Simulation Studies of 3-Stage Clos Switching Network with Prioritization Mechanism Used in Flexible Wavelength-Division Multiplexing Network Nodes

Abstract

Given the escalating need for greater bandwidth, there is a growing interest in implementing mechanisms that ensure reliable and optimal service levels for specific traffic classes, especially during periods of heavy network traffic. One such mechanism is the prioritization mechanism, where certain portions of resources are exclusively allocated to predefined services. In the context of contemporary flexible WDM networks that employ advanced data transmission techniques, efforts have been made to create a simulation program capable of assessing the traffic characteristics of nodes within flexible WDM networks. This article presents a simulator of flexible WDM nodes with an implemented mechanism for prioritizing call classes. The simulator allows us to determine the loss probability for individual traffic classes in a switching network with point-to-point selection. In the simulator, the Clos structure was adopted as the structure of the flexible WDM network node due to its popularity in many studies and applications.

1. Introduction

The ever-increasing bandwidth demands of today’s data networks require increasingly urgent changes to the network infrastructure in terms of performance, scalability, and maintenance costs. The amount of data being transmitted over networks is constantly increasing due to the growing variety and popularity of the services they provide. A significant increase in traffic could be observed for online video meetings, video conferencing, voice and video streaming applications, and online games. There is a growing number of web users who use the web on a daily basis to interact with others for work, education, and entertainment. Expectations regarding the quality of services provided are also growing. Network services often differ significantly in terms of the required data rates necessary to provide an acceptable quality of service to the recipients. Therefore, in order to minimize the mismatch of required bit rates between the data streams associated with a specific service and the optical layer of the backbone network, it is necessary to appropriately allocate the available spectral resources for these services. Flexible WDM networks have the property of flexible bandwidth and adaptive channel interval [1], and the channel width can be dynamically changed according to the requirements of the transmission rate that is needed for a given service in the network. In the proposed flexible WDM network architecture, 12.5 GHz channel spacing granularity is used for channel allocation. Finally, flexible WDM network channel spacing is compared with a fixed grid network presented in [2]. This allows us to improve spectral efficiency, reduces spectrum wastage, and promotes better utilization of spectral resources. Thus, flexible WDM networks allow an appropriate number of frequency units to be allocated depending on the required bit rate associated with a particular class of service. These units are called frequency slot units (FSUs). Flexible WDM technology employs the concept of frequency slot units (FSUs) to designate the unit of bandwidth in the frequency domain. Assigning bandwidth to a data stream flexibly is achieved by utilizing a defined quantity of consecutive FSUs. Flexible WDM technology employs the concept of FSUs to designate the unit of bandwidth in the frequency domain. Assigning bandwidth to a data stream flexibly is achieved by utilizing a defined quantity of consecutive FSUs [3,4,5,6,7]. Research on frequency slots in the flexible WDM networks is presented in [8,9], among others. In the work [8], two slot selection algorithms are discussed and their efficiency is compared. The work [9], on the other hand, presents a study of the effect of the size of requests expressed in slots on the performance of a network described by different quality assessment parameters. It is worth noting that other factors affecting the number of frequency units (FSUs) allocated can also be distinguished, which include modulation technique, distance, and connection path quality [10,11,12,13,14,15]. In [10], a spectrum-efficient and scalable optical transport network architecture called SLICE is shown. The architecture enables spectrum-efficient sub-wavelength, superwavelength, and multiple-rate data traffic accommodation. The paper [11] proposes to extend the flexible WDM network analysis in the space domain (in addition to time and frequency). It describes algorithms for routing, spectrum, spatial mode, and modulation format assignment. The paper [12] presents a comprehensive view of the elements that compose the flexible WDM networks. Technological aspects of the physical layer, network optimization for the flexible WDM networks, and aspects related to the flexible WDM network control plane are described. Ref. [13] investigates the possibility of establishing an optical path in a flexible WDM networks environment with variable bandwidth, flexi-grid, and distance-adaptive OFDM physical layer capability. The paper [14] proposes a strategy for the gradual migration of flexible WDM networks operating on single-mode fiber towards spectrally-spatially-flexible optical networks (SS-FONs) using spatially-divided multiplexing (SDM) technology. The work uses novel planning heuristics. In [15] an ultra-dense wavelength-switched network (UD-WSN) architecture assuming no aggregation optical transport network (OTN) switches is considered. The implementation of partial OTN switching within the UD-WSN and spectrum defragmentation is proposed to improve the cost and spectral efficiency of the network, respectively.

Emphasis should be placed on the fact that 3-stage W-S-W (wavelength-space-wavelength) switching networks are among the most commonly utilized structures for switching networks in flexible WDM netorks [4,16].

