Maximum Multicommodity Flow with Intermediate Storage

The multicommodity flow problem deals with the transshipment of more than one commodity from respective sources to corresponding sinks without violating the capacity constraints. Due to the capacity constraints, flows out from the sources may not reach their sinks, and so, the storage of excess flows at intermediate nodes plays an important role in the maximization of flow values. In this paper, we introduce the maximum static as well as maximum dynamic multicommodity flow problems with intermediate storage. We present polynomial and pseudopolynomial time algorithms for the former and latter problems, respectively. We also present the solution procedures to these problems in contraflow network having symmetric as well as asymmetric arc transit times. We transform the solutions in continuous-time settings by using natural transformation.

Capacitated Multicommodity Flow Problem for Heterogeneous Smart Electricity Metering Communications Using Column Generation

This paper addresses the planning and deployment of wireless heterogeneous networks (WHNs) for smart metering, based on a cross-layer solution. We combine the constraints of the network layer that considers routing and flow demands at each link in the WHN, while at the same time, we account for the restrictions of the physical layer referred to the capacity of a short range technology when used in a multi-hop fashion. We propose a model based on a column generation approach to solve the capacitated multicommodity flow problem (CMCF); the model includes wireless links capacities, coverage, and cost. The work integrates the multi-hop routing of packets in a mesh network formed by smart meters and concentrators connected to a cellular network via base stations. The traffic of each link is represented in a multigraph with the occupation percentage, and we build a scalable routing tree on a georeferenced map to represent a real deployment. The results describe the behavior of the proposed model in terms of the traffic load per concentrator, the network coverage, and the reduction of energy consumption. We demonstrate that an infrastructure cost reduction is achieved with the inclusion of multi-hop short range technology, which reduces the number of smart meters that require a direct connection to cellular technology. The model guarantees 100% coverage of the smart meters analyzed in each scenario. The calculation time of the CMCF for advanced metering infrastructure (CMCF-AMI) based on the column generation algorithm as the population increases is reduced by 10%, and this is the expected return when the population is considerable.

On three approaches to length-bounded maximum multicommodity flow with unit edge-lengths

The paper presents a comparison between three approaches to solving the length-bounded maximum multicommodity flow problem with unit edge-lengths. Following the first approach, Garg and K?nemann?s, we developed an improved fully polynomial time approximation scheme for this problem. As the second alternative, we considered the well-known greedy approach. The third approach is the one that yields exact solutions by means of a standard LP solver applied to an LP model on the time-expanded network. Computational experiments are carried out on benchmark graphs and the graphs that model software defined satellite networks, to compare the proposed algorithms with an exact linear programming solver. The results of the experiments demonstrate a trade-off between the computing time and the precision of algorithms under consideration.

Joint Channel Assignment and Power Allocation Based on Maximum Concurrent Multicommodity Flow in Cognitive Radio Networks

Emerging cognitive radio networking technology potentially provides a promising solution to the spectrum underutilization problem in wireless access. In this paper, a cross-layer routing for secondary multihop is studied in cognitive radio network operating in television white spaces. The framework considers a joint channel, power, and routing assignment under signal to interference noise ratio (SINR) constraints. The problem is formulated as a maximum concurrent multicommodity flow problem. The goal of conducting this research is to develop a new routing protocol for the secondary multihop cognitive radio network. Therefore, the objective of this paper focuses on maximizing a flow rate scaling factor. Moreover, the paper focuses on achieving multipath routing when it is possible under SINR constraints to utilize all possible unused channels efficiently. The numerical results proved the strength of the proposed algorithm in its routing ability under the physical model of SINR, in addition to the ability of using multipath routing if there are available free channels to be used in the cognitive communication paradigm.