Performance analysis of elastic optical networks (EONs) switches under unicast traffic
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Abstract
Bandwidth variablewavelength cross connect switches (BVWXCs) play an important role in the routing and spectrum assignment (RSA) problem in elastic optical networks (EONs). These switches, whose structure has been derived from micro electro mechanical systems technology, aim to switch the incoming traffic flexibly such that the existing resources are not wasted and more requests can be served. There exist different quality of service parameters which have to be provided in EON, such as delay, loss, jitter, and so forth. Among these parameters, blocking probability (BP) has been always taken into account in EON and several researches have been done to address it. The main objective of most RSA algorithms is to alleviate BP of requests through efficient usage of resources, such as frequency slots and BVWXC ports. To show the importance of BVWXC in routing and resource assignment in EON, its performance is analyzed in this paper. The BP of the BVWXC is evaluated by means of an analytical model under unicast traffic and the obtained results are compared to the blocking probability results acquired from simulations for different number of input/output ports and available resources. The obtained results show that the analytical model has a good agreement with the simulation results.
Keywords
Elastic optical networks (EONs) Bandwidth variablewavelength cross connect switch (BVWXC) Unicast traffic Blocking probability (BP)1 Introduction
The existing optical networks are divided into fixedgrid and flexgrid networks, where each of them has its own infrastructure. Fixedgrid networks, also known as wavelength division multiplexing (WDM) networks, are constructed based on wavelength, while the basis of flexgrid networks, named elastic optical networks (EONs), is spectrum. The nature of spectrum is flexible so that each spectrum can be divided into a set of frequency slots (FSs). Consequently, EON is a fine granular network whose flexibility is more than WDM in terms of resource assignment. In EON, if the size of a demand is less or more than the capacity of a spectrum, the network can assign resources to the demands, flexibly and hence, avoid resource wasting [1, 2].
The granularity of the EON is derived from FSs. Indeed, since the size of each FS can be 6.25 GHz, 12.5 GHz and 25 GHz, its granularity is better than the DWDM ITUT grid, where the size of its resources is constant [2].
Continuity and contiguity are two main constraints in assigning the FSs to the incoming requests. The continuity constraint implies that the assigned FSs to a request have to be free on all links of a lightpath; and based on the contiguity constraint, these FSs must be contiguous in all links of that lightpath. For preventing from collision of the assigned FSs to the requests, guardband (GB) is used between each two requests to separate them [2].
EON is a connectionbased network, where each request has its own source, destination, size and holding time (duration). Size of each request denotes the required number of FSs which are assigned to that request. If the BVWXC can find appropriate resources, it assigns the resources to the request. Otherwise, the request is blocked [2, 3].
In this paper, for the first time, we present a new analytical model for BVWXC performance under unicast traffic. We evaluate the blocking probability (BP) of BVWXC by means of this analytical model. The performance analysis is performed for different input/output ports and various amount of available resources. The network model is presented in Sect. 2. Section 3 provides a description for BVWXC. Traffic model is represented in Sect. 4. Section 5 illustrates the unicast scenario. The analytical model for BVWXC performance is introduced in Sect. 6. Section 7 includes future work. Finally, Sect. 8 concludes this paper.
2 Network model
3 Elastic optical network (EON) switches
Notations used for cost modeling
\(C_\mathrm{MD}\)  Complexity of multiplexers–demultiplexers 
\(C_\mathrm{Split}\)  Complexity of splitter 
\(C_\mathrm{TXRX}\)  Complexity of BVtransmitters and BVreceivers 
\(C_\mathrm{WXC}\)  Complexity of wavelength crossconnect 
k  A coefficient to consider effect of bandwidth variable feature 
f  Multicasting parameter 
G  Size of a guard band 
L  Size of a request or slot block 
M  Number of slot blocks in each link 
N  Number of input/output ports in BVWXC 
\(N_\mathrm{b}\)  Number of blocked requests 
\(N_\mathrm{f}\)  Number of frequency slots on each link 
\(N_\mathrm{g}\)  Number of guard bands on each link 
\(N_\mathrm{o}\)  Total number of offered requests 
\(N_\mathrm{sw}\)  Total number of switches 
P  Blocking probability 
\(P_\mathrm{sw}\)  The probability of selecting a switch 
p  The probability that a request is directed to a given output channel 
R  All number of incoming requests 
S  Number of data spectrums on each fiber 
\(u_{0}\)  The probability that a request arrives at a given input channel 
V  Average number of output fibers to which a request is directed 

Multiplexer and demultiplexer complexity (\(C_\mathrm{MD}\)): the complexity of MUX or DEMUX for S spectrums equals to \(C_\mathrm{MD} = ({S}  1)\) [1].