The rest of this article is structured as follows. Section 2 presents a description of the structure of the blocking switching network in which traffic prioritization management mechanisms have been introduced. The section discusses the traffic structure (Section 2.1), the operation of the prioritization mechanisms (Section 2.2), and the structure of the switching network (Section 2.3). Section 3 is devoted to the simulation environment and presents exemplary results of the simulation studies, along with their interpretation. This article ends with Conclusions (Section 4), which presents the most important conclusions resulting from this study.

2. Structure of the System

2.1. Structure of Offered Traffic

In the case of multi-service switching networks, a comprehensive modeling approach involves the utilization of Erlang, Engset, and Pascal call streams [17,18], particularly focusing on Erlang-type traffic in this research. The switching network offered is Erlang traffic streams. Each traffic stream can be generated by calls of particular traffic classes pre-defined in the system. Each distinct traffic class is characterized by a set of parameters, delineating the specific nature of the service it represents. The key parameters defining a traffic class include:

• Index (class identifier): denoted as c, this index uniquely identifies and labels the traffic class, distinguishing it from others within the network;
• Arrival Intensity of New Calls: Represented by ${\lambda }_c$, this parameter signifies the rate at which new calls of the designated class appear in the system. It provides insight into the influx of demands for the particular service;
• FSU Demand: Indicated by $t_c$, this parameter encapsulates the demand associated with the traffic class. The FSU demand characterizes the resources required for processing and handling a single call of the specified class;
• Priority: Denoted as $p_c$, priority assigns a relative importance or precedence level to the traffic class. This parameter becomes crucial in scenarios where certain classes may have varying degrees of significance or urgency. The higher the $p_c$ is, the more important the class is, taking precedence over lower priority classes;
• Average Service Time: Inverse of ${\mu }_c$, this parameter is represented as ${\mu }_c^{-1}$ and quantifies the average time required to service a call from the designated class. ${\mu }_c$ is the parameter of the exponential distribution of service time.

The aggregate traffic in the multi-service network node, modeled by Clos structure 3-stage W-S-W network (refer to Figure 1), is a composite of these individual traffic classes, each defined by its unique combination of the aforementioned parameters. Through this delineation, this research aims to comprehensively understand and model the dynamics of Erlang-type traffic within the node, considering the diverse demands, priorities, and characteristics associated with different service classes. By focusing on Erlang-type traffic and systematically examining the specified parameters, the research contributes to a nuanced understanding of the network’s behavior and performance under various scenarios.

2.2. Structure of Switching Network

One of the commonly employed configurations for switching networks in flexible WDM networks is the 3-stage W-S-W network with a Clos structure (Figure 1) [19,20]. The switching network in question is comprised of square switches with $\upsilon$ inputs and $\upsilon$ outputs. Each of the three stages in the network consists of $\upsilon$ switches. Therefore, the total number of inputs to the field is equal to the number of outputs and is $\upsilon \times \upsilon$. The input, output, and inter-stage links in the considered W-S-W network have capacities of f FSUs. Additionally, the output links of the switches in the last stage are organized into directions, with each direction incorporating one output link with capacity f from each $\upsilon$ switch in the third stage. The output direction is treated as a group of links and the total capacity of a single direction is equal to $\upsilon f$ FSUs. The call will be processed by the resources of a given direction if the following two conditions are met: (1) finding the desired number of FSUs as neighbors, (2) finding and then occupying the required number of FSUs in single link.

A more precise characterization of the W-S-W network’s structure discloses that the first and third stages are formed with bandwidth-variable waveband-converting switches (BV-WBCSs) (Figure 2) [1,4,16], whereas the second stage employs bandwidth-variable waveband-selective space switches (BV-WBSSSs) (Figure 3) [1,16].

In the network, it was assumed that switches in the first and last stages could modify both the wavelength and the switch output (optical fiber). Another assumption specified that switches in the middle stage were restricted to altering the outgoing optical fiber only. Consequently, for a switch in the second stage, any modifications to the channel frequency were not feasible.

2.3. Handling Prioritized Traffic

In a system implementing prioritized call handling, a set of well-defined rules govern the allocation of resources and the processing of different traffic classes [21]. Each traffic class is systematically assigned a specific priority level, forming the foundation for the system’s hierarchical approach to call management. This prioritization framework is crucial for ensuring that the system can intelligently handle a diverse array of communication needs, ranging from routine calls to critical and time-sensitive transmissions.

