Optimal dynamic routing in communication networks with continuous traffic

Hajek, Bruce; Ogier, Richard G.

doi:10.1002/net.3230140308

Cited by 68 publications

(16 citation statements)

References 9 publications

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“…(1) there is no cycle formed by arcs with both xk and zk nonzero, (2) there is no chain of arcs, with both xk and zk nonzero, joining two nodes both of which have yj and w j both nonzero.…”

Section: K = [ : : : : : ]mentioning

confidence: 99%

“…If the arc costs are zero, the arc capacities are constant, and the storage costs are positive except for a single destination node which has zero storage cost, then CNP is an example of the dynamic routing problem studied by Segall [5] and Hajek and Ogier [2] (the details of this equivalence are given in [4].) The dynamic routing problem is that of finding a set of flows which clear an accumulation of stock at each storage node of the network in such a way that the delay cost J;f sTy(r)dr is minimized.…”

Section: Introductionmentioning

confidence: 99%

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A continuous‐time network simplex algorithm

Anderson

Philpott

1989

Networks

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Given a network having costs and upper bound constraints on the flows in its arcs, the minimum‐cost network flow problem is that of finding flows which satisfy a flow‐conservation constraint at each node and minimize the total cost of the flow. If the arc capacities vary as functions of time, and storage is permitted at the nodes of the network, then the problem becomes an infinitedimensional linear program with a network structure. We describe an algorithm to solve such problems. This algorithm is a continuuous‐time version of the network simplex algorithm.

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“…(1) there is no cycle formed by arcs with both xk and zk nonzero, (2) there is no chain of arcs, with both xk and zk nonzero, joining two nodes both of which have yj and w j both nonzero.…”

Section: K = [ : : : : : ]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A continuous‐time network simplex algorithm

Anderson

Philpott

1989

Networks

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show abstract

“…For instance [6] studied the problem of finding the maximum flow that can be sent from a source to a sink in T time units, in a network with transit times on the arcs. Variations of the dynamic maximum flow problem with zero transit times are discussed in [5,8,9]. None of these have a scheduling component.…”

Section: Introductionmentioning

confidence: 99%

Scheduling unit time arc shutdowns to maximize network flow over time: Complexity results

et al. 2013

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We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NP-hard. Here we identify a number of characteristics that are relevant for the complexity of instance classes. In particular, we discuss instances with restrictions on the set of arcs that have maintenance to be scheduled; series parallel networks; capacities that are balanced, in the sense that the total capacity of arcs entering a (non-terminal) node equals the total capacity of arcs leaving the node; and identical capacities on all arcs.

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“…Such systems arise in several applications, such as manufacturing [5,6,7,8,9], communications [10,11], water distribution [12], logistics and traffic control [13].…”

Section: Introductionmentioning

confidence: 99%

Average flow constraints and stabilizability in uncertain production-distribution systems

Bauso¹,

Blanchini²,

Pesenti³

2007

2007 American Control Conference

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Consider multi-inventory systems with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of the two requirements: i) meeting any possible demand at each time (worst case stability) or ii) achieving a pre-defined flow in the average (average flow constraints). Necessary and sufficient conditions * D. Bauso is with Dipartimento di Ingegneria Informatica, Universitàd iP a l e r m o ,P a l e r m o-I t a l ydario.bauso@unipa.it † F. Blanchini is with Dipartimento di Matematica e Informatica, Università di Udine, Udine -Italy blanchini@uniud.it ‡ R. Pesenti is with Dipartimento di Matematica Applicata, Università "Ca' Foscari" di Venezia -Italy pesenti@unive.it § Research supported by PRIN "Robustness optimization techniques for high performance control systems", and MURST-PRIN 2007ZMZK5T "Decisional model for the design and the management of logistics networks characterized by high interoperability and information integration".for the achievement of both goals have been proposed by the authors. In this paper we face the case in which these conditions are not satisfied. We show that if we ignore the requirement on worst case stability, we can find a control strategy driving the expected value of the state to zero. On the contrary, if we ignore the average flow constraints, we can find a control strategy that satisfies worst case stability while optimizing any linear cost on the average control. In the latter case we provide a tight bound for the cost.

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Optimal dynamic routing in communication networks with continuous traffic

Cited by 68 publications

References 9 publications

A continuous‐time network simplex algorithm

A continuous‐time network simplex algorithm

Scheduling unit time arc shutdowns to maximize network flow over time: Complexity results

Average flow constraints and stabilizability in uncertain production-distribution systems

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