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May 2001 A LIFO queue in heavy traffic
Vlada Limic
Ann. Appl. Probab. 11(2): 301-331 (May 2001). DOI: 10.1214/aoap/1015345294


This paper describes the heavy-traffic behavior of an M/G/1 last-in-first-out preemptive resume queue. An appropriate framework for the analysis is provided by measure-valued processes. In particular, the paper exploits the setting of recent works by Le Gall and Le Jan.Their finite-measure-valued exploration process corresponds to our RES-measure (residual services measure) process, that captures all the relevant information about the evolution of the queue, while their height process corresponds to the queue-length process. The heavy-traffic “diffusion” approximations for the RES-measure and the queue-length processes are derived under the usual second moment assumptions on the service distributions. The tightness of queue lengths argument uses estimates for the total size and height of large Galton–Watson trees.


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Vlada Limic. "A LIFO queue in heavy traffic." Ann. Appl. Probab. 11 (2) 301 - 331, May 2001.


Published: May 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1015.60079
MathSciNet: MR1843048
Digital Object Identifier: 10.1214/aoap/1015345294

Primary: 60J80 , 60K25

Keywords: branching , heavy traffic , LIFO queue , Measure-valued process

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.11 • No. 2 • May 2001
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