Optimal attackaware RWA for scheduled lightpath demands
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Abstract
In Transparent optical networks (TONs), the data signals remain in the optical domain for the entire transmission path, creating a virtual topology over the physical connections of optical fibers. Due to the increasingly high data rates and the vulnerabilities related to the transparency of optical networks, TONs are susceptible to different physical layer attacks, including highpower jamming attacks. Developing strategies to handle such attacks and mitigating their impact on network performance is becoming an important design problem for TONs. Some approaches for handling physical layer attacks for static and dynamic traffic in TONs have been presented in recent years. In this work, we propose an integer linear program (ILP) formulation to control the propagation of such attacks in TONs for scheduled lightpath demands, which need periodic bandwidth usage at certain predefined times. We consider both the fixed window model, where the start and end timings of the demand are known in advance, and the sliding window model, where exact start and end times are unknown but fall within a larger window. We consider a number of potential objectives for attackaware RWA and show how the flexibility to schedule demands in time can impact these objectives, compared to both attackunaware and fixed window models.
Keywords
Transparent optical networks (TONs) Highpower jamming attacks Scheduled lightpath demands (SLDs) Integer linear program (ILP) Routing and wavelength Assignment (RWA)1 Introduction
Transparent optical networks allow highspeed endtoend connections in the optical domain, without undergoing optical to electronical to optical (OEO) conversion at intermediate nodes. However, such transparency can lead to increased vulnerabilities to physicallayer attacks caused by highpowered jamming signal and can seriously degrade network performance [1]. Transparency also enhances the difficulties in detecting and localizing attacks, because monitoring must be performed in the optical domain [2, 3, 4]. In addition, techniques to detect and localize attacks need information from specialized optical monitoring equipment and can be quite expensive. In general, the more reliable performance of the network required, the more resources are needed and thus the cost of the security equipment is higher [5]. Along with the development and wide application of transparent wavelength division multiplexing (WDM) optical networks, security issues and physicallayer attack management have become increasingly important to the network manager [6]. Existing approaches to optical networks security are generally aimed at minimizing the potential damage caused by several major physicallayer attacks including gain competition, interchannel crosstalk attack and inband crosstalk attack [7].
A number of different attackaware RWA algorithms have been proposed in the literature, for static [1, 5, 8, 9] and dynamic [10, 11, 12] lightpath allocation. Attackaware RWA approaches typically try to reduce the attackradius (AR) [11, 13, 14] for a given set of lightpaths, by suitably choosing the route and/or wavelength for each lightpath. The AR of a compromised lightpath p can be loosely defined as the number of lightpaths (including itself) that can be adversely affected by an attacking signal on p. This typically occurs when p shares at least one link or at least one node and a common channel [1, 15] with the other lightpath. The attackradius of a lightpath p, is a widely used metric to measure the impact of introducing an attack signal on p and we have also used this metric in this paper.
A novel ILP formulation (ILP_fixed) that can handle both inband and outofband attacks for fixed window scheduled traffic.
A second extended ILP (ILP_sliding) that can intelligently schedule demands in time, in addition to performing attackaware RWA, for slidingwindow scheduled traffic.
2 Related work
2.1 Scheduled traffic model
The models of traffic demand typically considered in the literature for the design of WDM network include static and dynamic traffic. For static demands, the set of traffic demands is known beforehand and does not change for relatively long periods. In dynamic traffic, the arrival time and duration of individual requests are not known ahead of time and lightpaths are established as needed, assuming sufficient resources are available. The RWA problem, under both the static and dynamic traffic models, has been widely investigated and a number of ILP formulations as well as heuristics are available to solve this problem [16].
In recent years there has been an increasing number of applications that require periodic use of lightpaths (e.g. once per day, or once per week) at predefined times. For example, an online “class” with one two hour lecture per week on a specified day and at a specified time, or a bank transferring its data to a central location every night between 2 and 4 am. A new model, called the scheduled traffic model (STM), has been proposed in the literature [17] to handle such demands. This model is appropriate for applications that require periodic use of lightpaths and exploits the fact that the setup and teardown times of the demands are known in advance, so that the RWA algorithm can optimize resource allocation in both space and time. An excellent survey of RWA for this model is available in [18].
