Roots, Symmetry, and Contour Integrals in Queuing-Type Systems

DOI10.1137/19M1287729zbMath1474.60215OpenAlexW2910127894WikidataQ114074233 ScholiaQ114074233MaRDI QIDQ5164712

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Publication date: 12 November 2021

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1287729

zbMATH Keywords

rootsprobability generating functionscontour integralsqueuing systems

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Queueing theory (aspects of probability theory) (60K25) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Uses Software

• GitHub

Cites Work

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• The discrete-time single-server queue
• Queues where customers of one queue act as servers of the other queue
• An exact root-free method for the expected queue length for a class of discrete-time queueing systems
• Pollaczek contour integrals for the fixed-cycle traffic-light queue
• An algebraic identity and the Jacobi-Trudi formula
• Spitzer's identity for discrete random walks
• ANALYTICALLY EXPLICIT RESULTS FOR THE GI/C-MSP/1/∞ QUEUEING SYSTEM USING ROOTS
• On a class of discrete time renewal risk models
• Back to the roots of the M/D/s queue and the works of Erlang, Crommelin and Pollaczek
• Newton's Identities
• Optimal replacement under a general failure model
• Equivalences of Batch-Service Queues and Multi-Server Queues and Their Complete Simple Solutions in Terms of Roots

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