HCIS

• Home
• About
• Articles
• Submission

Over a number of years the ever-increasing growth of traffic transferred over the internet has become a common pattern. This particular trend was made even more discernible in 2020 when it was a common practice to use videoconferencing and other services that provide the possibility of distributed group work. This increasing use of the network is also related to the fast growing of data centers in different parts of the globe that more and more often apply dynamic applications, i.e., data center synchronization and backup. A large number of the aforementioned services require copies of the same data to be sent to different places in the network. Effective traffic distribution of such traffic, particularly important for dynamic applications, can be provided, for example, by multicast transmission offered by elastic optical networks (EONs). Therefore, the provision of the full service of multicast traffic should also include the nodes of an EON network. This article attempts to solve the problem of the distribution of these traffic streams in nodes of elastic optical networks. The article proposes a model of a node of this type. The model of an appropriate node is proposed along with a research study of its effectiveness with respect to traffic efficiency measured by the call blocking probability. The study assumes that the internal structure of the node is the one based on the so-called Clos network. The accompanying assumption is that the node can service mixtures of different streams of multiservice traffic. The results of the study are presented for two systems and four possible scenarios of traffic branching.

Elastic Optical Networks, Frequency Slot Unit, Multicast Connections, Switching Networks, Traffic Management

Over the past years a continuous increase in the amount of traffic transmitted over the Internet has been clearly observable. This increase has been brought about not only by the increased number of users that make use of the network, but mainly results from the dynamic increase in the interest in services that require transfer of a large amount of data [1, 2]. A significant part of these services include cloud services and services related to video streaming [3]. This trend became even more apparent in 2020, in which it was more and more common to use videoconferencing services and other services that provided possibilities of distributed group work. The ever-increasing use of the network is also related to the fast growing data centers in different parts of the world that more and more frequently make use of dynamic applications, i.e., data center synchronization and backup [4, 5]. A large number of the above services require copies of the same data to be transmitted to different places in the world. Effective traffic distribution of this traffic, particularly significant for dynamic applications, can be provided by, for example, multicast transmission within elastic optical networks (EONs) [6, 7].
Over the recent years a large number of publications addressed the problem of effective, including dynamic, setting up of multicast sessions in EONs [6–15]. The most recent works (e.g., [14]) propose the application of ML methods for dynamic managements of sessions. As it is stated in the recommendations concerning the structuring (building) of data centers and the provision of communication between them, the developing trends tend to indicate the growing significance of the entirely optical communications between data centers, and possibly even within data centers themselves [16]. As a result, the provision of a full (and all-round) service of multicast traffic should also include the nodes of EON networks [17].
This article attempts to solve the problem of the distribution of such traffic streams in a node of EONs. The issue of the traffic analysis of the structure of blocking EON nodes that service multiservice multicast traffic has not been, to the best belief of the present authors, addressed in the works of other authors. The present article presents the results of a research study on the determination of the value of the loss probability for traffic calls offered in EON networks, in which part of calls is that of the multicast type. In addition, an analysis is made of the share of the external loss probability in the total losses for calls of individual traffic classes in nodes of EON networks.
The article is divided into eight parts. The first part of the article presents the structure of nodes in EONs (Section 2) and the structure of traffic offered to them (Section 3). The following section presents the path choice algorithm in the network (Section 4) and the structure of the simulation environment that was used to perform the study (Section 5). The next section provides a discussion on the obtained results. The article is concluded with a brief summary that includes a juxtaposition of the most important results and a proposition of the direction of further research on the subject.

Fig. 1. Structure of three-stage W-S-W Clos switching network.

The structures of EON networks can take on different forms and types. One of the most common structures of switching networks, within which connections in the nodes of EON networks are executed is the three-stage W-S-W network with Clos structure [15, 18–20] (Fig. 1). The switching network under consideration is composed of a number of square switches with υ inputs and υ outputs. In each of the three stages of the considered network there are υ switches. The input, output and inter-stage links of the considered W-S-W network have their capacities equal to $f$ frequency slot unites (FSUs) each [21–25]. In addition, output links of the switches of the last stage are organised in directions. A direction includes one link of each output link of each switch of the third stage.
If we look more closely into the structure of the W-S-W network, it is observable that the first and the third stage of the network are composed using bandwidth-variable wavelength converting switches (BV-WSs) [15, 20] (Fig. 2). Whereas the second stage of the network is built using bandwidth-variable wavelength selective space switches (BV-SSs) [15, 20] (Fig. 3).

