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Baraba′si has proposed a queue model of the human behavior. In this paper we compare the Baraba′si results and Va′zquez results. We proposed a model of human behavior dynamics by taking into consideration the service-time distribution. We obtained exact results for the model by calculating the waiting time distribution and sojourn time distribution of active tasks. The results show that the waiting time distribution of the model is a power-law distribution with exponent 2 for the highest priority first selection protocol. This exponent approximates to degree exponent 2.1 observed in Hsue-Shen Tsien correspondence pattern.
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Keywords:
- human behavior dynamics /
- Poisson process /
- power-law distributions /
- queueing theory
[1] ［1］Ross S M 1983 Stochastic Processes (New York: John Wiley & Sons)
[2] ［2］Cohen J W 1982 The Single Server Queue (Amsterdam： North Holland)
[3] ［3］Baraba′si A L 2005 Nature 435 207
[4] ［4］Va′zquez A 2005 Phys. Rev. Lett. 95 248701
[5] ［5］Va′zquez A 2007 Physica A 373 747
[6] ［6］Blanchard P， Hongle M O 2007 Phys. Rev. E 75 026102
[7] ［7］Grinstein G， Linsker R 2006 Phys. Rev. Lett. 97 130201
[8] ［8］Kentsis A 2006 Nature 441 E5
[9] ［9］Va′zquez A, Oliveira J G, Dezs Z, Goh K, Kondor I, Baraba′si A L 2006 Phys. Rev. E 73 036127
[10] ］Dezs Z, Almaas E, Luka′cs A, Ra′cz B, Szakada′t I, Baraba′si A L 2006 Phys. Rev. E 73 066132
[11] ］Zhou T, Kiet H A T, Kim B J, Wang B H, Holme P 2008 Europhys. Lett. 82 28002
[12] ］Han X P, Zhou T, Wang B H 2008 New J. Phys. 10 073010
[13] ］Alfi V, Parisi G, Pietronero L 2007 Nat. Phys. 3 746
[14] ］Duan Z S, Wang W X, Liu C, Chen G R 2009 Chin. Phys. B 18 3122
[15] ］Guo J L 2007 Chin. Phys. 16 1239
[16] ］Du H F, Li S Z, Marcus W F, Yue Z S, Yang X S 2007 Acta Phys. Sin. 56 6886 (in Chinese)［ 杜海峰、 李树茁、 Marcus W F、 悦中山、杨绪松 2007 56 6886］
[17] ］Abate J, Whitt W 1997 Queu. Syst. 25 173
[18] ］Li N N, Zhang N, Zhou T 2008 Physica A 387 6391
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[1] ［1］Ross S M 1983 Stochastic Processes (New York: John Wiley & Sons)
[2] ［2］Cohen J W 1982 The Single Server Queue (Amsterdam： North Holland)
[3] ［3］Baraba′si A L 2005 Nature 435 207
[4] ［4］Va′zquez A 2005 Phys. Rev. Lett. 95 248701
[5] ［5］Va′zquez A 2007 Physica A 373 747
[6] ［6］Blanchard P， Hongle M O 2007 Phys. Rev. E 75 026102
[7] ［7］Grinstein G， Linsker R 2006 Phys. Rev. Lett. 97 130201
[8] ［8］Kentsis A 2006 Nature 441 E5
[9] ［9］Va′zquez A, Oliveira J G, Dezs Z, Goh K, Kondor I, Baraba′si A L 2006 Phys. Rev. E 73 036127
[10] ］Dezs Z, Almaas E, Luka′cs A, Ra′cz B, Szakada′t I, Baraba′si A L 2006 Phys. Rev. E 73 066132
[11] ］Zhou T, Kiet H A T, Kim B J, Wang B H, Holme P 2008 Europhys. Lett. 82 28002
[12] ］Han X P, Zhou T, Wang B H 2008 New J. Phys. 10 073010
[13] ］Alfi V, Parisi G, Pietronero L 2007 Nat. Phys. 3 746
[14] ］Duan Z S, Wang W X, Liu C, Chen G R 2009 Chin. Phys. B 18 3122
[15] ］Guo J L 2007 Chin. Phys. 16 1239
[16] ］Du H F, Li S Z, Marcus W F, Yue Z S, Yang X S 2007 Acta Phys. Sin. 56 6886 (in Chinese)［ 杜海峰、 李树茁、 Marcus W F、 悦中山、杨绪松 2007 56 6886］
[17] ］Abate J, Whitt W 1997 Queu. Syst. 25 173
[18] ］Li N N, Zhang N, Zhou T 2008 Physica A 387 6391
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