Paper Info
Title
An exact root-free method for the expected queue length for a class of discrete-time queueing systems
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.
Year
DOI
Venue
2019
10.1007/s11134-019-09614-1
Queueing Systems
Keywords
Field
DocType
Bulk-service queue, Fixed-cycle traffic-light model, Roots, Contour integrals, 60K25, 90B22
Applied mathematics,Mathematical optimization,Characteristic equation,Polling system,Queue,Methods of contour integration,Flow (psychology),Queueing theory,Discrete time queueing,Mathematics,Computation
Journal
Volume
Issue
ISSN
92.0
3-4
1572-9443
Citations 
PageRank 
References 
0
0.34
0
Authors
5
Name
Order
Citations
PageRank
A. Oblakova100.34
Ahmad Al Hanbali215811.74
Richard J. Boucherie331137.73
Jan-Kees Van Ommeren4214.35
W. H. M. Zijm516223.24