hanbali, R. J. Boucherie, J. C. W. Ommeren and W. H. M. Zijm
Additional contact information
A. Oblakova: University of Twente
A. Al Hanbali: King Fahd University of Petroleum and Minerals
R. J. Boucherie: University of Twente
J. C. W. Ommeren: University of Twente
W. H. M. Zijm: University of Twente

Queueing Systems: Theory and Applications, 2019, vol. 92, issue 3, No 3, 257-292

Abstract: 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.

Keywords: Bulk-service queue; Fixed-cycle traffic-light model; Roots; Contour integrals; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-019-09614-1

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