The mathematical model of an two-phases-service M/M/1/N queuing system with the server breakdown and multiple vacations was realized and established in the Graduate Employment Services system. Secondly, equations of steady-state probability were derived by applying the Markov process theory. Then, we obtained matrix form solution of steady-state probability by using blocked matrix method. Final...

We describe a method for converting the problem of computing steady-state probabilities of a continuous-time Markov chain into the problem of computing absorption probabilities for a related chain. The construction enables us to apply compositional techniques for computing absorption probabilities that we have previously developed for probabilistic I/O automata to be used for computing certain ...

Network survivability is the key ability of ad hoc network under all kinds of attacks, which is a foundation to the design and evaluation of wireless ad hoc network routing protocol. The definitions of network survivability are analyzed and compared. We propose a novel survivability model based on Finite State Machine (FSM) and District Time Markov Chain (DTMC) model. DTMC steady-state probabil...

Steady state simulation is used to study long-run behavior. Usually only the expected value of the steady state probability distribution function is estimated. In many cases quantiles of this distribution are of higher interest. In this paper a new usage of quantile estimators is proposed, which is derived from mean value analysis and is based on multiple independent replications. The advantage...

A general classification scheme for nonequilibrium steady states in terms of their stationary probability distribution and the associated probability currents is proposed. This scheme allows us to identify all choices of transition rates, based on a master equation, which generate the same nonequilibrium steady state. One important consequence is a generalized detailed balance condition.

Here we provide more details of the results in the main text. First, we outline our notation. The time dependent probability of state i is pi = pi(t), while the steady state probability of state i is p ss i . The Laplace transformed probability of state i is Pi(s). The rate to go from state i to state j is kij . The probability to transition from state i to state j is qij . The time it takes to...

We consider Markov models of multicomponent systems with synchronizing interaction. Under natural regularity assumptions about the message routing graph, they have nice longtime behavior. We are interested in limit probability laws related to the steady state viewed from the center-of-mass coordinate system.

Performance evaluation of modern complex systems has become compulsory in order to understand a system's behavior before it is constructed or implemented. Usually either Simulation of Analytical approaches are used to obtain such understanding. However, the system must, somehow, be represented. The paper describes PerformCharts, a tool to analytically obtain performance evaluation of a system s...

is paper considers the M/M/NN repairable queuing system. e customers’ arrival is a Poisson process. e servers are subject to breakdown according to Poisson processes with different rates in idle time and busy time, respectively. e breakdown servers are repaired by repairmen, and the repair time is an exponential distribution. Using probability generating function and transform method, we ob...

This paper shows that timely development of fusion nuclear technology (FNT) components, e.g. blanket, for DEMO requires the construction and operation of a fusion facility parallel to ITER. This facility, called VNS, will be dedicated to testing, developing and qualifying FNT components and material combinations. Without VNS, i.e. with ITER alone strategy, the probability of achieving operating...