One class of STM is the fixedwindow model [13], where the start and end time for each SLD is fixed and known beforehand. A lightpath p in this model can be represented by a tuple p = (s_{p}, d_{p}, st_{p}, τ_{p}), where s_{p} (d_{p}) is the source (destination) node of the demand, st_{p} is the start time and τ_{p} is the duration. The second class of STM is the slidingwindow model [15], where a demand has a specified duration τ_{p}, and can be scheduled any time within a larger window (α_{p}, ω_{p}), such that the demand can only start after α_{p}, and must be completed before ω_{p}. For the sliding window model, a demand is represented by a tuple p = (s_{p}, d_{p}, α_{p}, ω_{p}, τ_{p}), since the actual start time for the demand is not known ahead of time.
2.2 Handling attacks in alloptical networks
2.2.1 Attack types in TONs
Signal insertion attacks,
Signal splitting attacks, and
Physical infrastructure attacks
A common type of signal insertion attack is the high power jamming attack, where an optical signal with high power (5–10 dB above normal) is introduced on a legitimate channel. When the attacker introduces a highpowered signal into the optical fiber, it can interfere with the signals on other wavelengths because of the optical fiber non linearities. The inter channel crosstalk between signals on different wavelengths transmitted over the same optical fiber can be exploited to mount outofband jamming attacks [1, 22]. The Raman gain effect and crossphase modulation are some of the causes that create non linearities in optical fibers [22]. A high power signal can also cause gain competition attack [6] in optical amplifiers, as the attack signal acquires more energy at the expense of legitimate signals. Older networks, that are not equipped with variable optical amplifiers (VOAs) to regulate output power of signals, are typically the most susceptible to high power jamming attacks. However, even when the jamming signal is attenuated at the first downstream node in steadystate, shortlived oscillations, called transients, can cause errorbursts and may even propagate through multiple links [21]. Repeated, intermittent injection of highpower signals on a malicious lightpath can cause transients. The harmful effects of such transients may be multiplied, if they cause multiple ‘restorations’, which lead to even more transients as legitimate lightpaths are disrupted and reestablished.
In addition to affecting copropagating channels on the same link, a highpower signal also introduces intrachannel (or inband) crosstalk between the signals on the same wavelength inside an optical switch [10]. When a highpowered attacking signal is injected on a wavelength, all the signals using that wavelength and sharing a common switch gets attacked. This can be more harmful than the outofband highpower jamming attacks, as the signals are on the same wavelength as that of the attacker signal [23].
Another attack, called lowpower QoS attack [21]—a type of signal splitting attack, can also be used to affect lightpaths on multiple links. In this type of attack, the attacker deliberately attenuates a channel, e.g. by attaching a splitter. This not only degrades the performance of the attacked channel, but the attack can propagate if nodes are equipped with fixed attenuation based power equalization. Such equipment is helpful for limiting propagation of high power jamming attacks but a low power attack can still propagate as legitimate signals on the link will be attenuated to ensure a flat power spectrum.
Another attack scenario outlined in [1] involves the attacker requesting a legitimate channel but not transmitting any data on it. In this case, the channel will carry only leakage signals picked up through crosstalk. The weak leakage signal can then be amplified along its path and delivered to the attacker at the destination node.
2.2.2 Attackaware RWA
The lightpath attack group (LAG_{p}) for a lightpath p consists of the set of lightpaths (including p itself) that shares at least one common link with p. The lightpath attack radius (LAR_{p}) is a commonly used metric for measuring the impact of an outofband attack carried out on a lightpath p and is defined as the number of lightpaths in LAG_{p} i.e., LAR_{p} = LAG_{p}.
The inband attack group (IAG_{p}) is defined as the set of lightpaths (including p itself) that use the same wavelength and share at least one common node with p. The corresponding value of inband attack radius (IAR_{p}) is defined as the number of lightpaths in IAG_{p} i.e., IAR_{p} = IAG_{p}.
