Mateusz Zotkiewicz

Reoptimization of dynamic flexgrid optical networks after link failure repairs

In dynamic flexgrid optical networks, the usage of capacity may not be optimal due to the permanent process of setting up and tearing down connections, which, if not controlled, leads to spectrum fragmentation and, as a result, to increase of connection blocking. On top of this, a restoration mechanism that is launched in reaction to a link failure (cable cut) restores the affected lightpaths. Eventually, when the cable is repaired and its capacity becomes available for new connections, the unbalance between lightly and heavily loaded links increases, thus further decreasing the probability of finding optical paths with continuous and contiguous spectrum for future connection requests. In this paper we study the effects of reoptimizing the lightpath connections after a link failure has been repaired [namely, the after-failure-repair optimization (AFRO) problem] as an effective way for both reducing and balancing capacity usage and, by these means, for improving network performance. To solve AFRO a column generation decomposition method is presented. Illustrative numerical results show that AFRO allows us to significantly decrease the request blocking probability in realistic dynamic network scenarios. Moreover, the proposed column generation algorithm delivers quasi-optimal solutions in reasonable times. Besides, traffic disruptions resulting from lightpath rerouting are practically negligible. Finally, we show that it is sufficient to apply AFRO only for a selected set of link failures in order to achieve high network performance.

Solving large instances of the RSA problem in flexgrid elastic optical networks

We present an optimization procedure that mixes advanced large-scale optimization methods and heuristics to solve large instances (with over 1.7 million integer variables) of the routing and spectrum allocation (RSA) problem - a basic optimization problem in flexgrid elastic optical networks. We formulate the problem as a mixed-integer program for which we develop a branch-and-price algorithm enhanced with such techniques as problem relaxations and cuts for improving lower bounds (LBs) for the optimal objective value, and an RSA heuristic for improving the upper bounds. All these elements are combined into an effective optimization procedure. The results of numerical experiments run on network topologies of different dimensions and with large demand sets show that the algorithm performs well and can be applied to the problem instances that are difficult to solve using commercial solvers such as CPLEX.

Complexity of a classical flow restoration problem

In this article, we revisit a classical optimization problem occurring in designing survivable multicommodity flow networks. The problem, referred to as FR, assumes flow restoration that takes advantage of the so-called stub release. As no compact linear programming (LP) formulation of FR is known and at the same time all known noncompact LP formulations of FR exhibit NP-hard dual separation, the problem itself is believed to be NP-hard, although without a proof. In this article, we study a restriction of FR (RFR) that assumes only elementary (cycle-free) admissible paths—an important case virtually not considered in the literature. The two problems have the same noncompact LP formulations as they differ only in the definition of admissible paths: all paths (also those including cycles) are allowed in FR, while only elementary paths are allowed in RFR. Because of that, RFR is in general computationally more complex than FR. The purpose of this article, is three-fold. First, the article reveals an interesting special case of RFR—the case with only one failing link—for which a natural noncompact LP formulation obtained by reducing the general RFR formulation still exhibits NP-hard dual separation, but nevertheless this special case of RFR is polynomial. The constructed example of a polynomial multicommodity flow problem with difficult dual separation is of interest since, to our knowledge, no example of this kind has been known. In this article, we also examine a second special case of RFR, this time assuming two failing links instead of one, which turns out to be NP-hard. This implies that problem RFR is NP-hard in general (more precisely, for two or more failure states). This new result is the second contribution of the article. Finally, we discuss the complexity of FR in the light of our new findings, emphasizing the differences between RFR and FR. (Less)

Complexity of resilient network optimisation

Path restoration (PR) is one of the basic mechanisms for securing telecommunication networks against failures. In the paper, we discuss the complexity of certain variants of a multi-commodity flow network optimisation problem in directed graphs related to state-independent path restoration mechanisms. We demonstrate that most variants of the considered problem are NP-hard. Depending on the variant, we show how the problem can be reduced either from the partition problem or from the problem of finding an arc-disjoint pair of paths that connect two distinct pairs of nodes. We also demonstrate that at the same time the considered problem is difficult to approximate. The complexity results of the paper are important as they can help to devise proper algorithms for resilient network design tools. Copyright (C) 2009 John Wiley & Soils, Ltd. (Less)

