Link Weight Design Adopting Traffic-Engineering Links Based on Preventive Start-Time Optimization Against Link Failures

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.

Optimizing link weights in an OSPF network is a key traffic engineering problem to reduce the network congestion. Previous studies introduced three policies on link weight optimization, which are called Start-time Optimization (SO), Runtime Optimization (RO), and Preventive Start-time Optimization. All of them were used to be applied to a pipe mode, in which a traffic matrix, representing the traffic demand between each source and destination node pair, is exactly known. In practical, it is difficult for a network operator to measure or specify an exact traffic matrix. On the other hand, it is easy for a network operator to specify a hose model, in which only the total amount of traffic each node injects into the network and the total amount of traffic each node receives from the network, has to be known. This paper proposes a preventive start-time optimization scheme for the hose model. It employs a heuristic algorithm to determine an optimal set of link weights to minimize the worst-case congestion ratio for any single link failure. A straight-forward method to find an optimal set of link weights is to search the link weight space against all the possible traffic matrices and topologies created by link failure. Obviously, this approach needs a huge amount of computation time. The proposed scheme effectively selects the worst-case performance traffic matrix and tries to reduce the worst-case congestion ratio. Numerical results via simulations show that the proposed scheme effectively reduces the worst-case congestion ratio compared to SO.

This paper reviews research on preventive start-time optimization (PSO). PSO determines a suitable set of link weights in an open shortest path network at the network operation start time that can handle any link failure scenario preventively. PSO minimizes the worst-case congestion ratio in case of failure. PSO can avoid both unexpected network congestion and network instability. We formulate the original PSO problem as a mixed integer liner programming problem by extending the starttime optimization model and describe heuristic approaches. We also introduce mathematical programming models for the PSO variations. In addition, we expand PSO into generalized preventive start-time optimization (GPSO) to find a link weight set that balances both congestion ratios under no failure and the worst-case 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.

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.

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.

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.

This paper proposes a Preventive Start-time Optimization with no penalty (PSO-NP). The penalty being the generation of a higher than normal congestion ratio in non-failures scenario when the link weight set used in our network only targets the failure scenario. PSO-NP determines a suitable set of OSPF link weights at the start time that can handle any link failure scenario preventively while suppressing the penalty for the non-failure scenario. Previously, a preventive start time optimisation was presented to minimize the worst case congestion ratio in case of failure. That scheme unfortunately presents a non-negligible penalty when there is no link failure in the network because it only focuses on the failure scenario. In this paper we consider both the worst case failure scenario and the non-failure scenario.We suppress that penalty while enhancing the Preventive Start-Time scheme to counter failures. Simulation results show that PSO-NP achieves substantial congestion reduction for any failure case while eliminating the penalty in case of no failures in the network.

In an Internet protocol network running a link-state routing protocol, determining link weights corresponds to determining a route from a source to a destination that the protocol selects to minimize the sum of the link weights. Previous studies have focused on determining physical link weights to reduce network congestion ratio in case of link failures. However, no study has yet to address a model that determines link weights by including traffic-engineering (TE) links and investigate the effect of including TE links on reducing network congestion. The link-state routing protocol treats a TE link as a logical, direct link between non-adjacent nodes. This paper proposes a link-weight design model with TE links based on preventive start-time optimization (PSO) for handling single link failures, called PSO-TE. The model considers physical and TE links when determining the link weights under the assumption of all single physical link failures. It identifies the set of link weights that minimizes the worst-case network congestion ratio across all considered failure patterns. The numerical findings demonstrate that PSO-TE effectively reduces the worst-case network congestion ratio compared to the baseline model that does not employ TE links, highlighting the advantage of including TE links.

This paper proposes a heuristic approach for distributed server allocation with preventive start-time optimization against a single server failure. Server allocation is decided beforehand under each failure pattern to minimize the largest maximum delay among all failure patterns. The Previous work formulated the model as an an integer linear programming (ILP) problem. As the number of users and that of severs increase, the size of ILP problem increases; the computation time to solve the ILP problem becomes large. The proposed heuristic approach adopts both simulated annealing and ILP approach in a hybrid manner. The numerical results reveal that the proposed approach reduces computation time by 26% compared with the ILP approach with increasing the largest maximum delay by 3.4% in average. It reduces the largest maximum delay compared with the start-time optimization model; it avoids instability caused by the unnecessary disconnection, which occurs in the run-time optimization model.