Fig. 2. Structure of bandwidth-variable wavelength converting switch.
BV-WSS=bandwidth variable wavelength selective switch, TWBC=tunable waveband converter, PC=passive combiner.

Fig. 3. Structure of bandwidth-variable wavelength selective space switch.
BV-WSS=bandwidth variable wavelength selective switch, PC=passive combiner.

The switches used to construct the first and the third stages make it possible to change both the wavelength and an output link (optical fibre). In the case of the switches of the second stage, only a change in the output link is possible, whereas the wavelength remains unchanged.

The inputs of a node of EON networks are offered traffic that is composed of calls generated by Erlang traffic sources. Calls can belong to different service classes. In turn, each traffic class is defined by a different requirement for transmission rate (bit rate), and what follows a different number of demanded FSUs for a given call to be serviced.
Therefore, each traffic class whose calls create an Erlang traffic stream can be defined by the following parameters:

In the case of an Erlang traffic stream, the intensity of new call arrival does not change along with a change in the load (occupancy state) in the system. In the further stages of the research, the present authors also plan to introduce services of other types of traffic stream to the simulation program, including Engset and Pascal traffic streams. In the case of Engset and Pascal traffic streams, the intensity of new call arrivals in the system will be dependent on the occupancy state of this system.

Because of the fact that in the node of an EON network not only unicast connections but also multicast connections will arrive, it is necessary to introduce an additional parameter that would describe particular traffic classes. The parameter $q_i$ will determine the number of directions demanded by calls of class $i$.
The assumption in the developed simulation program is that the method for the choice of connecting path in the switching network will be in compliance with the point-to-point selection algorithm [26–28]. The algorithm that controls setting up unicast connections in the point-to-point selection mode operates as follows: first, the algorithm registers the input link where a call of a given class i arrives, that requires $t_i$ unoccupied (free), neighbouring FSUs in each link of the connection path in the switching network. Then, the algorithm pseudo-randomly chooses one switch in the last stage that has an unoccupied (free) output link (i.e., a link that has $t_i$ unoccupied, neighbouring FSUs) in the direction demanded by the call. If the demanded direction does not have any unoccupied links for the call of class i, then this call will be rejected due to the occurrence of the external blocking phenomenon. In the case when a free output link does exist, the control algorithm attempts to set up a connecting path in the switching network between the registered input switch (in the first stage) and an output switch (of the last stage). If this path can be found, the algorithm can set up a connection. Otherwise, this call will be rejected due to the occurrence of the internal blocking phenomenon.
The execution of a multicast connection in the point-to-point selection mode in the multiservice switching network (Fig. 1) can be described by the following assumptions:
switching network services different streams of multiservice traffic, including multicast traffic,

The node simulator of nodes in an EON network that makes a simulation of switching networks with multicast connections possible was implemented in the C++ language, using the object programming technique and the process interaction method [29]. The designed simulator allows the value of the loss probability (total, internal and external) in optical switching networks with multicast connections service in the point-to-point selection mode to be determined. The simulator was written in such a way as to facilitate its further improvement in new functionalities, analysis of new structures of switching networks, service of new types of traffic streams, and implementation of new calls admission control mechanisms. In further stages of the research work, the present authors intend to develop and improve the possibilities of the presented simulation program and plan a publication of new results of the research work. In the future, this simulator will be also used to verify developed analytical models that would allow traffic characteristics of optical switching networks with multicast connections to be determined. In the nearest future, the authors intend to develop and then publish methods that would make it possible to determine the loss probability in such systems analytically.

