Biased diffusion and universality in model queues

Physical Review Letters

Volumn 97, Issue 13, 2006, Pages

  Grinstein, G ^a   Linsker, R ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; MATHEMATICAL MODELS; ROBUSTNESS (CONTROL SYSTEMS);

BIASED DIFFUSION; CONTINUOUS-VALUED PRIORITIES; PRIORITY-BASED MODELS;

QUEUEING THEORY;

EID: 33749160685     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.97.130201     Document Type: Article

References (11)

1. D.R. Cox and W.L. Smith, Queues (Methuen, London, 1961).
2. D. Gross and C.M. Harris, Fundamentals of Queueing Theory (Wiley, New York, 1998), 3rd ed.
3. J. Abate and W. Whitt, Queueing Syst. Theory Appl. QUSYE8 0257-0130 25, 173 (1997), and references therein. 10.1023/A:1019104402024
4. A.-L. Barabási, Nature (London) NATUAS 0028-0836 435, 207 (2005), and supplementary online information. (Our model A and the fixed-length-queue model of Ref. differ, insignificantly, in the order of adding and executing tasks within a given time step). 10.1038/nature03459
5. A. Vázquez, Phys. Rev. E 73, 036127 (2006). PLEEE8 1063-651X 10.1103/PhysRevE.73.036127
6. J.G. Oliveira and A.-L. Barabási, Nature (London) NATUAS 0028-0836 437, 1251 (2005). 10.1038/4371251a
7. A. Vázquez, Phys. Rev. Lett. 95, 248701 (2005) showed that the P(τ)∼1/τ result also holds, for τ<τp1/l(21+p), in a stochastic version of the fixed-length-queue model, wherein the highest priority task is executed with probability p. PRLTAO 0031-9007 10.1103/PhysRevLett.95.248701
8. Some researchers have argued that P(τ) for the Email data is actually log-normal. See comment by D.B. Stouffer, R.D. Malmgren, and L.A.N. Amaral, physics/0510216;
9. and reply by A.-L. Barabási, K.-I. Goh, and A. Vázquez, physics/0511186.
10. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, New York, 2001).
11. H. Kobayashi, J. Assoc. Comput. Mach. JACOAH 0004-5411 21, 316 (1974). 10.1145/321812.321827