One fundamental rule dictates that the handling of a call from a lower-priority class has no bearing on the probability of blocking calls from higher-priority classes. This key principle underscores the system’s commitment to treating calls of different priorities independently. In practical terms, this means that the processing of lower-priority calls does not compromise the resources and service quality for higher-priority calls, fostering a robust and reliable system for critical traffic. Moreover, the system incorporates a dynamic mechanism to address resource scarcity. In instances where the available resources are insufficient to accommodate incoming calls, the system takes into consideration the call priority. Higher-priority calls are granted precedence and may, if necessary, displace currently serviced calls with lower priority. This proactive approach ensures that the system adapts to changing demands in real time, safeguarding the uninterrupted provision of critical services even under resource constraints.

In summary, the prioritized call handling system is meticulously designed to allocate resources judiciously, taking into account the urgency and significance of different service needs. The ability to terminate lower-priority calls to prioritize higher-priority ones becomes a strategic feature, particularly in scenarios where certain tasks or services demand immediate attention and take precedence over others in the interest of overall system efficiency and effectiveness.

Within the Clos structure 3-stage W-S-W network nodes (Figure 1), the prioritized traffic rules are designed to seamlessly integrate with the point-to-point selection algorithm. The operational flow involves an initial attempt by the system to accept an incoming call without immediately applying priorities and their associated consequences. In other words, the model endeavors to process the call based on general criteria, prioritizing acceptance without initially factoring in the assigned priority levels. Should the initial attempt prove unsuccessful, the system then engages in a subsequent attempt, this time incorporating the prioritized traffic rules. In this phase, the system reevaluates the incoming call, taking into account its assigned priority level. The systems searches for lower priority calls to displace in order to provide enough resources for higher priority. Lower priority calls are treated equally as one group meaning that every lower priority call, no matter the priority relation between the calls in the group, can be displaced. This two-step process allows for a comprehensive and dynamic approach, wherein the system first aims for acceptance based on general criteria and only resorts to priority considerations if the initial attempt falls short. This nuanced strategy ensures a balanced and flexible approach to call processing within said network nodes, optimizing resource utilization and service quality in varying scenarios. The coexistence of point-to-point selection algorithm and priorities is shown in Figure 4.

3. Results

3.1. Simulator Implementation

The authors created a simulator for experiments, employing C++ language and object-oriented programming. The simulation model was developed using the process interaction method [22,23]. This simulator can calculate loss probability for specific traffic classes in considered systems with implemented prioritization mechanisms.

3.2. Input Data

The simulation program takes the system capacity as input data. Each traffic class is characterized by the number of demanded FSUs and the mean service time. Additionally, a parameter a is defined, representing the traffic offered to a single FSU. The simulation program determines the intensity parameter ${\lambda }_c$ based on these specified parameters:

$$\sum _{c=1}^m{\lambda }_c/{\mu }_c{t}_c=a\upsilon \upsilon f.$$

(1)

In Equation (1), the expression ${\lambda }_c/{\mu }_c$ determines the total traffic $A_c$ offered by class c calls. Therefore, by giving the value of a as input to the simulation, we can determine the total amount of traffic offered to the switching network, which is $a\upsilon \upsilon f$. Assuming the traffic proportion $A_1{t}_1:\cdots :A_c{t}_c:\cdots :A_M{t}_M=1:\cdots :1:\cdots :1$, and knowing the values $t_c$ and $m{u}_c$ defining individual traffic classes, we can use Equation (1) to determine the ${\lambda }_c$ parameter, which determines the intensity of the appearance of new class c calls in the system. In order to properly implement the prioritization mechanism, priority values for individual traffic classes are also provided.

Thus, in summary, the following parameters are given as input parameters to the simulator:

• number of input/output links in each switch: $\upsilon$;
• capacity of single link: f FSUs;
• number of traffic classes: M;
• for each class c from M classes:

  −

  number of demanded FSUs: $t_c$;

  −

  average service time: ${\mu }_c^{-1}$;

  −

  priority value: $p_c$;

• traffic value a offered to a single FSU.

3.3. Simulation Algorithm

While incorporating the simulator through the process interaction method, two events were specified: the arrival of a new call and the termination of call service. In the case of the arrival of a new call event, it is verified whether a new call can be accepted for service. If feasible, the system’s resources are utilized; otherwise, the call is forfeited. The termination of call service event indicates the completion of service for a specific call, leading to the release of the system’s resources. The simulation program executes the handling of these events through dedicated functions, which are elaborated in other publications [17,18]. The overall block diagram of the simulation algorithm is depicted in Figure 5.

