From the viewpoint of quality of service, the packet unreliability and latency are both of critical performance indicators to assess internet quality for supervisor and customers. A computer system is usually modeled as a network topology with arcs and vertices where each arc denotes a delivery medium and each vertex represents an Internet data center. Due to failure, partial failure, maintenance, etc., each component (arc and vertex) should be multi-state. The network with imperfect vertices is more complex to evaluate the reliability because vertex failure results in the disablement of adjacent arcs. Such a network named a multi-state imperfect vertex computer network is addressed in this paper. We study how the data can be delivered through plural minimal paths simultaneously within both permitted packet unreliability and latency. A solution procedure is proposed to assess delivery reliability accordingly. A benchmark network is demonstrated to show the efficiency and effectiveness of the proposed solution procedure.