Statistical analysis and market modeling of dynamic resource provisioning in elastic optical networks / Adriana de Nazaré Farias da Rosa. Simulated blocking probabilities for the different blocking events are provided for a larger scale node- and network-wise operation scenario in elastic optical networks.
Motivation of the Thesis
Since they are compatible with the already established 50 GHz ITU network, the need to change the network has not yet arisen. Unfortunately, the spectral width occupied by 400 Gb/s using reasonable modulation formats is too wide to fit the ITU-T 50 GHz network, and forcing it to fit by adopting a higher spectral efficiency modulation format would only allow short transmission distances [11]. ].
Challenges and Contributions
However, due to the high complexity of the model performance, evaluation was only possible using simulations. In this regard, the analytical study of the effect of fragmentation on the probability of request blocking is presented.
Outline of the Thesis
For the latter, we propose new event blocking classifiers that we use below to statistically analyze the performance of different SA schemes. Finally, the new definitions of event blocking are applied to the analysis of dynamic resource provisioning in an elastic optical network scenario.
Evolution of Optical Nodes and Networks
In the early 2000s, the micro-electromechanical system (MEMS) switches were introduced, which provided lower insertion loss and better scalability [39]. In the hierarchical version of MC-OXC, it is possible to switch the content of an entire fiber using a single cross-connection (ie, fiber switching).
State-of-the-Art of Optical Nodes and Networks
High Capacity Transmission
Other types of functionality can also add flexibility to the system, e.g. wavelength, conversion, regeneration, etc. In ROADM architectures, however, it is difficult to introduce additional functionality for the through traffic, since several wavelengths are exchanged simultaneously on the same port.
High Speed Channel Generation
- Nyquist WDM
- Coherent Optical Orthogonal Frequency-Division Multi-
However, as can be deduced from (2.3), the wider the window, the more constrained the left term in the convolution in (2.4) becomes. As can be seen, within the OFDM symbol period, all sinusoidal carrier pulses have their full periods.
Optical Networks that Provide Dynamic Bandwidth
In a mixed line rate network, transceivers with dynamic bit rate and modulation format can provide redundancy for multiple fixed transceivers, e.g. Therefore, when the OSNR of a given channel deteriorates, the control plane initiates a modulation format change to a more robust scheme, which typically also requires more spectrum. Conversely, when the OSNR channel improves, the control plane switches the modulation format back to one that is more efficient and requires less spectrum.
Need for Elastic Spectrum Allocation
A key enabler of dynamic bandwidth provisioning is the advent of bandwidth variable transceivers, which can adjust their bit rate and modulation format according to requirements. Single-carrier and multicarrier systems can also adjust modulation formats to increase or decrease the number of bits per symbol. In this way, elastic spectrum allocation can be used to adjust allocated bandwidths according to channels' requirements.
Progress toward Elastic Spectrum Allocation
In addition, bit rates above 100G are unlikely to fit into a 50 GHz channel, as this would require more complex multilevel modulation formats with higher OSNR requirements and thus shorter range. These channels are not supported by the current optical network infrastructure designed to comply with the standard 50 GHz or 100 GHz network. For example, OXCs and ROADMs only allocate discrete 50 GHz slots of bandwidth due to their internal WDM (de-)multiplexers.
Issues and Challenges in Elastic Optical Networking
A frequency slot is defined by its nominal central frequency in the entire spectrum range and its slot width. This means that the central frequency can be shifted in the C-band in 6.25 GHz steps. In the next chapter, we will discuss in more detail issues involving the design and optimization of elastic optical networks.
Design Scope Aspects of Networking Optimization
Efficient spectrum allocation schemes, discussed in the following subsection 3.3.1, can be used to minimize blocking of new connection requests in the context of spectrum fragmentation. Mathematical optimization methods such as integer linear programming (ILP) and Markov modeling can be used. In this case, optimality may be sacrificed to reduce the computation time.
Dynamic Resource Provisioning in EONs: Definition and Complexity
Routing and Spectrum Allocation (RSA) Problem
Furthermore, unlike the fixed network WDM network, where the guard band frequencies are pre-assigned and fixed, the guard bands in EON can be any of the subcarriers and are determined during the process of spectrum path establishment. However, unlike the successive subcarriers of a spectrum path, the grouped wavelengths can originate from different node pairs that share at least one common fiber [74]. The subcarriers with index 1 and 2 are assigned to SP1, which requires two adjacent slots.
Off-line and On-line Approaches
In the following, we formally define the routing and spectrum allocation (RSA) problem in the case of off-line (static) and on-line (dynamic) approaches. To mitigate the effects of spectrum fragmentation, spectrum defragmentation strategies have been proposed in the literature [76, 77]. Therefore, spectrum allocation (SA) schemes have been proposed to reduce fragmentation in the optical spectrum.
Spectrum Fragmentation Problem
Spectrum Allocation (SA) Policies
Based on this, in [35] we proposed a new spectrum allocation policy called Exact-Fit; and compare it with the existing ones in terms of average BP and fragmentation based on an analytical modeling approach for flexible spectrum allocation under dynamic traffic conditions. First-Fit (FF): the First-Fit policy places the request in the first available frequency band large enough to meet the demand;. Smallest-Fit (SF): this policy allocates the smallest free block, thus filling gaps to reduce fragmentation;.
