A retrial system with two input streams and two orbit queues

2012/06/22 by Konstantin Avrachenkov, Avrachenkov, Konstantin, Philippe Nain +3
Business, Management and Accounting · Computer Science · Decision Sciences · #Advanced Queuing Theory Analysis #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Network Traffic and Congestion Control #Simulation Techniques and Applications

paper · doi:10.48550/arxiv.1206.5673

openalex publication_date 2012/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. This creates a system with three dependent queues. Such a queueing system serves as a model for two competing job streams in a carrier sensing multiple access system. We study the queueing system using multi-dimensional probability generating functions, and derive its necessary and sufficient stability conditions while solving a boundary value problem. Various performance measures are calculated and numerical results are presented.

Related

• A two-class queueing system with constant retrial policy and general class dependent service times
• On the BMAP₁, BMAP₂/PH/g, c retrial queueing system
• Stability Analysis of GI/G/c/K Retrial Queue with Constant Retrial Rate
• On the power series approximations of a structured batch arrival\n two-class retrial system with weighted fair orbit queues
• The generalized join the shortest orbit queue system: Stability, exact tail asymptotics and stationary approximations