Real-time applications require low latency and strict event ordering to ensure seamless operation. Distributed server processing is effective for this purpose, and there are two synchronization algorithms: a conservative synchronization algorithm (CSA) and an optimistic synchronization algorithm (OSA). OSA improves delay performance compared to CSA. While prior studies have considered OSA, they have not incorporated the impact of server failures. This paper proposes an OSA-based server allocation model for delay-sensitive applications with preventive start-time optimization (PreSO) under single-server failures (OSA-PreSO). The proposed OSA-PreSO model minimizes the largest total delay across all failure scenarios while satisfying constraints in OSA with PreSO under single-server failures. We formulate the proposed model as an integer linear programming (ILP) problem. In OSA-PreSO, the objective is to minimize the largest total delay across all failure scenarios, without giving special consideration to the total delay in the no-failure scenario. As a result, a penalty arises in the form of an increased total delay in the no-failure scenario. To reduce the penalty, we develop an improved OSA-PreSO model, OSA-PreSO-LP (low-penalty), which reduces the total delay in the nofailure scenario while maintaining the same delay characteristics in failure scenarios. We prove that the decision version of OSA-PreSO is NP-complete. We introduce heuristic algorithms to handle large-scale problems. Numerical results show that the proposed OSA-PreSO model reduces the delay compared to the conventional CSA-based model by effectively utilizing server memory resources. We observe that the proposed model achieves a lower largest total delay than start-time optimization and provides greater stability by preventing unnecessary user reassignments compared to run-time optimization. Numerical results also show that OSA-PreSO-LP reduces the penalty at most by 83%, while maintaining the same delay characteristics in failure scenarios.

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.

Real-time applications require low latency and strict event ordering. Distributed server processing is effective for this purpose, and there are two synchronization algorithms: a conservative synchronization algorithm (CSA) and an optimistic synchronization algorithm (OSA). OSA allows servers to process events without prior order enforcement, rolling back their status to the time of the event occurrence if an out-of-order event is detected, which improves delay performance compared to CSA. While prior studies have considered OSA, they have not incorporated the impact of server failures. This paper proposes an OSA-based server allocation model for delay-sensitive applications with preventive start-time optimization (PSO) under single-server failures. The proposed model minimizes the largest total delay across all failure scenarios while satisfying the maximum status holding time constraints with PSO under single-server failures. PSO proactively assigns users to servers to minimize the maximum delay across all failure scenarios, while ensuring that users connected to operational servers are not unnecessarily reassigned. We formulate the proposed model as an integer linear programming (ILP) problem. We prove that the decision version of the server allocation problem is NPcomplete. Numerical results show that the proposed OSA-based model reduces the delay compared to the conventional CSAbased model by effectively utilizing server memory resources. We observe that the proposed model achieves a lower largest total delay than start-time optimization and provides greater stability by preventing unnecessary user reassignments compared to runtime optimization.

Real-time applications require low latency and event order guarantees. Distributed server processing is effective for this purpose, and data consistency between servers is crucial. Although existing models in previous work handle data consistency, they do not address server failures. This paper proposes a server allocation model for a consistency-aware multi-server network for delay-sensitive applications with preventive start-time optimization (PSO) under single-server failures. The proposed model considers data consistency between servers and handles single-server failures with PSO. PSO determines the assignment to minimize the worst-case delay over all possible failure scenarios while avoiding service disruption for users connected to non-failed servers. We formulate the proposed model as an integer linear programming (ILP) problem. The decision version of the server allocation problem is proven to be NP-complete, and it becomes difficult to solve in a practical time when the problem size is large. We develop two polynomial-time approximation algorithms with theoretical performance analysis. Numerical results show that the proposed model outperforms start-time optimization in terms of the largest total delay and run-time optimization in terms of avoiding instability. The results also show that the faster of our two developed algorithms achieves a speedup ranging from 2.26×10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> to 4.37×10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> times compared to the ILP approach, while the maximum delay is, on average, only 1.029 times the optimal value. The results indicate that the speedup effect becomes more significant as the number of users and servers increases.

This paper proposes a distributed server allocation model with the preventive start-time optimization against a single server failure. The proposed 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 problem. We prove the NP-completeness for the considered problem. The numerical results reveal that the proposed model reduces the largest maximum delay compared to one baseline; it avoids instability caused by the unnecessary disconnection, which frequently occurs in the other baseline.