3.4. Simulator Application and Termination Condition

The simulation program allows for the calculation of loss probability, obtained by dividing the number of lost calls by the number of generated calls and expressed by the following formula:

$$E_c=\frac{L_c}{G_c},$$

(2)

where $E_c$ denotes the loss probability value, $L_c$ the number of lost calls of class c, and $G_c$ the number of generated calls of class c. The number of lost calls includes calls lost due to the inability to find free resources and calls that have been displaced.

Additionally, it facilitates the determination of loss probability for displaced calls, computed as the ratio of displaced calls to generated calls. The termination condition is based on the number of generated calls for the least-active class, where calls are generated with the lowest intensity. The final result, given a set of input parameters, is derived as the average from five simulation series. Confidence intervals of 95% are also computed, typically not exceeding 5% of the average value in practical scenarios. To achieve this, up to 10,000,000 calls of the least intense class are generated.

3.5. Numerical Results

The simulation investigation was carried out on systems with parameters outlined in

Table 1. Parameters of the systems under investigation.

	System 1	System 2	System 3
Structure of switching network	$\upsilon =4$, $f=160$ FSUs	$\upsilon =4$, $f=320$ FSUs	$\upsilon =4$, $f=160$ FSUs
Number of traffic classes	3	3	4
Number of required FSUs *	$t_1=1$, $t_2=6$, $t_3=12$	$t_1=2$, $t_2=7$, $t_3=14$	$t_1=2$, $t_2=4$, $t_3=7$, $t_4=11$
Mean service time	${\mu }_1^{-1}=1$, ${\mu }_2^{-1}=1$, ${\mu }_3^{-1}=1$	${\mu }_1^{-1}=1$, ${\mu }_2^{-1}=1$, ${\mu }_3^{-1}=1$	${\mu }_1^{-1}=1$, ${\mu }_2^{-1}=1$, ${\mu }_3^{-1}=1$, ${\mu }_4^{-1}=1$
Priority	$p_1=p_2=0$, $p_3=1$	$p_1=0$, $p_2=2$, $p_3=1$	$p_1=p_2=0$, $p_3=1$, $p_4=2$

* The choice of appropriate number of demanded FSUs was performed on the basis of the data included in [24,25].

. Furthermore, an examination was conducted to explore the relationship between the loss probability of calls in specific traffic classes and the priority values.

The structure of the system and the traffic offered in the three cases was selected in such a way as to take into account systems with different link capacities, different numbers of classes offered to the system, and different priorities introduced for different traffic classes.

The simulation outcomes (Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18) are illustrated in graphs, portraying data points along with confidence intervals computed using Student’s t-distribution (at a 95% confidence level). The data are derived from five series, each consisting of 10,000,000 calls from the least-active class. The confidence intervals were determined using the following formula:

$$\left(\overline{X}-t_{\alpha }\frac{\sigma }{\sqrt{d}};\overline{X}+t_{\alpha }\frac{\sigma }{\sqrt{d}}\right).$$

(3)

In (3), $\overline{X}$ represents the arithmetic mean computed from d results (simulation runs), and $t_{\alpha }$ is the value from the Student’s t-distribution with $d-1$ degrees of freedom. The parameter $\sigma$, defining the standard deviation, is subsequently determined through the following equation:

$${\sigma }^2=\frac{1}{d-1}\sum _{s=1}^d{x}_s^2-\frac{d}{d-1}{\overline{X}}^2,$$

(4)

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

Figure 6, Figure 7 and Figure 8, Figure 10, Figure 11 and Figure 12, and Figure 14, Figure 15, Figure 16 and Figure 17 depict the loss probability values corresponding to individual traffic classes concerning the traffic parameter a directed to a single FSU. The graphs compare the loss probability values between a system with an implemented prioritization mechanism and a system without such prioritization. Notably, for classes with the lowest priority ($p_c=0$), the loss probability values increase compared to the non-prioritized system. Conversely, for classes with the highest priorities ($p_c=1$ or $p_c=2$), a noticeable decrease in the loss probability is observed compared to the corresponding classes in the system without prioritization. Therefore, at the expense of increasing the loss probability for low-priority classes, we obtain a decrease in the loss probability value for high-priority classes.

During the research, simulation experiments were also carried out to determine the loss probability only for displaced calls (with a lower priority than the maximum one) in systems with a prioritization mechanism. The results of the obtained loss probability values are presented in Figure 9, Figure 13, and Figure 18. Comparing the obtained values with the total loss probability values presented in Figure 6, Figure 7 and Figure 8, Figure 10, Figure 11 and Figure 12, and Figure 14, Figure 15, Figure 16 and Figure 17, we can see that losses due to call displacement constitute the largest share. Therefore, the main reason for call losses in the system is their displacement resulting from the lack of available resources for higher priority class.

