Local Virtual Times Analysis in PCS Model
preprintposted on 2021-06-15, 15:59 authored by Liliia ZiganurovaLiliia Ziganurova, Lev Shchur
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.