The simulator of nodes in EON networks makes it possible to determine the loss probability for unicast and multicast calls of individual traffic classes. Each class in the simulator has to be appropriately defined by a number of parameters. These parameters are then fed to the simulator in an appropriately prepared text file. Beside the parameters that relate to the traffic classes offered to the system, the system also receives parameters that define the structure of the network and the capacities of individual input links, inter-stage and output links.
Therefore, for the simulation program to be properly operated the following parameters are to be given: On the basis of the values of the parameters that can be fed to the simulator, the intensity of new calls arrival of new calls of class i in the system can be determined:

$\displaystyle\sum_{i=0}^C A_i t_i=aυυf,$(1)

where the intensity of traffic offered by calls of class i is $A_i=λ_i/μ_i$. In addition, with the assumption of the traffic proportion $A_1 t_1:A_2 t_2: …∶A_i t_i:…∶A_C t_C=1:1:…∶1:…:1$ , we can present the formula that determines the parameter $λ_i$ of the intensity of new call arrival for calls of class $i$ in the following form:

$λ_i=\frac{aυυf}{μ_i^{-1} C}.$(2)

In the implementation process for the simulator using the process interaction method, two events were defined: “arrival of a new call” and “termination of call service.” In the case of the event “arrival of a new call,” it is checked whether a new call can be admitted for service. If it is possible, then the resources of the system will begin to be occupied, if it is not, the call is lost. The event “termination of call service” means that service of a given call has terminated and the system resources should be released. The execution of the service of these events in the simulation program is performed using appropriate functions. These functions are thoroughly discussed in other publications [26, 27], whereas the general block scheme of the simulation algorithm is shown in Fig. 4.

Fig. 4. Main simulation algorithm.

The simulation program makes it possible to determine the loss probability that can be calculated as the quotient of the number of lost calls lost by the number of generated calls. Consequently, the number of generated calls of the least active class, i.e., the class whose calls are generated with the least intensity, was adopted as the termination condition. The final result for a given set of input parameters is determined as the arithmetic mean, with five series of simulations. In addition, 95% confidence intervals are determined, and in practice do not exceed 5% of the average value. In practice, for this purpose it is necessary to generate the maximum number of 10,000,000 calls of the class with the lowest value of call intensity.

The simulation experiments were performed for the systems whose parameters are shown in Table 1.

Table 1. Parameters of studies systems

	System 1	System 2
Number of inputs/outputs in single switch	$v$ = 4	$v$ = 4
Capacity of single link	$f$=320 FSUs	$f$=320 FSUs
Number of traffic classes	$C$ = 3	$C$ = 4
Number of required FSUs	$t_1$=5 FSUs $t_2$=10 FSUs $t_3$=20 FSUs	$t_1$=12 FSUs $t_2$=15 FSUs $t_3$=20 FSUs $t_4$=30 FSUs

In EON networks, the channel width changes dynamically according to the requirements related to bit rate (transmission speed) required for a given service to be executed in the network [30]. This helps improve the spectral efficiency, lowers the waste of the spectrum and effects in a better use of spectral resources. Therefore, depending on the required bit rate related to a given class of services, an appropriate number of the spectrum units has to be allocated. The number of allocated FSUs is also influenced by the applied modulation technique [21–25]. The choice of the appropriate number of demanded FSUs for the systems under investigation was based on the data included in Table 2.
The results of the simulation (Figs. 5–11) are presented in the graphs in the form of plotted points with confidence intervals calculated after the t-Student distribution (with 95% confidence level) for five series with 1,000,000 calls (of the least active class) each. The confidence intervals were determined on the basis of the following formula:

$(\overline X - t_α \frac{σ}{\sqrt{d}}; \overline X + t_α \frac{σ}{\sqrt{d}}),$(3)

where $\overline X$ ̅is the arithmetic average calculated from d results (simulation runs), $t_α$ is the value of the t-Student distribution for d-1 degrees of freedom. The parameter $σ$, that determines the standard deviation, is then calculated after the following formula:

$σ^2=]frac{1}{d-1} \displaystyle\sum_{s=1}^d x_s^2 - \frac{d}{d-1} \overline X^2,$(4)

where $x_s$ is the result obtained in the s-th run of the simulation.

