Network Case Flows
Network Flows Case Study
MTH221
University of Phoenix
February 23, 2014
Network Flows Case Study
The following is a series of case studies on Network Flows. Network flows can be representative of many types of systems. Whether the network is used to transmit data from computer to computer or server to server, transfer goods across the county, or deliver liquid flows to the desired location, networks must be studied to find the most efficient path for the given media to travel across. Locating the most efficient path for media allows systems to run at maximum efficiency without overloading any particular portion of the network, which would slow or even inhibit delivery to the desired destination.
Example 1 Example 1 introduces the scenario of Joe the plumber, and his piping network. Joe states that his system of connections can deliver a flow of 3 gpm from point s to point t through his series of connections. By studying his system on a capacitated s,t graph the flow tolerances can be mapped from point to point. Point s supplies 4 gpm to point a, point a then splits into two edges to points b and d which can flow 3 and 2 gpm respectively. Throughout the network there are differing capacities among the connections however, combined the edges always equal a flow of ≥3. This implies that the network will be able to deliver the necessary flow demands to t.
Example 2 Example 2 introduces the need to block an inland city from the sea using mines. These mines are placed in channels of river R in varying amounts as needed by the area that needs to be covered. The task is to block access to sea from city s using the least amount of mines possible. City s can be isolated from the sea with a minimum of 7 mines. The mines should be placed in the following locations and amounts:
1 mine placed between point d and point g
2 mines placed between point e and point g
2 mines placed between point e and point h
1 mine placed
MTH221
University of Phoenix
February 23, 2014
Network Flows Case Study
The following is a series of case studies on Network Flows. Network flows can be representative of many types of systems. Whether the network is used to transmit data from computer to computer or server to server, transfer goods across the county, or deliver liquid flows to the desired location, networks must be studied to find the most efficient path for the given media to travel across. Locating the most efficient path for media allows systems to run at maximum efficiency without overloading any particular portion of the network, which would slow or even inhibit delivery to the desired destination.
Example 1 Example 1 introduces the scenario of Joe the plumber, and his piping network. Joe states that his system of connections can deliver a flow of 3 gpm from point s to point t through his series of connections. By studying his system on a capacitated s,t graph the flow tolerances can be mapped from point to point. Point s supplies 4 gpm to point a, point a then splits into two edges to points b and d which can flow 3 and 2 gpm respectively. Throughout the network there are differing capacities among the connections however, combined the edges always equal a flow of ≥3. This implies that the network will be able to deliver the necessary flow demands to t.
Example 2 Example 2 introduces the need to block an inland city from the sea using mines. These mines are placed in channels of river R in varying amounts as needed by the area that needs to be covered. The task is to block access to sea from city s using the least amount of mines possible. City s can be isolated from the sea with a minimum of 7 mines. The mines should be placed in the following locations and amounts:
1 mine placed between point d and point g
2 mines placed between point e and point g
2 mines placed between point e and point h
1 mine placed