Minimum Dependencies Energy-Efficient Scheduling in Data Centers

This work presents an on-line, energy- and communication-aware scheduling strategy for SaaS applications in data centers. The applications are composed of various services and represented as workflows. Each workflow consists of tasks related to each other by precedence constraints and represented by Directed Acyclic Graphs (DAGs). The proposed scheduling strategy combines advantages of state-of-the-art workflow scheduling strategies with energy-aware independent task scheduling approaches. The process of scheduling consists of two phases. In the first phase, virtual deadlines of individual tasks are set in the central scheduler. These deadlines are determined using a novel strategy that favors tasks which are less dependent on other tasks. During the second phase, tasks are dynamically assigned to computing servers based on the current load of network links and servers in a data center. The proposed approach, called Minimum Dependencies Energy-efficient DAG (MinD+ED) scheduling, has been implemented in the GreenCloud simulator. It outperforms other approaches in terms of energy efficiency, while keeping a satisfiable level of tardiness.

Modelling the NFV forwarding graph for an optimal network service deployment

The NFV is focused at virtualizing network functions such as gateways, path computing devices, resource allocation mechanisms, proxies, firewalls and transcoders, traditionally carried out by specialized hardware devices, and migrating these functions to software-based appliances. In this paper, an analytic model for the NFV forwarding graph is proposed with the aim to optimize the execution time of the network services deployed.

Optimization models for flexgrid elastic optical networks

In the paper we present integer programming (IP) optimization models for flexgrid elastic optical networks (EON). We consider several different basic assumptions regarding flexibility of EON that lead to a variety of IP formulations differing in precision and complexity. As usual, detailed models aiming at precisely describing technological aspects of EON suffer from tractability issues resulting from their greater complexity and have to be reasonably simplified. To achieve this, we consider cases where the bandwidth is divided into predefined slots, cases where the bandwidth is continuous and can be divided between demands with no restrictions, cases where a list of predefined paths is available, and finally cases where all the paths are indirectly taken into account. We present both compact and non-compact formulations. The non-compact formulations are accompanied with brief description of the dedicated column generation algorithms.

Flow optimization in IP networks with fast proactive recovery

The post-failure convergence of the shortest path routing (SPR) protocols used in IP networks can be too slow to meet the restrictive requirements (i.e., maximum allowable delay, jitter, etc.) of the multimedia services and therefore new restoration mechanisms combined with IP routing are of interest. The paper addresses optimization of three potential rerouting mechanisms based on the IP fast reroute mechanism proposed by Shand and Bryant [1]. The first mechanism takes advantage of equal-cost multiple (shortest) paths (ECMP) where two or more ECMP paths outgoing from one router can be used to protect one another in the IP fast reroute mechanism. Due to a limited number of the ECMP paths, the ECMP protection cannot be used as a stand-alone rerouting mechanism which assures protection against all link failures. Therefore, two other mechanisms, called loop-free alternate (LFA) and multi-hop repair path (MHRP) are considered. The LFA protection consists in determining an alternative next-hop address used in the case of a link failure. MHRP is a generalization of LFA which uses multi-hop tunnels to redirect packets from the failing link to a router that is able to send them to the destination based on a shortest path based forwarding. For each of the mechanisms we formulate an appropriate optimization problem as a mixed integer program (MIP). Moreover, we consider a combined approach where protection is assured through ECMP paths, LFA next-hop addresses, or MHRP paths. Thanks to the variety of protection mechanisms, the IP fast reroute technique is able to provide protection for any single link failure. The associated optimization problem (consisting in a simultaneous optimization of a weight system, LFA alternative next-hop addresses and MHRP paths) is difficult and is thus approached with a heuristic method. In our numerical experiments we evaluate effectiveness of this method.

Spectrum allocation problem in elastic optical networks - a branch-and-price approach

In the paper we present a branch and price approach to routing and spectrum allocation - a basic optimization problem in elastic optical networks. We formulate the problem as a mixed-integer program for which we develop a branch and price algorithm enhanced with such techniques as cutting planes for improving lower bounds for the optimal objective value, and a greedy and a simulated annealing heuristics for improving the upper bounds. All these elements are combined into an effective optimization procedure. Preliminary results show that the algorithm is able to produce optimal solutions and in a vast majority of the considered cases it performs better than a standard branch-and-bound method implemented in the CPLEX solver.

Volume oriented routing

Assuming that the traffic matrix belongs to a polytope, we present a new routing paradigm where each traffic demand is routed independently of the other demands. The routing of each demand is a combination of two extreme routing depending on the current volume of the demand. This new routing paradigm is easy to implement in networks and quite efficient in terms of network cost.