This fact can also be supported by the results presented in

Table 2. Number of generated, lost, and displaced calls in system 1.

Simulation	Generated Calls			Lost Calls			Displaced Calls
No.	Class 1	Class 2	Class 3	Class 1	Class 2	Class 3	Class 1	Class 2
$a=0.6$ Erl
1	120,018,976	20,000,305	10,000,000	89,639	236	7937	89,639	64
2	120,023,193	20,008,812	10,000,000	86,710	198	7702	86,710	70
3	119,999,006	20,000,781	10,000,000	87,752	199	7865	87,752	65
4	120,029,889	20,002,919	10,000,000	88,446	178	7716	88,446	61
5	119,903,196	19,985,187	10,000,000	90,590	199	8008	90,590	54
$a=0.7$ Erl
1	120,017,649	20,005,048	10,000,000	5,787,577	37,989	140,782	5,787,577	31,478
2	119,964,840	19,990,200	10,000,000	5,774,697	37,798	142,139	5,774,697	31,352
3	120,016,604	19,997,382	10,000,000	5,729,572	37,666	140,260	5,729,572	31,162
4	119,944,400	19,992,671	10,000,000	5,772,419	38,212	140,791	5,772,419	31,456
5	120,040,297	20,007,917	10,000,000	5,784,770	38,007	141,575	5,784,770	31,536
$a=0.8$ Erl
1	120,006,537	20,003,937	10,000,000	24,471,851	455,696	451,214	24,471,851	418,305
2	120,039,295	20,005,593	10,000,000	24,426,828	454,560	451,558	24,426,828	417,185
3	120,033,255	19,997,696	10,000,000	24,464,868	456,113	449,706	24,464,868	418,812
4	120,060,771	20,003,691	10,000,000	24,557,610	457,647	450,111	24,557,610	421,379
5	120,035,097	19,997,720	10,000,000	24,480,514	454,882	453,502	24,480,514	417,932
$a=0.9$ Erl
1	120,042,989	20,009,173	10,000,000	42,629,786	1,375,938	773,958	42,629,786	1,279,089
2	120,056,097	20,003,358	10,000,000	42,597,514	1,373,416	777,892	42,597,514	1,276,160
3	120,079,743	20,007,866	10,000,000	42,632,873	1,375,425	773,379	42,632,873	1,279,090
4	120,036,068	20,005,976	10,000,000	42,666,721	1,376,483	775,765	42,666,721	1,279,239
5	120,081,887	20,015,386	10,000,000	42,589,890	1,373,840	776,637	42,589,890	1,276,015
$a=1.0$ Erl
1	120,117,950	20,019,251	10,000,000	55,868,606	2,530,486	1,095,873	55,868,599	2,333,013
2	120,066,772	20,011,887	10,000,000	55,914,793	2,531,528	1,094,979	55,914,781	2,334,130
3	120,092,517	20,021,400	10,000,000	55,875,016	2,531,640	1,094,494	55,875,012	2,334,554
4	120,142,025	20,026,575	10,000,000	55,863,606	2,527,668	1,095,886	55,863,602	2,331,146
5	120,117,551	20,019,828	10,000,000	55,912,856	2,533,535	1,090,251	55,912,844	2,337,060
$a=1.1$ Erl
1	120,446,723	20,068,777	10,000,000	65,278,242	3,757,717	1,398,059	65,278,215	3,402,455
2	120,520,595	20,095,006	10,000,000	65,310,811	3,756,381	1,405,511	65,310,764	3,398,858
3	120,417,958	20,073,366	10,000,000	65,293,338	3,760,984	1,403,650	65,293,293	3,404,368
4	120,420,057	20,064,674	10,000,000	65,306,793	3,760,529	1,405,005	65,306,731	3,403,769
5	120,445,301	20,080,368	10,000,000	65,277,165	3,760,220	1,401,416	65,277,111	3,403,659
$a=1.2$ Erl
1	121,015,386	20,174,922	10,000,000	72,167,496	5,020,155	1,680,223	72,167,264	4,413,322
2	121,043,522	20,168,675	10,000,000	72,200,588	5,017,003	1,676,141	72,200,387	4,415,690
3	121,043,094	20,171,541	10,000,000	72,178,482	5,009,958	1,677,194	72,178,307	4,406,949
4	121,036,966	20,163,260	10,000,000	72,134,298	5,005,565	1,676,843	72,134,078	4,402,452
5	121,035,662	20,164,256	10,000,000	72,106,150	5,006,079	1,685,742	72,105,881	4,400,478

,

Table 3. Number of generated, lost, and displaced calls in system 2.