Splitter complexity (\(C_\mathrm{Split}\)): there is one splitter in the front of each link or input, which broadcasts input fiber to other BVWSSs. Therefore, in a BVWXC, there are N splitters [1].

BVtransponder and BVreceiver complexity (\(C_\mathrm{TXRX}\)): there are S BVtransmitters and \(S \) BVreceivers in a BVWXC for local ports. Moreover, the BV feature affects the complexity. Hence, for a BVWXC, the complexities of BVtransmitters and BVreceivers are calculated as \(C_\mathrm{TXRX} = k \times S \), where \(k \) is a weight coefficient to show the effect of BV [1].
 BVWSS complexity (\(C_\mathrm{BVWSS}\)): there are \(N + 2\) number of (\(M * 1\)) BVWSSs in a BVWXC [7]. It is assumed that a BVWSS switch is based on the Clos (2) switch architecture [11] that uses \((\mathrm{input}\_\mathrm{numbers}  1)\) switching elements. As mentioned before, there are \(S \) switches in a BVWSS, \(M \) demultiplexers, one multiplexer and \(S \) VOAs. Hence, the cost of a BVWSS is calculated as Eq. (1) [1]:$$\begin{aligned} C_\mathrm{BVWSS} = N\times C_\mathrm{MD} + S\times C_\mathrm{SE} + S\times C_\mathrm{VOA}. \end{aligned}$$(1)
4 Traffic modeling
We assume that each request arrives independently on the \(MN \) number of SBs. In our analysis, we consider unicast traffic, where an arriving request can be directed only to one output fiber (OF) and this event occurs with probability \(p \). Since all OFs have equal probability, \(p \) equals 1.
5 Dimensioning models of the EON switches under unicast traffic (\(V = 1\) )
When a request arrives at a BVWXC, the BVWXC finds the OF that the request has to be directed to it and checks the available SBs on that OF. If there is an available SB on the OF, the BVWXC assigns the SB to the request. Otherwise, the request is blocked. In this section, we calculate the blocking probability of the arriving requests at the BVWXC.
6 Numerical results
In this section, we compare the obtained results from simulations and the analytical model. In the simulations, we assume that the traffic is symmetric to all output fibers in each switch. Each request is generated according to Erlang distribution for \(\mathrm{Load}~=~800\), where the holding time of each request (\(H \)) is set to 5 s. In addition, we calculate the blocking probability for \(N_\mathrm{sw}~=~1\). The sizes of GBs and SBs are 2 FSs and 20 FSs, respectively. There are two scenarios, where in the first scenario, we have \(N = 4\), \(N_\mathrm{f} = \{20,~42,~64,~86\}\), and hence, \(M = \{1,~2,~3,~4\}\). In the second scenario, we have \(N = 8\), \(N_\mathrm{f} = \{86,~108,~130,~152\}\), and hence, \(M = \{4,~5,~6,~7\}\). In the following diagrams, each point in every diagram is the average taken from ten replication scenarios, with 95% confidence intervals within at most \(5\%\) of the mean values. Figure 4a, b show the results of both simulation and analytical model in the first and second scenarios, respectively. As seen in these figures, the analytical model is in very good agreement with simulation results, specially at high values of \(M \).
7 Future works
In this paper, we have presented an analytical model for BVWXC under unicast traffic. However, multicast traffic and broadcast traffic have not been considered. Each of these traffic has its special conditions which their performance can be analyzed as future works.
8 Conclusion
In this paper, we have discussed an EON switch that is BVWXC, calculated the complexity of BVWXC, and presented an analytical model for BVWXC under unicast traffic. Obtained results from both simulations and proposed analytical model show that the presented analytical model has a good agreement with the simulation results.
Notes
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