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 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.

Scalability, Random Surfaces, and Synchronized Computing Networks

2005 ◽  
Author(s):  
Zoltan Toroczkai ◽  
György Korniss
Keyword(s):  
Message Passing ◽  
Discrete Event ◽  
Queueing Systems ◽  
The State ◽  
Local State ◽  
Surface Growth ◽  
State Variables ◽  
Discrete Event Simulations ◽  
Parallel Discrete Event ◽  
The Individual

In most cases, it is impossible to describe and understand complex system dynamics via analytical methods. The density of problems that are rigorously solvable with analytic tools is vanishingly small in the set of all problems, and often the only way one can reliably obtain a system-level understanding of such problems is through direct simulation. This chapter broadens the discussion on the relationship between complexity and statistical physics by exploring how the computational scalability of parallelized simulation can be analyzed using a physical model of surface growth. Specifically, the systems considered here are made up of a large number of interacting individual elements with a finite number of attributes, or local state variables, each assuming a countable number (typically finite) of values. The dynamics of the local state variables are discrete events occurring in continuous time. Between two consecutive updates, the local variables stay unchanged. Another important assumption we make is that the interactions in the underlying system to be simulated have finite range. Examples of such systems include: magnetic systems (spin states and spin flip dynamics); surface growth via molecular beam epitaxy (height of the surface, molecular deposition, and diffusion dynamics); epidemiology (health of an individual, the dynamics of infection and recovery); financial markets (wealth state, buy/sell dynamics); and wireless communications or queueing systems (number of jobs, job arrival dynamics). Often—as in the case we study here—the dynamics of such systems are inherently stochastic and asynchronous. The simulation of such systems is nontrivial, and in most cases the complexity of the problem requires simulations on distributed architectures, defining the field of parallel discrete-event simulations (PDES) [186, 367, 416]. Conceptually, the computational task is divided among n processing elements (PEs), where each processor evolves the dynamics of the allocated piece. Due to the interactions among the individual elements of the simulated system (spins, atoms, packets, calls, etc.) the PEs must coordinate with a subset of other PEs during the simulation. For example, the state of a spin can only be updated if the state of the neighbors is known. However, some neighbors might belong to the computational domain of another PE, thus, message passing will be required in order to preserve causality.

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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