Amir Hossein Aminzadeh - Department of Industrial Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran
Farhaneh Hamzezadeh - Assistant Professor of Department of Industrial Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran

Optimization problems are of the most important problems which have been considered in the recent years. Each optimization model has its special structure. This structure miraculously decreases the calculating complexity ( data processing time). The current networks also accounts the important component of these issues. Networks have the extent aspect and they are used for the various situatios.The system capacity is equal to the maximum sent flow from the source node to sink node in the single commodity flow network. clearly, this systems capacity has a constant value in the definite flow network and is variable in the stochastic flow network ( the network which its capacity has a stochastic value in each arc). In this research, a new constraint under the heading of passing time of commodity from each path has been added to the evaluated reliability of the network flow problem. Hereby, passing duration of commodity in each path is considered as an exponential distribution with

probable network, minimum path, exponential distribution, network flow, queue system