1 edition of **Dynamic multicommodity flow schedules** found in the catalog.

Dynamic multicommodity flow schedules

Adam Feit

- 360 Want to read
- 5 Currently reading

Published
**1981**
by Naval Postgraduate School in Monterey, California
.

Written in English

Some new results in the scheduling of dynamic multicommodity flows in data communication networks are presented. A new performance measure for effective delivery of backlogged data to their destinations is defined and the solution to the resulting delivery problem is obtained through a sequential linear optimization methodology. Properties of an optimal dynamic multicommodity flow schedule are studied in detail, taking advantage where possible of the linear programming formulation. The special case of the delivery problem in a single destination network also is analyzed. Application of the results to stochastic delivery problems in which the data inputs to the network are modelled as Poisson processes is addressed, and a new dynamic data communication network analysis is presented. Finally, the delivery problem on networks with capacitated links and with traversal delays is considered and some new results obtained.

**Edition Notes**

Statement | Adam Feit |

The Physical Object | |
---|---|

Pagination | 258 p. : |

Number of Pages | 258 |

ID Numbers | |

Open Library | OL25510345M |

The thesis is structured as follows. In Chapter 1, we introduce two dynamic flow man-agement problems that are the topic of this thesis and review the literature to provide a framework for our contribution. In Chapter 2, we formally introduce the air traffic flow management problem, present our formulation, address the complexity, discuss some. In rare cases, your flow can take up to 2 hours to trigger. When the trigger occurs, the flow receives a notification, but the flow runs on data that exists at the time the action runs. For example, if your flow triggers when a new record is created, and you update the record twice before the flow runs, your flow runs only once with the latest.

3 Multicommodity Flow A multicommodity ow network is a graph G= (V;E) with pairs of vertices s i;t i 2V, each representing a source and sink for a commodity i a demand D i for each commodity a capacity function Con the edges of Gsuch that X all i f i(e) c e: Let f2[0;1]. Then we de ne the concurrent max-ow of a multicommodity ow network to be. Network Flow Algorithms Andrew V. Goldberg, Eva Tardos and Robert E. Tarjan 0. Introduction Network flow problems are central problems in operations research, computer science, and engineering and they arise in many real world applications. Starting with early work in linear programming and spurred by the classic book of.

For a k-commodity multicommodity flow problem, the running time of our randomized algorithm is (up to log factors) the same as the time needed to solve k single-commodity flow problems, thus giving the surprising result that approximately computing a k-commodity maximum-flow is not much harder than computing about k single-commodity maximum. 2 Simple Network Flow Problems In this section we discuss the basic framework of multicommodity ow by describing two simpler network ow problems. In Section , the details of a single commodity maximum ow are discussed. Section deals with the minimum cost single commodity ow problem. Maximum Flow Consider a directed network G= (V;E).

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Dynamic form. It has been shown that the same approach is also valid minimum cost for dynamic multicommodity flows (Fonoberova ). In this case the problem that has to be solved on the time-extended network is a minimum-cost multicommodity network flow problem (AssadMcBrideCastro and NabonaKarakostas ).Author: Sebastian Raggl, Judith Fechter, Andreas Beham.

Flows over time problems consider finding optimal dynamic flows over a network where capacities and transit times on arcs are given.

In this paper we study a multicommodity flow over time problem in which no storage of flow at nodes is allowed and solutions are restricted to loopless flow Cited by: 1.

The minimum cost multicommodity ﬂow problem in dynamic networks commodity k 2 K allowed on each arc e 2 E in every moment of time t 2 T. We also consider that every arc e 2 E has a nonnegative time- varying capacity for all commodities, which is known as the mutual.

In the Quickest Multicommodity k-Splittable Flow Problem (QMCkSFP), we are given a dynamic digraph D = (V, A), with V being the set of nodes and A the set of directed arcs; each arc (i, j) is associated with labels defining a strictly positive capacity c ij, i.e.

the maximum number of flow units that can concurrently enter the arc during a time Cited by: 1. In the minimum-cost dynamic flow problem (MCDFP), the goal is to compute, for a given dynamic network with source s, sink t, and two integers v and T, a feasible dynamic flow from s to t of value.

Solutions. In the decision version of problems, the problem of producing an integer flow satisfying all demands is NP-complete, even for only two commodities and unit capacities (making the problem strongly NP-complete in this case).

