A new analytical algorithm and generation of Gaussian quadrature formula for stochastic network

An analytical algorithm is presented to compute the network completion time distribution function, where each arc has a continuous, defined, and independent completion time distribution function. Through a transformation method, the algorithm is simplified into simple multiple integrals. Then Gaussian quadrature formula is generalized for numerical solution of these integrals. Also the generalized Gaussian quadrature formula is applied for conditional Monte Carlo simulation to increase its speed and develop its domain of application. A suitable criterion is presented for the efficiency of conditional Monte Carlo simulation. For variance reduction in estimation, the antithetic random variates are used for simulation methods, conditional Monte Carlo simulation and crude Monte Carlo simulation. Several examples are presented and solved through generalized Gaussian quadrature formula, conditional Monte Carlo simulation, and crude Monte Carlo simulation. For the aspects of speed and accuracy, different methods are compared, where analytical solutions are provided and used for comparision purposes. Finally, conclusions and recommendations are made.