EXTREME FLUCTUATIONS IN SMALL-WORLD-COUPLED AUTONOMOUS SYSTEMS WITH RELAXATIONAL DYNAMICS

2005 ◽  
Vol 05 (01) ◽  
pp. L43-L62 ◽  
Author(s):  
H. GUCLU ◽  
G. KORNISS
Keyword(s):  
Power Law ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Autonomous Systems ◽  
Small World ◽  
System Size ◽  
Discrete Event Simulations ◽  
Synchronization Problem ◽  
Parallel Discrete Event ◽  
Average Size

Synchronization is a fundamental problem in natural and artificial coupled multi-component systems. We investigate to what extent small-world couplings (extending the original local relaxational dynamics through the random links) lead to the suppression of extreme fluctuations in the synchronization landscape of such systems. In the absence of the random links, the steady-state landscape is "rough" (strongly de-synchronized state) and the average and the extreme height fluctuations diverge in the same power-law fashion with the system size (number of nodes). With small-world links present, the average size of the fluctuations becomes finite (synchronized state). For exponential-like noise the extreme heights diverge only logarithmically with the number of nodes, while for power-law noise they diverge in a power-law fashion. The statistics of the extreme heights are governed by the Fisher–Tippett–Gumbel and the Fréchet distribution, respectively. We illustrate our findings through an actual synchronization problem in parallel discrete-event simulations.

scholarly journals Local Virtual Times Analysis in PCS Model

2021 ◽  
Author(s):  
Liliia Ziganurova ◽  
Lev Shchur
Keyword(s):  
High Performance ◽  
Essential Feature ◽  
Discrete Event ◽  
Universality Class ◽  
Personal Communication ◽  
Surface Growth ◽  
Model Parameters ◽  
Discrete Event Simulations ◽  
Zone Cell ◽  
Parallel Discrete Event

Efficient scalability and process synchronization are critical for achieving high performance in distributed computing environments. Analysis of the scalability is usually done using intensive case studies, which give an answer only for the particular set of model parameters. We found an efficient way to analyze the time evolution in models simulated with the Parallel Discrete Event Simulations (PDES) approach. The essential feature of PDES is the concept of local virtual time (LVT) associated with the evolution of each process of the model. The LVT of processes evaluates in simulations and forms a complicated profile.These profiles remind the profiles of the surface growth in the physical devices. In physics, researchers use the concept of universality, which helps to divide the different regimes of the class's surface growth—each class is described by some universal laws and does not depend on the details of the model. We demonstrate the applicability of this concept and present a model of LVT profile evolution in Personal Communication Service (PCS) model. The PCS network consists of a square grid of radio ports that serve users in their zone (cell). We build the LVT-PCS model, which describes the evolution of the LVT profile associated with the PCS model. We simulate the PCS model using the ROSS simulator (optimistic PDES) and compare results with those simulated by our LVT-PCS model. We found the profile demonstrates property, which is known in physics as roughening transition. We estimate the values of ``critical’’ exponents for two models, which seem to belong to the same universality class. We believe that the similarity we found can be helpful for the preliminary analysis of the model scalability, process desynchronization, and possible deadlocks.

scholarly journals Going Through Rough Times: from Non-Equilibrium Surface Growth to Algorithmic Scalability

2001 ◽  
Vol 701 ◽  
Author(s):  
G. Korniss ◽  
M.A. Novotny ◽  
P.A. Rikvold ◽  
H. Guclu ◽  
Z. Toroczkai
Keyword(s):  
Time Horizon ◽  
Discrete Event ◽  
Parallel Discrete Event Simulation ◽  
Discrete Event Simulations ◽  
Kinetic Roughening ◽  
Event Simulation ◽  
Evolving System ◽  
Progress Rate ◽  
Parallel Discrete Event ◽  
Synchronization Scheme

ABSTRACTEfficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively parallel algorithms for discrete-event simulations which employ conservative synchronization to enforce causality. We do this by looking at the simulated time horizon as a complex evolving system, and we identify its universal characteristics. We find that the time horizon for the conservative parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like kinetic roughening. This implies that the algorithm is asymptotically scalable in the sense that the average progress rate of the simulation approaches a non-zero constant. It also implies, however, that there are diverging memory requirements associated with such schemes.

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