In [1], an ILP is proposed to handle the outofband and gain competition attacks for static traffic. The main objective of this ILP is to minimize the Maximum linkshare attack radius (maxLAR), which can be calculated as the maximum number of lightpaths that are link sharing with a single lightpath demand in the network. The secondary objective of this formulation is to reduce the average load on the network.
In [25], the authors propose ILP formulations to handle inband attack propagation in all optical WDM networks for offline planning problem. Both the direct and indirect inband crosstalk propagations are examined and are minimized to control the propagation. The main objectives of these two ILPs are minimizing the maximum primary attack radius (PAR) and the maximum secondary attack radius (SAR) values respectively. The ILPPAR simply checks for the lightpaths that are sharing the same switch and are using the same wavelength and calculates the PAR value. ILPSAR takes the constraints of ILPPAR and calculates the secondary attack radius (SAR) value, by checking the spread of inband crosstalk over the network indirectly, by already attacked signals. The wavelength assignment (WA) problem for inband attacks are also considered in [5, 26, 27]. The concept of propagating crosstalk attack radius (PCAR) is proposed in [5] and an attackaware wavelength assignment that minimizes the worstcase potential propagation of inband crosstalk jamming attacks is presented. In [26], the authors select a wavelength based on estimated BER to improve BER and blocking probability for dynamic lightpath allocation. In [27], the authors propose both ILP and heuristic formulations and define new objective criteria for wavelength assignment.
In [12], an ILP is proposed to handle the propagation of both inband and outofband jamming attacks for the static lightpath allocation problem. Interactions among the lightpaths, which are sharing a common link are calculated and are added to the objective to cover the inter channel crosstalk susceptibility. In the first phase of programming, a set of K candidate paths is obtained using Dijkstra’s algorithm [4]. The acquired routes for all the source and destination pairs are given as an input to the ILP, with the objective of controlling the spread of both inter and intra channel crosstalk attacks.
A number of papers have also considered attackaware RWA for survivable optical networks. In [28] the authors propose a twostep ILP for RWA of working and backup lightpaths using dedicated path protection and a heuristic for larger problems. Heuristic approaches that ensure attack groups of primary and backup paths are disjoint and use the minimum number of wavelengths are presented in [24] and [29]. Finally, in [30], the authors formulate and ILP for jammingaware shared path protection (JASPP) in WDM networks.
3 Attackaware integer linear program (ILP) formulations
In this section, we introduce our proposed approaches for solving the attackaware RWA of for both fixedwindow and slidingwindow STM. The objectives of the proposed ILP formulations is to minimize the maximum combined attack radius (maxAR) for the set of lightpaths. We are given a physical network G(N, E), where N is the set of nodes and E is the set of fiber links in the network, and each link has a set of W available channels for establishing lightpaths. We are also given a set P of scheduled lightpath demands, where each \(p \in P\) can be specified as a tuple p = (s_{p}, d_{p}, st_{p}, τ_{p}) (p = (s_{p}, d_{p}, α_{p}, ω_{p}, τ_{p})) for fixedwindow (slidingwindow) STM.
The entire time period is divided into M nonoverlapping intervals, numbered 1, 2, …, M. The proposed ILPs are independent of the duration of each interval and the number of such intervals. The duration of each interval can vary from a few seconds to several minutes or even hours, depending on the application, and is set by the user. In the proposed ILPs, the start and end times of a demand (or corresponding window for sliding window model) are specified in terms of the interval in which the demand (or window) starts and/or ends. Similarly, the duration τ_{p} of a demand p is specified in terms of the number of time intervals during which the demand is active. We use the notation \(a_{p,m}\) to denote that a demand p is active during interval m, where \(m = 1, 2, \ldots , M\). We note that for the fixedwindow model, the values of \(a_{p,m}\) are known ahead of time for all \(p \in P\) and for all possible values of m, since the demand start times and durations are fixed. However, for the slidingwindow model, the values of \(a_{p,m}\) must be determined by the ILP.
3.1 Proposed ILP for fixedwindow SLDs (ILP_fixed)
Equations (1) and (2) determine if two different lightpaths p and q overlap in time (\(t_{p,q}\) = 1) or are timedisjoint (\(t_{p,q}\) = 0). Eq. (1) sets \(t_{p,q}^{m} = 1\), if lightpaths p and q are both active during interval m. If Eqs. (2a)–(2c) set \(t_{p,q} = 1\) if there is at least one interval (possibly more) during which both lightpaths are active; otherwise, \(t_{p,q} = 0\), indicating that p and q are time disjoint. The \(t_{p,q}\) values are precalculated and given as input to the ILP.
The following variables are defined for the ILP.