Table 2. Number of FSUs in different connections depending on required bit rate and modulation format

Number of FSUs	Bit rate (Gbps)	Modulation format
1	40	64-QAM
1	40	32-QAM
1	40	16-QAM
2	40	QPSK
2	100	64-QAM
2	100	32-QAM
3	100	16-QAM
5	100	QPSK
3	160	64-QAM
4	160	32-QAM
4	160	16-QAM
8	160	QPSK
7	400	64-QAM
8	400	32-QAM
10	400	16-QAM
20	400	QPSK
10	600	64-QAM
12	600	32-QAM
15	600	16-QAM
30	600	QPSK

Source from [20].

Fig. 5. Total loss probability for class 1 calls in System 1.

Fig. 6. Total loss probability for class 2 calls in System 1.

Fig. 7. Total loss probability for class 3 calls in System 1.

In addition, Tables 3 and 4 show a comparison of the total blocking probability and the external blocking probability for calls of given traffic classes. Due to the limited capacity of this article the presentation of the values of the confidence intervals for individual results has been omitted. However, the length of the simulation was matched in such a way as for these confidence intervals not to be higher than 5% of the average value (of the result) presented in Tables 3 and 4.
Figs. 5–7 show the values of the total loss probability for traffic calls in System 1. Class 3 in System 1 generates multicast traffic. It can be observable then that the loss probability dynamically increases along with an increase in the number of demanded output directions. In the case of the remaining classes, i.e., the classes that generate unicast traffic, we can observe opposite situation with the increase in the load of the system.

Table 3. Total and external loss probabilities for class 1 calls in System 2

	Total loss probability				External loss probability
	$q$=1	$q$=2	$q$=3	$q$=4	$q$=1	$q$=2	$q$=3	$q$=4
$a$ = 0.6	0.00026	0.00388	0.05729	0.16211	0.00001	0.00386	0.05729	0.16211
$a$ = 0.7	0.00201	0.02033	0.12933	0.25498	0.00009	0.02022	0.12933	0.25498
$a$ = 0.8	0.006	0.0517	0.20453	0.33558	0.0003	0.05153	0.20453	0.33558
$a$ = 0.9	0.01239	0.09297	0.27497	0.404	0.00068	0.0928	0.27497	0.404
$a$ = 1.0	0.02108	0.13803	0.33748	0.46179	0.00117	0.13787	0.33748	0.46179
$a$ = 1.1	0.032	0.18428	0.39247	0.51092	0.00188	0.18413	0.39247	0.51092
$a$ = 1.2	0.04451	0.22837	0.44148	0.55295	0.00275	0.22826	0.44148	0.55295

Table 4. Total and external loss probabilities for class 4 calls in System 2

	Total loss probability				External loss probability
	$q$=1	$q$=2	$q$=3	$q$=4	$q$=1	$q$=2	$q$=3	$q$=4
$a$ = 0.6	0.04429	0.12572	0.35644	0.51089	0.00563	0.11857	0.35641	0.51089
$a$ = 0.7	0.2142	0.33861	0.55815	0.65722	0.0249	0.3151	0.55811	0.65722
$a$ = 0.8	0.41212	0.53322	0.68977	0.74715	0.05312	0.50558	0.68974	0.74715
$a$ = 0.9	0.57224	0.672	0.77315	0.80512	0.08555	0.64948	0.77313	0.80512
$a$ = 1.0	0.68799	0.76394	0.82729	0.844	0.12015	0.74756	0.82727	0.844
$a$ = 1.1	0.77017	0.82618	0.86321	0.87144	0.15536	0.81475	0.86319	0.87144
$a$ = 1.2	0.82844	0.86757	0.88928	0.89201	0.19247	0.85955	0.88926	0.89201

A different situation is observed for System 2 (Figs. 8–11), in which the class that demands the lowest number of FSUs to set up a connection, generates multicast calls. For all classes, we can observe an increase in the loss probability for calls. Whereas the most rapid increase can be observed for class 1 (i.e., the one that generates multicast traffic).
Additionally, for both systems, as the number of output directions demanded by the calls of classes that generate multicast traffic increases we can also observe an increase in the share of the external loss probability in the total losses (Tables 3 and 4). This phenomenon results from the fact that the propagation (distribution) of traffic takes place as late as the third stage of the switching network (node of EON network).

Fig. 8. Total loss probability for class 1 calls in System 2.

Fig. 9. Total loss probability for class 2 calls in System 2.

Fig. 10. Total loss probability for class 3 calls in System 2.

