Waiting time dynamics of priority-queue networks.

We study the dynamics of priority-queue networks, generalizations of the binary interacting priority-queue model introduced by Oliveira and Vazquez [Physica A 388, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.

[1]  Kwang-Il Goh,et al.  Burstiness and memory in complex systems , 2006 .

[2]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[3]  Bruno Gonçalves,et al.  Human dynamics revealed through Web analytics , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  H. K. Lee,et al.  Internet Data Packet Transport: from Global Topology to Local Queueing Dynamics , 2007, Int. J. Bifurc. Chaos.

[5]  G. Madey,et al.  Uncovering individual and collective human dynamics from mobile phone records , 2007, 0710.2939.

[6]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[7]  B Kahng,et al.  Priority queues with bursty arrivals of incoming tasks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[9]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Beom Jun Kim,et al.  Role of activity in human dynamics , 2007, EPL (Europhysics Letters).

[11]  Alan Cobham,et al.  Priority Assignment in Waiting Line Problems , 1954, Oper. Res..

[12]  Jure Leskovec,et al.  Worldwide Buzz: Planetary-Scale Views on an Instant-Messaging Network , 2007, WWW 2008.

[13]  R Linsker,et al.  Biased diffusion and universality in model queues. , 2006, Physical review letters.

[14]  Albert-László Barabási,et al.  Modeling bursts and heavy tails in human dynamics , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

[16]  Albert-László Barabási,et al.  Scale-free networks , 2008, Scholarpedia.

[17]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[18]  Adilson E. Motter,et al.  A Poissonian explanation for heavy tails in e-mail communication , 2008, Proceedings of the National Academy of Sciences.

[19]  G Caldarelli,et al.  Invasion percolation and critical transient in the Barabási model of human dynamics. , 2007, Physical review letters.

[20]  A. Barabasi,et al.  Human dynamics: Darwin and Einstein correspondence patterns , 2005, Nature.

[21]  Ph Blanchard,et al.  Modeling human activity in the spirit of Barabasi's queueing systems. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Alexei Vazquez.  Impact of memory on human dynamics , 2007 .

[23]  John Scott.  What is social network analysis , 2010 .

[24]  A. Vazquez,et al.  Impact of interactions on human dynamics , 2007, 0710.4916.