\(x_{p,e}\) = 1 if lightpath p uses edge e; 0 otherwise.

\(y_{p,i}\) = 1 if lightpath p passes through node i; 0 otherwise.

\(\omega_{p,k}\) = 1 if lightpath p is assigned channel k; 0 otherwise.

\(\alpha_{p,q} \left( {\beta_{p,q,} } \right)\) = 1 if lightpaths p and q share at least one common edge (node); 0 otherwise. \(0 \le \alpha_{p,q} , \beta_{p,q} \le 1\)

\(\alpha _{p,q}^{e} \left( {\beta _{p,q}^{i} } \right)\) = 1 if lightpaths p and q share a common edge e (node i); 0 otherwise.

\(\gamma_{p,q}^{k}\) = 1 if lightpaths p and q both use channel k; 0 otherwise.

\(\gamma_{p,q}\) = 1 if lightpaths p and q both use the same channel; 0 otherwise. \(0 \le \gamma_{p,q} \le 1\)

\(\delta_{p,q}\) = 1 if lightpaths p and q use the same channel and have at least one common node; 0 otherwise.

\(LAR_{p,q}^{m} \left( {IAR_{p,q}^{m} } \right)\) = 1 if lightpath \(q \in LAG_{p}\) (\(q \in IAG_{p}\)) during time interval m.

LAR_{p,q} (IAR_{p,q}) = 1 if lightpath \(q \in LAG_{p}\) (\(q \in IAG_{p}\)) during at least one time interval. \(0 \le LAR_{p,q} ,\;IAR_{p,q} \le 1\)

LAR_{p,m} (IAR_{p,m}) = An integer value specifying the lightpath attack radius (inband attack radius)of p during time interval m.

LAR_{p} (IAR_{p}) = An integer value specifying the lightpath attack radius (inband attack radius)of p over all time intervals.