Fig. 11. Total loss probability for class 4 calls in System 2.

Due to the limited capacity of the article, the results are presented for two systems only. The authors though made analyses of a larger number of systems that confirmed the dependencies described for the systems presented in the article.

This article presents the results of a research study that investigated methods for a determination of the value of the loss probability for calls of traffic classes offered in EON networks, in which part of calls is that of multicast flows. An analysis is made of the share of the external loss probability in the total losses for calls of individual traffic classes in nodes of EON networks. In the future, the present authors intend to develop a number of analytical methods for a determination of the loss probability in EON networks with Clos structure in which both unicast and multicast calls are serviced, while the developed simulator will be used as a verification tool for these methods.

Not applicable.

Conceptualization, MS, PZ. Methodology, PZ. Software, MS. Validation, EL, MS, PZ. Formal analysis, EL. Investigation, MS. Resources, EL. Writing—original draft preparation, MS, PZ. Writing—review and editing, MS. Visualization, MS. Supervision, PZ. Project administration, EL. Funding acquisition, PZ. All authors have read and agreed to the published version of the manuscript.

This research was funded in part by the Polish Ministry of Science and Higher Education (No. 0313/SBAD/1305 and 0313/SBAD/1304). The APC was funded by Polish Ministry of Science and Higher Education.

The authors declare that they have no competing interests.

Maciej Sobieraj received his master's degree in electronics and telecommunications from Poznan University of Technology, Poland, in 2008. Then, in 2014, he obtained a Ph.D. degree in the field of telecommunication networks. Since 2007 he has been working at Poznan University of Technology, Poland, first at the Chair of Communications and Computer Networks at the Faculty of Electronics and Telecommunications, and then, since 2019, at the Institute of Communications and Computer Networks at the Faculty of Computing and Telecommunications. He is the co-author of more than 50 scientific papers. Maciej Sobieraj is engaged in research in the area of modeling multi-service cellular systems and switching networks and traffic engineering in TCP/IP networks. In recent years, Dr. Sobieraj has been involved in research related to elastic optical networks.


Piotr Zwierzykowski received his master's degree in telecommunications from Poznan University of Technology, Poland, in 1995, and then a Ph. D. degree (with honours) and D.Sc. degree in telecommunications from the same university in 2002 and 2015, respectively. Since 1995, Piotr has been working at Poznan University of Technology, Poland, first at the Institute of Electronics and Telecommunications at the Faculty of Electrical Engineering, and then, since 2005, at the Chair of Communications and Computer Networks at the Faculty of Electronics and Telecommunications and since 2019, at the Institute of Communications and Computer Networks at the Faculty of Computing and Telecommunications at Poznan University of Technology. Piotr Zwierzykowski is engaged in research and teaching activities in the field of analysis and modelling of multi-service switching systems and networks. Prof. Piotr Zwierzykowski is the author/co-author of more than 200 publications, including 4 books, 33 chapters in books, over 50 journal articles and more than 140 conference papers. Recently, Piotr has also been working as the Guest/Lead Editor for numerous journals published by Elsevier, Hindawi, IEICE, IET, MDPI and Wiley.


Erich Leitgeb received his M.Sc. and Ph.D. (with honours) at Graz University of Technology in 1994 and 1999, respectively. From 1982 to 1984, he attended the military service, including training to become an officer for communications in the Austrian army, and he is still active as an expert in military communications (current military rank: Lieutenant-Colonel). In 1994, he started research in optical communications at the Department of Communications and Wave Propagation (TU Graz). Since January 2000, he has been a project leader of international research projects in the field of optical communications, and he established and leads the research group for Optical Communications at TU Graz and joined several international projects (such as COST 270, COST 291, COST IC0802, the EU project SatNEx and SatNEx 2, and IC1101; currently, he participates in MP1401, CA15127, and CA16220) and ESA projects in different functions. Since 2011, he has been Professor of Optical Communications and Wireless Applications at the Institute of Microwave and Photonic Engineering at Graz University of Technology. Erich Leitgeb is the author or co-author of 7 book chapters, around 50 journal publications, 150 peer-reviewed conference papers, around 45 invited talks and more than 70 international scientific reports.