Quantitative Modeling and Analytical Calculation of Anelasticity for a Cyber-Physical System

This paper investigates resource provisioning in cyber-physical systems (CPSs) by developing a new definition of anelasticity. A flat semi-dormant multicontroller (FSDMC) model is established on a special type of CPS platform named arbitrated networked control system with dual communication channels. A novel, quantitative, and formal definition of anelasticity for the FSDMC is proposed. A new finite capacity M/M/c queuing system with N-policy and asynchronous multiple working vacations of partial servers is established, and the FSDMC is modeled as a quasi-birth-and-death process to obtain the stationary probability distribution of the system. Based on the queueing model, we quantify various performance indices of the system to build a nonlinear cost-performance ratio (CPR) function. An optimization model is presented to minimize the CPR. A particle swarm optimization (PSO) algorithm is used to find the optimum solution of the optimization model and obtain the optimal configuration values of the system parameters under stability condition. By changing the system parameters, the sensitivity of the system performance indices and the CPR are analyzed, respectively. The unexpected workload varies randomly over time. Thus, an M/M/1/K queue is constructed in a Markovian environment by employing a three-state, irreducible Markov process. In this queue, the conditional average queue length and the probabilities of the three-state process are calculated. Then, the anelasticity value of the system is precisely determined. When the average arrival rate exceeds the average service rate in the queueing system, an optimal CPR unchanged adaptive algorithm based on PSO is designed to dynamically adjust the controller service rate. Extensive numerical results show the usefulness and effectiveness of the proposed techniques and exhibit that the system can maintain elastic invariance in adaptive adjustment parameters.