Simulation	Generated Calls			Lost Calls			Displaced Calls
No.	Class 1	Class 2	Class 3	Class 1	Class 2	Class 3	Class 1	Class 3
$a=0.6$ Erl
1	70,028,900	20,014,095	10,000,000	102	3	66	102	0
2	69,971,927	19,996,396	10,000,000	143	0	47	143	0
3	70,023,610	20,001,480	10,000,000	0	0	52	0	0
4	70,033,221	20,009,051	10,000,000	16	0	40	16	0
5	69,997,849	19,999,287	10,000,000	93	0	63	93	0
$a=0.7$ Erl
1	69,999,037	20,000,565	10,000,000	286,187	236	20,626	286,187	89
2	69,953,476	19,991,704	10,000,000	287,064	269	21,327	287,064	74
3	70,005,144	19,998,941	10,000,000	296,225	273	21,060	296,225	81
4	70,033,905	20,004,093	10,000,000	292,797	283	20,962	292,797	83
5	69,992,064	20,001,617	10,000,000	290,640	289	20,751	290,640	75
$a=0.8$ Erl
1	70,016,800	20,006,001	10,000,000	9,070,309	5875	235,978	9,070,309	10,765
2	69,973,306	19,990,318	10,000,000	9,085,530	5770	236,277	9,085,529	10,809
3	70,016,996	20,006,828	10,000,000	9,083,016	5776	234,228	9,083,016	10,999
4	69,960,744	19,988,488	10,000,000	9,066,771	5692	236,190	9,066,769	11,118
5	70,022,190	20,005,831	10,000,000	9,086,474	5929	237,172	9,086,473	10,995
$a=0.9$ Erl
1	69,979,647	19,985,498	10,000,000	24,424,107	16,117	491591	24,424,099	68,400
2	69,991,691	19,998,984	10,000,000	24,378,227	16,499	495,390	24,378,215	68,113
3	69,989,405	19,992,005	10,000,000	24,369,756	16,382	495,393	24,369,749	68,290
4	70,003,379	20,003,815	10,000,000	24,375,054	16,753	497,306	24,375,037	68,568
5	70,019,709	19,995,654	10,000,000	24,390,033	16,165	494,998	24,390,013	67,743
$a=1.0$ Erl
1	70,031,711	20,003,915	10,000,000	36,185,694	31,269	862,120	36,185,619	194,102
2	70,025,125	20,008,569	10,000,000	36,133,414	31,834	862,211	36,133,350	193,956
3	70,017,260	20,007,575	10,000,000	36,165,239	31,152	862,512	36,165,177	193,792
4	70,019,733	20,011,720	10,000,000	36,160,686	31,301	863,005	36,160,607	192,969
5	70,047,166	20,012,092	10,000,000	36,157,910	31,858	865,175	36,157,840	193,547
$a=1.1$ Erl
1	70,082,670	20,018,757	10,000,000	41,784,594	62,985	1,705,123	41,784,352	404,268
2	70,028,387	20,016,313	10,000,000	41,757,581	62,598	1,700,427	41,757,308	404,625
3	70,035,373	20,010,926	10,000,000	41,784,635	63,311	1,707,049	41,784,374	406,025
4	70,059,697	20,014,586	10,000,000	41,756,651	62,875	1,699,493	41,756,384	404,123
5	70,110,895	20,032,021	10,000,000	41,802,702	63,928	1,701,860	41,802,440	405,436
$a=1.2$ Erl
1	70,296,431	20,090,971	10,000,000	44,449,358	113,646	2,773,730	44,448,402	655,290
2	70,261,979	20,076,551	10,000,000	44,424,253	113,459	2,772,653	44,423,418	652,299
3	70,296,794	20,081,775	10,000,000	44,457,939	113,210	2,766,393	44,457,045	653,125
4	70,301,099	20,087,573	10,000,000	44,459,421	114,254	2,772,427	44,458,524	655,337
5	70,277,536	20,083,119	10,000,000	44,438,878	113,659	2,774,936	44,438,019	653,813

and

Table 4. Number of generated, lost, and displaced calls in system 3.

