Minimizing Bypass Transportation Expenses in Linear Multistate Consecutively-Connected Systems

Many continuous transportation systems can be represented as multi-state linear consecutively connected systems consisting of N+1 linearly ordered nodes. Some of these nodes contain statistically independent multistate elements with different characteristics. Each element j can provide a connection between the node to which it belongs and X_j next nodes, where X_j is a discrete random variable with known probability mass function. If the system contains nodes not connected with any previous node, then gaps exist that require bypass transportation solutions associated with considerable expenses. An algorithm based on the universal generating function method is suggested for evaluating the expected value of these expenses. A problem of finding the multi-state element allocation that minimizes the expected bypass transportation expenses is formulated and solved. Illustrative examples are presented.