Closed parasitic flow loops and dominated loops in networks

Abstract

The paper raises awareness of the presence of highly undesirable closed parasitic flow loops in the solutions of published algorithms for maximising the throughput flow in networks. Parasitic flow loops increase the cost of transportation of the flow unnecessarily, consume residual capacity from the edges of the network, increase the likelihood of deterioration of perishable products, increase congestion and energy wastage. By using the presented theoretical framework, it is demonstrated that the probability of existence of closed and dominated flow loops in networks is surprisingly high. The paper also demonstrates that the successive shortest path strategy fails to minimise the total length of transportation routes from multiple interchangeable origins to destinations. By using the developed theoretical framework, it is shown that a minimum total length of the transportation routes in a network with multiple interchangeable origins is attained if and only if no closed parasitic flow loops and dominated flow loops exist in the network.