Simulation	Generated Calls				Lost Calls				Displaced Calls
No.	Class 1	Class 2	Class 3	Class 4	Class 1	Class 2	Class 3	Class 4	Class 1	Class 2	Class 3
$a=0.6$ Erl
1	55,007,974	27,505,113	15,713,970	10,000,000	213,339	13,598	1797	6405	213,339	13,574	1314
2	55,008,029	27,504,649	15,717,040	10,000,000	210,448	13,250	1804	6128	210,448	13,233	1280
3	55,028,527	27,506,205	15,728,933	10,000,000	212,547	13,342	1789	6436	212,547	13,327	1331
4	55,033,233	27,518,389	15,725,188	10,000,000	209,676	13,384	1854	6438	209,676	13,360	1306
5	55,004,346	27,498,276	15,724,576	10,000,000	213,140	13,411	1918	6424	213,140	13,391	1402
$a=0.7$ Erl
1	55,006,688	27,501,873	15,722,418	10,000,000	6,116,947	730,377	163,578	92,392	6,116,946	729,428	152,726
2	54,987,877	27,498,565	15,714,619	10,000,000	6,146,412	736,311	165,810	93,774	6,146,412	735,313	154,505
3	54,966,697	27,480,322	15,706,702	10,000,000	6,133,438	734,103	165,285	93,911	6,133,438	733,151	154,039
4	55,037,510	27,519,343	15,722,419	10,000,000	6,119,568	729,834	164,130	93,375	6,119,568	728,864	152,792
5	55,020,548	27,505,805	15,711,986	10,000,000	6,109,420	730,586	163,998	92,816	6,109,416	729,576	153,090
$a=0.8$ Erl
1	54,982,773	27,490,287	15,711,742	10,000,000	15,278,359	2,895,323	884,512	249,392	15,278,345	2,890,173	846,329
2	54,988,296	27,488,804	15,707,398	10,000,000	15,291,566	2,897,654	883,539	249,139	15,291,548	2,892,512	845,845
3	55,014,856	27,500,898	15,715,255	10,000,000	15,279,538	2,891,676	882,696	248,607	15,279,523	2,886,381	844,502
4	55,062,625	27,531,332	15,729,839	10,000,000	15,279,759	2,894,694	882,481	249,567	15,279,746	2,889,422	844,509
5	55,000,739	27,512,370	15,718,020	10,000,000	15,281,161	2,892,446	881,411	248,614	15,281,151	2,887,140	843,754
$a=0.9$ Erl
1	55,031,395	27,514,119	15,714,226	10,000,000	22,198,786	5,308,914	1,895,142	412,219	22,198,740	5,293,726	1,819,911
2	55,004,774	27,507,522	15,714,401	10,000,000	22,189,293	5,311,009	1,898,864	416,680	22,189,231	5,295,727	1,823,541
3	54,981,664	27,492,521	15,711,237	10,000,000	22,205,630	5,314,836	1,899,745	415,993	22,205,575	5,299,689	1,823,799
4	55,022,538	27,501,614	15,707,756	10,000,000	22,207,855	5,313,528	1,898,438	413,512	22,207,788	5,298,092	1,823,332
5	55,013,137	27,501,958	15,709,576	10,000,000	22,193,243	5,310,665	1,896,814	413,021	22,193,185	5,295,562	1,822,190
$a=1.0$ Erl
1	55,006,451	27,515,745	15,712,319	10,000,000	27,137,586	7,475,568	2,970,240	588,732	27,137,385	7,442,130	2,847,751
2	54,988,467	27,502,476	15,713,387	10,000,000	27,143,768	7,481,510	2,971,245	586,191	27,143,575	7,448,157	2,850,307
3	54,995,066	27,502,881	15,718,055	10,000,000	27,152,868	7,479,235	2,973,286	588,464	27,152,683	7,445,959	2,851,393
4	54,959,409	27,494,010	15,706,158	10,000,000	27,142,351	7,483,840	2,971,983	587,395	27,142,181	7,450,792	2,850,843
5	55,013,734	27,507,957	15,713,743	10,000,000	27,141,736	7,482,753	2,970,585	588,659	27,141,550	7,449,220	2,848,421
$a=1.1$ Erl
1	55,006,414	27,504,827	15,713,770	10,000,000	30,813,887	9,362,419	4,017,840	761,582	30,813,435	9,299,900	3,843,083
2	54,995,138	27,490,235	15,712,437	10,000,000	30,814,829	9,363,945	4,018,363	761,159	30,814,308	9,299,733	3,842,553
3	55,044,891	27,506,244	15,723,996	10,000,000	30,832,398	9,361,452	4,016,443	759,971	30,831,913	9,297,743	3,841,484
4	54,981,891	27,497,591	15,712,771	10,000,000	30,801,951	9,365,864	4,019,503	761,106	30,801,474	9,302,740	3,845,175
5	54,999,239	27,508,206	15,716,861	10,000,000	30,826,039	9,373,120	4,024,082	762,163	30,825,463	9,309,423	3,849,148
$a=1.2$ Erl
1	55,035,791	27,504,858	15,730,480	10,000,000	33,502,657	10,917,113	4,978,308	956,917	33,501,564	10,809,088	4,738,521
2	55,017,270	27,514,922	15,721,019	10,000,000	33,496,155	10,930,117	4,984,885	955,285	33,494,945	10,821,052	4,743,136
3	55,039,460	27,518,114	15,719,839	10,000,000	33,490,201	10,925,758	4,981,504	956,519	33,489,104	10,816,569	4,741,097
4	55,012,056	27,512,819	15,713,779	10,000,000	33,475,600	10,920,065	4,977,806	956,891	33,474,440	10,810,963	4,736,829
5	55,055,391	27,521,889	15,735,785	10,000,000	33,491,439	10,915,150	4,983,634	958,474	33,490,347	10,806,034	4,742,086