Fragmentation Ratio Calculation
Exact-Fit (EF) [35]: Starting at the beginning of the frequency channel, EF searches for an available block with the number of slots equal to that required by the connection. Such a definition allows direct analysis of fragmentation as a function of the number of contiguous slots required by a connection request. The reason for this is that in the metric (3.1) F F and SF mostly do not affect the maximum interval of the free spectrum.
Markov Modeling
Continuous Time Markov Chains (CTMC)
As mentioned earlier, a system can be represented as a stochastic process by describing the range of different states that the system can occupy and by identifying the transitions that can occur between the different states of the system. The values that the random variable X(t) can take are called states, and the set of all possible values forms the state space of the process. The set of all states that can be reached from the initial state is called the set of reachable or possible states of the model.
Numerical Methods
- Jacobi Method
- Gauss-Seidel Method
- Successive Over-Relaxation (SOR) Method
- Sparse Equations and Least Squares (LSQR) Method
We now consider the iterative methods for the solution of the system of equationsAx=b, where A is a square of size n. Note that the new approximation of the solution vector is only calculated using the old approximation of the solution. The other advantage of the Gauss-Seidel algorithm is that it can be implemented with only one iteration vector.
Elastic SA Framework
State-Space Generation
In the pseudo-code, |S| denotes the size of S at any time, i.e. the number of current states in S. Thus, if NSA denotes the number of states for a given SA policy, we have |S| = NSA. To be able to track state transitions, each state si is attached with its parent states, i.e. the states that can transition to si, as attributes.
Transition-Rate Matrix Generation and Steady-State Probabilities . 58
For a given statesi ∈S, PcR(si) indicates the probability that a specific request of type c, that is, requiring nc slots, cannot be satisfied due to a lack of resource. It can be calculated based on the number of free or idle slots (#idleslots) in a state si as. 4.31) By summing these probabilities weighted by the probabilities of being in these states, we obtain the blocking probability BPcR(si), due to lack of resources, for a specific. The BP due to spectrum fragmentation, for a specific incoming connection type c, can be calculated by summing the probabilities PcF(si) weighted by the steady-state probabilities of being in these states, as expressed in (4.34 ).
Performance Results of Node-Wise Modeling
Spectrum Fragmentation Analysis
14 shows the average spectrum fragmentation according to (3.3), which relates the combination of both internal and external, as defined in (3.4) and (3.5), to the amount of currently free resources. The fragmentation metric defined in (3.2) relates the number of slots requested for a given connection, and the number of such requests that can be accepted before congestion occurs, to the total number of free slots on the connection. The main contribution to fragmentation in the case of Random-Fit, which shows the worst average fragmentation performance, is mainly due to the requirements for a large number of slots.
Blocking Probability Analysis
This is not what one would expect from the observation of fragmentation performance over load. For the scenarios considered, it appears that beyond a certain load (about 3.5 to 4 Erlang), the contribution to BP of larger requests is independent of the system load. It seems that for higher loads, the blocking of larger requests becomes much more secure and therefore more or less constant, whereas the service availability for smaller requests only decreases with increased load.
Resource- and Fragmentation-Blocking Analysis
This interrelationship between BP due to lack of resources and fragmentation for Random-Fit is shown in Figure. Comparing the magnitude of BP due to lack of resources and fragmentation, one can see in Figure 20(d) at a burden less than 1 Erlang BP due to lack of resources is similar for all SA policies.
Monte Carlo Simulation
20(c), where the transition point in BP is already at a relatively low load due to two different blocking reasons and is therefore not very pronounced compared to the Random-SA policy. In case of arrival events, slot allocation to connection requests is done according to the SA policy in question. This suggests that the analysis of the dynamic behavior of small-scale EOLs can already provide useful information on spectrum occupancy and performance measures in terms of blocking and fragmentation of larger-scale EOLs.
Performance Results of Network-Wise Modeling
Description of the Network
Description of the Simulation
For the simulations performed, the number of required spectrum slots for each light path is randomly selected from the set of (n1, n2, n slots. The procedure to derive the BP for our network evaluation is similar to that of the link evaluation, section 5.2 The occurrence of each blocking event type is tracked by individual counters and is related to the number of arrival events.
Results
As we can see, both SA policies show the same behavior as found in our evaluation for small-scale link modeling (see Fig. Note that the load for the network scenario should be significantly higher than for the model of 30-slot connection On the other hand, the considered sizes of requests in the case of network modeling are much more granular, compared to the amount of resources, when compared to link modeling.
Conclusion
Our study of the effect of fragmentation on request blocking probability also concludes that only the fragmentation ratio analysis is not sufficient to make the decision about when it may be beneficial to perform the defragmentation process, since the fragmentation ratio does not always reflect the blocking performance. Therefore, the decision to initiate a defragmentation process to reduce blocking probability should be based on the relationship between blocking probability, spectrum fragmentation, and requested bandwidths. Our Monte Carlo simulation, on the other hand, can be easily adapted to analyze more complex network topologies.
Future Research
InOptical Fiber Communication Conference and Exposition (OFC/NFOEC), 2012 en die National Fiber Optic Engineers Conference, bladsye 1–3, Maart 2012. In Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2012 en die Nasionale Fiber Optic Engineers Conference , bladsye 1–3, Maart 2012. In Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 en die National Fiber Optic Engineers Conference, bladsye 1–3, Maart 2011.