If fractional flows are allowed, the problem can be solved in polynomial time through linear programming, or through (typically much faster) fully polynomial. Multicommodity flow complementary slackness conditions – Let denote a specific value of the flow variable – The commodity flows are optimal in the multicommodity flow problem if and only if they are feasible and for some choice of (nonnegative) arc prices wij and (unrestricted in sign) node potentials πk(i), the reduced.

Theorem. The multicommodity flow x = (xk) is an optimal multicommodity flow for (17) if there exists non-negative prices w = (w ij) on the arcs so that the following is true 1. If 0, then. ¦ k ij ij ijk w x u 2. The flow xk is optimal for the k-th commodity if ck is replaced by cw,k, where.

We first formulate the problem as a multicommodity flow problem with parameters associated with each arc–commodity pair. We then reduce the problem to an equivalent single-commodity flow problem and develop a complete characterization of conformality among production, sales, and inventory activities in various instances of the problem.

Descent direction algorithm with multicommodity flow problem for signal optimization and traffic assignment jointly Applied Mathematics and Computation, Vol. No. 1 Chapter 5 Dynamic Models for Freight Transportation. The implementation of the schedule construction is freely available as open source, and distributed with the hardware implementation of the NoC.

few results on the dynamic multicommodity flow. () Algorithms for multiplayer multicommodity flow problems. Central European Journal of Operations Research() Dynamic adaptive anti-jamming via controlled mobility.

() Cell-Based Local Search Heuristics for Guide Path Design of Automated Guided Vehicle Systems With Dynamic Multicommodity Flow. IEEE Transactions on Automation Science and Engineering The multicommodity minimal cost network flow problem may be described in terms of a distribution problem over a network [ V, E], where V is the node set with order n and E is the arc set with order decision variable x jk denotes the flow of commodity k through arc j, and the vector of all flows of commodity k is denoted by x k = [ x 1k, x mk].

Multicommodity Network Flow -Methods and Applications Joe Lindstrom¨ Linkopi¨ ng University [email protected] Abstract This survey describes the Multicommodity Network Flow problem, a network ﬂow problem where several commodi-ties must share resources in a common capacitated network.

The problem has many interesting and important applica. Graphs are excellent mathematical tools applied in many fields such as transportation, communication, informatics, economy.

A network and a flow network is a useful device to solve many problems in many fields in reality. However, most of the network applications in traditional graphs have only considered the weights of edges and vertexes independently, in which the length of a path is the.

Barnhart C, Hane CA, Johnson EL, Sigismondi G () A column generation and partitioning approach for multicommodity flow problems. Telecommunication Systems – CrossRef Google Scholar Multicommodity Flow Given a directed network with edge capacities u and possibly costs c.

Give a set K of k commodities, where a commodity i is de ned by a triple (s i;t i;d i) { source, sink and demand.

For each commodity, you want to nd a feasible ow, subject tojoint capacity constraints. The authors study the relationship between the max-flow and the min-cut for multicommodity flow problems. The min-cut is an upper bound for the max-flow, and the fundamental theorem of Ford and Fulkerson shows that for a 1-commodity problem, the two are equal.

It has also been shown that they are equal for 2-commodity problems. % Say net flow describes for a commodity the sum of flow going into and out % of a node. The conservation constraint can then be defined as net flow % should equal zero if the node isn't any commodity's source or target.

% But, if the node is a source, the netflow should equal the demand. If a % target, netflow should equal negative demand.

multicommodity flow problem has been the subject of substantial interest since Ford and Fulkerson’s famous result for 1-commodity flows. Hu [] showed that the max-flow and min-cut are always equal in the case of two commodities.

More generally, by combining results .the optimal multicommodity ﬂow formulation takes the form minimize l∈L D l(f l) subject to conservation of ﬂow constraints plus any additional special constraints, where f l denotes the total ﬂow on link l, and L is the set of links in the network.

The link cost function D l is typically chosen to be a convex monotonically increasing.Multicommodity Flows and Column Generation The goal of this chapter is to give a short introduction into multicommodity ﬂows and column generation.

Both will be used later on. Multicommodity Flows We begin our journey to multicommodity ﬂows with a review of maximum ﬂows, i.e., the case where we have only one commodity. The main goal in.