maxAR = An integer value specifying the maximum combined attack radius for all lightpaths.
The objective function minimizes the maximum attack radius (maxAR), where maxAR is the upper bound of \(AR_{p} = LAR_{p} + IAR_{p}\), for all lightpaths \(p \in P\). This objective minimizes the maximum Attack Radius (\(AR_{p}\) value) for any lightpath.
Subject to:
3.2 Proposed ILP for slidingwindow SLDs (ILP_sliding)
\(st_{p,m}\) = 1 if m is the starting interval for demand p and 0 otherwise.
\(a_{p,m}\) = 1 if demand p is active during time interval m and 0 otherwise.
We note that for the fixed window model, \(a_{p,m}\) and \(a_{q,m}\) are constant values given as input to the ILP. However, for the sliding window these are variables whose values are determined by the ILP. Therefore, we cannot use Eq. (1) directly to calculate \(t_{p,q}^{m}\). So, constraints (38)–(40) are used to calculate the value of \(t_{p,q}^{m}\), in a way that ensures that constraints are still linear.
3.2.1 Alternative objective functions
A number of different objective functions can be used for RWA, for both attackaware and attackunaware cases. In the formulations given in Sect. 3.1, we use a traditional objective function, which minimizes the maximum attack radius of a lightpath. Another commonly used objective is to minimize the total attack radius (AR_{p} = LAR_{p} + IAR_{p}) for all the lightpaths, as given in Eq. (41). Both of these objectives [i.e. Eqs. (3) and (41)] have been proposed in the literature for conventional attackaware RWA and do not take into consideration the temporal nature of the demands. Since our proposed formulations focus on demands that are active during a specific time window, we also propose a new objective to incorporate their temporal nature. This objective, in Eq. (42), minimizes the total attack radius \(AR_{p,m} = IAR _{p,m} + LAR_{p,m}\) over all lightpaths and all intervals. In other words, we consider not only if a lightpath q belongs to the attack group of p, but also the duration for which both lightpaths are active. The longer the duration, the more it will contribute to the objective value.
 Minimize the sum of attack radius for all lightpaths p.$${\text{Minimize}}\;Total\_AR_{p} = \mathop \sum \limits_{p \in P} (LAR_{p} + IAR_{p} )$$(41)
 Minimize total attack radius for all lightpaths p over all intervals m.$$\text{Minimize}\;Total\_AR_{p,m} = \mathop \sum \limits_{\varvec{p}} \mathop \sum \limits_{\varvec{m}} (\varvec{LAR}_{{\varvec{p},\varvec{m} }} + \varvec{IAR}_{{\varvec{p},\varvec{m} }} )$$(42)
 Minimize total path length$$\text{Minimize}\;Total\_path\_length = \mathop \sum \limits_{{\varvec{p} \in \varvec{P}}} \mathop \sum \limits_{{\varvec{e}:\varvec{i} \to \varvec{j} \in \varvec{E}}} \varvec{x}_{{\varvec{p},\varvec{e}}}$$(43)
4 Simulation results
The proposed ILP (ILP_sliding) for sliding window scheduled traffic.
The proposed ILP (ILP_fixed) for fixed window scheduled traffic.
The attackunaware RWA using the shortest available path (SPATH)
 1.
Low Demand Overlap (LDO): For each SLD \(p \in P\), the value of the demand holding time (\(\tau_{p}\)) is between 1 and 10 time intervals, i.e. \(1 \le \tau_{p} \le 10.\)
 2.
Medium Demand Overlap (MDO): For each SLD \(p \in P\), the value of the demand holding time (\(\tau_{p}\)) is between 1 and 24 time intervals, i.e. \(1 \le \tau_{p} \le 24.\)
 3.
High Demand Overlap (HDO): For each SLD \(p \in P\), the value of the demand holding time (\(\tau_{p}\)) is between 10 and 24 time intervals, i.e. \(10 \le \tau_{p} \le 24.\)
source (s_{p}) and destination (d_{p}) for the demand,
duration τ_{p} of the demand and
start and end time of the window (α_{p}, ω_{p}) during which the demand can be active
We note that the total value for this objective can seem high, given the number of demands. For example, in Fig. 1, the objective value for all lightpaths is around 900 for the HDO set with shortest path routing or around 45 per lightpath. This is because, for each lightpath the attack radius is summed overall all active intervals. For HDO a demand p is active for 10–24 intervals. So, if we consider τ_{p} = 15 and assume 2–4 lightpaths are in its attack group in any given interval, then \(\sum\nolimits_{\varvec{m}} {(\varvec{LAR}_{{\varvec{p},\varvec{m }}} + \varvec{ IAR}_{{\varvec{p},\varvec{m }}} )}\) will be between 30 and 60 for lightpath p.
In this section, we have shown the total attack radius values (LAR + IAR) for different approaches and network configurations. We have observed that the LAR values contribute more towards the total attack radius (AR) compared to the IAR values. Typically, LAR contributes 65–85% of the total AR, while IAR contributes 15–35% of the total AR. This is because for each node i traversed by a lightpath p, there can be at most deg_{i} lightpaths in its inband attack group (IAGp), where deg_{i} is degree of node i. For the topologies considered in this paper, the nodal degree varies between 2 and 4, i.e. 2 ≤ deg_{i} ≤ 4. For each link i → j traversed by a lightpath p, there can be at most W lightpaths in its lightpath attack group (LAGp), where W is the number of wavelengths in link i → j. For our simulations, we have used W = 8. Therefore, it makes sense that LAR contributes more heavily to the total AR compared to IAR values.
In our simulations, the total attack radius increased consistently for a given network and demand size, with the amount of demand overlap (i.e. attack radius increases as the duration of the demands increase). But there were significant variations in the objective values when the actual demand sets were changed, even for demand sets that had the same number of demands. This means that the attackradius values depend not only on the number of demands but the actual demands themselves (i.e. start and destination nodes) that were selected. However, despite the variation in the actual attackradius based objective values for different demand sets, we observed following clear trend: ILP_sliding consistently provides the lowest attackradius, followed by ILP_fixed and SPATH has the highest attack radius values. This improvement was evident as we varied both the network topologies and demand set sizes.
5 Conclusions and future work
In this study we consider the attackaware RWA problem for scheduled demands using the fixed and sliding window models. We have presented a new ILP formulation for the fixed window model, with different objectives to minimize the total and the maximum attack radius. We have also shown how this ILP can be extended to handle the sliding window model as well. Our results show that by routing the scheduled demands in a way that reduces sharing of switches and/or fibers among simultaneously active demands, we can reduce the damaging effects of jamming attacks and therefore enhance the network security. We compare and evaluate the performance of the attackaware fixed window and sliding window scheduling algorithms through extensive simulations. The slidingwindow model not only selects an appropriate route and an effective wavelength for the lightpaths, but also assigns a suitable start time for them, within a predefined time range. Our experimental results indicate that, the time flexibility associated with sliding window scheduling gives best objective values compared to fixed window and attackunaware approaches.
In case of sliding and fixed window scheduled traffic models, the data transmission is continuous, once the lightpath is established between the source and destination nodes. The transmission process doesn’t terminate until the entire data is transmitted to the other end. As a future work, it may be possible to divide the scheduled lightpath demand into two or more individual segments and send them separately within the predefined time range. This traffic model is called segmented or noncontinuous sliding window scheduled traffic model [37]. It adds another degree of flexibility that can be exploited by various resource allocation techniques. In this work, we have not considered the issue of fault tolerance. In the future, an attack aware RWA for the scheduled traffic model with dedicated and/or shared path protection can be implemented.
Notes
Acknowledgements
The work of A. Jaekel has been supported by research Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC).
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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