Start-time Optimization Research Articles

Approximation Algorithms to Distributed Server Allocation With Preventive Start-Time Optimization Against Server Failure

This letter proposes two polynomial-time approximation algorithms for the distributed server allocation problem with preventive start-time optimization against a failure. Server allocation is decided in advance to minimize the largest maximum delay among all failure patterns. We analyze the approximation performances of proposed algorithm when only the delay between servers or all the delays including that between servers and users hold the triangle inequality. Numerical results reveal that the proposed algorithms are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.0\times 10^{3}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.9\times 10^{7}$ </tex-math></inline-formula> times faster than the integer linear programming approach while increasing the largest maximum delay by 1.033 times in average.

Heuristic Approach to Distributed Server Allocation with Preventive Start-Time Optimization against Server Failure

This paper presents a distributed server allocation model with preventive start-time optimization against a single server failure. The presented model preventively determines the assignment of servers to users under each failure pattern to minimize the largest maximum delay among all failure patterns. We formulate the proposed model as an integer linear programming (ILP) problem. We prove the NP-completeness of the considered problem. As the number of users and that of servers increase, the size of ILP problem increases; the computation time to solve the ILP problem becomes excessively large. We develop a heuristic approach that applies simulated annealing and the ILP approach in a hybrid manner to obtain the solution. Numerical results reveal that the developed heuristic approach reduces the computation time by 26% compared to the ILP approach while increasing the largest maximum delay by just 3.4% in average. It reduces the largest maximum delay compared with the start-time optimization model; it avoids the instability caused by the unnecessary disconnection permitted by the run-time optimization model.

Preventive Start-Time Optimization to Determine Link Weights Against Probabilistic Link Failures

This article proposes a network design model to minimize the worst-case network congestion against multiple link failures, where open shortest path first link weights are determined at the beginning of network operation. In the proposed model, which is called the preventive start-time optimization model against multiple link failures (PSO-M), the number of multiple link failure patterns to support is restricted by introducing a probabilistic constraint called probabilistic guarantee . If the total probability of non-connected failure patterns does not exceed a specified probability, PSO-M provides a feasible solution of link weights. Otherwise, no feasible solution can be obtained. We introduce an extended model of PSO-M, called PSO-M with link reinforcement (PSO-MLR), where links are reinforced under a budget constraint. Link reinforcement in PSO-MLR has two purposes: maintaining network connectivity and reducing the worst-case congestion ratio. Numerical results show that PSO-M offers lower worst-case congestion ratios than the start-time optimization model, where link weights are obtained against the non-failure pattern assuming that multiple link failures are possible. The superiority of PSO-M strengthens as the average node degree of the network increases. Given a fixed budget, PSO-MLR allows the worst-case congestion ratio to be varied within a specific range. PSO-MLR can support a part of non-connected failure patterns to determine link weights, and so is a valuable enhancement of PSO-M.

Preventive Start-Time Optimization Considering Both Failure and Non-Failure Scenarios

Preventive Start-Time Optimization Considering Both Failure and Non-Failure Scenarios

Preventive Start-Time Optimization of Link Weights With Link Reinforcement

A conventional start-time optimization scheme, which determines an optimal OSPF link weight set that minimizes the network congestion ratio at network operation start, is not suitable under failure. Link reinforcement through protection techniques is effective in providing robustness against link failure, but cannot be applied on every link due to resource limitations. This letter proposes a preventive start-time link-weight optimization scheme with link reinforcement considering all possible single-link failure scenarios. When the upper bound of the manageable congestion ratio is given, our proposed scheme determines a suitable link weight set at the network operation start that minimizes the number of links to reinforce, specifying the reinforced links, so as to guarantee a congestion ratio lower than or equal to the manageable congestion ratio upper bound under any single-link failure scenario. Numerical results demonstrate the effectiveness of the proposed scheme.

Optimization of OSPF Link Weights to Counter Network Failure

A key traffic engineering problem in the Open Shortest Path First (OSPF)-based network is the determination of optimal link weights. From the network operators' point of view, there are two approaches to determining a set of link weights: Start-time Optimization (SO) and Run-time Optimization (RO). We previously presented a Preventive Start-time Optimization (PSO) scheme that determines an appropriate set of link weights at start time. It can counter both unexpected network congestion and network instability and thus overcomes the drawbacks of SO and RO, respectively. The previous work adopts a preventive start-time optimization algorithm with limited candidates, named PSO-L (PSO for Limited candidates). Although PSO-L relaxes the worst-case congestion, it does not confirm the optimal worst-case performance. To pursue this optimality, this paper proposes a preventive start-time optimization algorithm with a wide range of candidates, named PSO-W (PSO for Wide-range candidates). PSO-W upgrades the objective function of SO that determines the set of link weights at start time by considering all possible single link failures; its goal is to minimize the worst-case congestion. Numerical results via simulations show that PSO-W effectively relaxes the worst-case network congestion compared to SO, while it avoids the network instability caused by the run-time changes of link weights caused by RO. At the same time, PSO-W yields performance superior to that of PSO-L.

PSO: preventive start-time optimization of OSPF link weights to counter network failure

This letter proposes a scheme, named Preventive Start-time Optimization (PSO), that determines a suitable set of OSPF link weights at the start time that can handle any link failure scenario preventively. The set of link weights determined by PSO minimizes the worst-case network congestion ratio for all possible link failure scenarios. Numerical results via simulations show that PSO relaxes the worst-case network congestion compared to a conventional scheme that optimizes a set of link weights without considering any link failure at the start time, while PSO avoids the network instability due to the run-time changes of re-optimized link weights whenever a link failure occurs.