. The presented numerical results confirm a very large share of displaced calls in the total number of lost calls in the system.

When we compare the loss probability values in the system with the priorities (Figure 6 and Figure 7), we can see that the loss probability value for class 1 calls is higher than for class 2 calls, even though it requests a smaller number of FSUs. The described situation results from the fact that when lower priority calls (classes 1 and 2) are displaced, class 1 calls have a larger share among the displaced calls (which is confirmed by the results presented in Figure 9).

In the case of System 2, we notice that at the expense of displacing a large number of class 1 calls, we achieve a reduction in the loss probability for calls with the highest priority (class 2) and for class 3 calls (Figure 11 and Figure 12). The lower loss probability for class 3 calls results from the fact that a lot of class 1 calls were displaced (Figure 13, Table 3).

As in the case of System 1, when we compare the loss probability values in System 3 with the priorities (Figure 14, Figure 15, Figure 16 and Figure 17), we can see that the loss probability value for class calls requesting fewer FSUs is higher than for calls requesting a larger number of FSUs. This is due to the fact that in the case of displacing lower priority calls (classes 1 and 2), calls with a smaller number of FSUs have a greater share among the displaced calls (Figure 18, Table 4).

In order to more comprehensively present the traffic characteristics of the considered systems, research was carried out showing the percentage utilization of system resources. The utilization of resources in the output directions of the switching network was examined. The resource utilization percentages were determined using the following formula:

$$\overline{u}=\frac{{\displaystyle \sum _i}{n}_i\Delta T_i}{\upsilon fT}·100\%,$$

(5)

where $n_i$ is the number of occupied FSUs in the output direction (link group) of the switching network at a given moment $T_i$ of time, $\Delta T_i=T_i-T_{i-1}$ is the time interval between events i, and $i-1$ and T is the duration of the simulation experiment.

Figure 19, Figure 20 and Figure 21 show the percentage of resource utilization in the output directions of the switching network in the considered systems. We can see that when the prioritization mechanism is used, we obtain lower resource utilization. This translates directly into a lower value of traffic serviced. Therefore, at the expense of shaping the traffic characteristics (loss probability) of the system, we reduce the value of traffic serviced in the system. We also notice that regardless of the system capacity and the number of traffic classes offered, the trend of changes is very similar.

As an additional research element, the impact of using different CAC mechanisms on shaping the traffic characteristics of the systems was compared. As part of the research, the loss probability values were compared for individual call classes in system 1, in which three cases were considered: without the CAC mechanisms introduced, with the prioritization mechanism, and with the reservation mechanism. In the case of the reservation mechanism, the reservation limit value was set to 75% of the system capacity. The implemented reservation mechanism was described in detail in [18].

As we can see in Figure 22, Figure 23 and Figure 24, by implementing the traffic prioritization mechanism, we can shape the traffic characteristics of the considered systems in a similar way to using the reservation mechanism.

4. Conclusions

This article presents a simulator of flexible WDM nodes with an implemented mechanism for prioritizing call classes. The simulator allows us to determine the loss probability for individual traffic classes in a switching network with point-to-point selection. The simulation studies carried out confirmed the possibility of using the traffic prioritization mechanism to manage traffic in the nodes of the flexible WDM network. This mechanism, similar to the dynamic reservation mechanism [18], or the threshold mechanism [17], allows differentiating the quality of service of individual services represented by different traffic classes. Due to its nature, the greatest benefits can be obtained by using it for classes (services) that require relatively low bit rates and are usually associated with low traffic volumes, e.g., those associated with maintenance traffic, monitoring, or alarms. Otherwise, when used for prioritizing high-volume traffic, it can greatly downgrade the quality of service and experience of other classes. Furthermore, it is worth noting that by applying priorities, we can reduce the use of system resources, which directly translates into the value of the traffic served and can therefore be used as a traffic-shaping mechanism. Prioritization can also be used as a kind of preventive mechanism that activates when a certain type of traffic (service) occurs in the network that must be handled with the best possible quality.