Poznan University of Technology

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Poznan University of Technology

Faculty of Electronics and Telecommunications

Doctoral Thesis

Strict-sense and Wide-sense

Non-blocking W-S-W Switching Fabrics for Elastic Optical Networks

Author

mgr in˙z. Mustafa Abdulsahib

Supervisor

prof. dr hab. in˙z. Wojciech Kabaci´nski

Pozna´n 2018

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List of Figures

1.1 ITU fixed and flexible grids. . . . 2

1.2 Assignment of time slots for two 6-slot connections in 32 Pulse-Code Modulation (PCM) link using: (a) floating and (b) flexible assignment. . . . 4

2.1 Crosspoint in: (a) off and (b) on states. . . . 7

2.2 Bar and cross states of 2 × 2 BSE. . . . 8

2.3 The 4 × 4 switch implemented with: (a) crosspoints and (b) 2 × 2 BSEs. . . . . 8

2.4 Electronic 4 × 4 crossbar. . . . 11

2.5 Mirrors in MEMS based optical switch. . . 12

2.6 The 2D 2 × 2 MEMS crossbar optical switch. . . 13

2.7 Cross-sectional view of a conventional 3D MEMS optical switch. . . 14

2.8 Liquid crystal cell without (a) and with voltage (b). . . 14

2.9 A 8 × 8 switching fabric composed of:(a) one stage, (b) two stages and (c) three stages of 4 × 4 switches. . . 16

2.10 The 16 × 16 Banyan switching fabric. . . . 17

2.11 The 16 × 16 Baseline switching fabric. . . 18

2.12 The 16 × 16 Omega switching fabric. . . 19

2.13 Three stage Clos switching fabric C(q, p, r). . . 19

2.14 Space-division switching fabrics with SDM (a), TDM (b) and WDM (c) transmission. . . . 21

2.15 Time slots in time-division multiplexing. . . . 21

2.16 Wavelength-division multiplexing operation. . . 22

3.1 The transmission losses of optical communication wavelength bands. . . 24

3.2 The spectrum assignment in the flexgrid. . . 26

3.3 Spectrum assignment in a CWDM grid. . . 28

3.4 CWDM operation. . . 29

3.5 Inefficient spectrum utilization in WDM fixed grid. . . 30 3.6 When a collimated polychromatic light beam impinges on a diffraction grating,

each wavelength component is diffracted and directed to a different point in space. 31

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3.7 A diagrammatic representation showing the principle concept of WSS operation. 31

3.8 A figure representing the main components of a 1 × 2 port WSS switch. . . 32

3.9 WSS: (a) legacy, (b) Bandwidth-Variable. . . 33

4.1 The N × N switch which is composed of only BV-WBSSs and PCs elements. . 35

4.2 The NA-I architecture. . . . 37

4.3 The NA-II architecture. . . . 37

4.4 The NA-III architecture. . . 38

4.5 The NA-IV architecture. . . 38

4.6 The WSW1(r, n, k) switching fabric architecture. . . 39

4.7 The BV-WBCS in WSW1(r, 9, 9) architecture. . . 40

4.8 The BV-WBSSS in WSW1(3, 9, 9) architecture. . . . 41

4.9 The WSW2(q, p, r, n, k) switching fabric architecture. . . . 41

4.10 The BV-WBCS in WSW2(q, p, r, n, k) architecture. . . 42

4.11 The SWS1 switching fabric architecture. . . 42

4.12 The SWS2 switching fabric architecture. . . 43

4.13 A DCN architecture divided into two parts: EPS and OCS. . . 44

4.14 The OCS part of a DCN based on the WSW1(r, n, k) switching fabric. . . 44

4.15 The T-S-T switch. . . 45

4.16 The T-T-T switch. . . 45

4.17 Worst-case scenario in C-C-C architecture without considering the adjacency constraint. . . . 47

4.18 Difference between WSW2(2, 9, r, 6, 6) and C-C-C architecture of similar parameters with considering the adjacency constraint. . . . 47

5.1 The worst-case scenario in interstage links from switch Ii and to switch Oj for connection (Ii, Oj, m). . . 50

5.2 Function kssnb(m) = −2m²+ (2n + 1)mfor WSW1(r, 8, k) and WSW1(r, 9, k). 51 5.3 The block diagram of 2sFixFSU algorithm. . . 55

5.4 The block diagram of 2sVarFSU Algorithm. . . 55

5.5 The block diagram of 3sFixFSU algorithm. . . 56

5.6 The block diagram of 3sVarFSU algorithm. . . . 57

5.7 The pseudo-code of XsVarFSU algorithm. . . 58

5.8 The worst-case scenario of FSUs occupation in F². . . . 61

5.9 kssnbvs mmaxfor different values of n. . . 65

5.10 kwsnbversus m1under 2sVarFSU algorithm; mmax= n. . . 66

5.11 k_wsnb^3sFixFSUversus m1; m2 = ⁿ₂, mmax= n. . . . 67

5.12 k^3sVarFSUversus m ; m = n. . . 68

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5.13 Relationship between kssnb, kwsnb and mmax under 2sVarFSU and 3sVarFSU

control algorithms: (a) n = 20, (b) n = 80, (c) n = 320. . . 70

5.14 C_FSUs^XsVarFSUvs mmax; n = 20. . . . 71

5.15 C_FSUs^XsVarFSUvs mmax; n = 40. . . 72

6.1 The worst-case scenario in switches Ii and Oj for a 4-slot connection in architecture WSW2(2, 17, r, 10, 10). . . 76

6.2 The block diagram of 2sFixSWITCH algorithm. . . . 77

6.3 The block diagram of 2sVarSWITCH algorithm. . . 78

6.4 The block diagram of 3sFixSWITCH algorithm. . . 79

6.5 The block diagram of 3sVarSWITCH algorithm. . . 79

6.6 The pseudo-code of XsVarSWITCH algorithm. . . 80

6.7 An example of the worst-case scenario in P² under 2sFixSWITCH algorithm. . 83

6.8 Examples of worst-case scenarios in P2 under 2sVarSWITCH algorithm: (a) case 1, (b) case 2, (c) case 3, and (d) case 4. . . 86

6.9 pssnbvs mmaxfor different values of n; WSW2(2, p, r, n, n). . . 89

6.10 p2sVarSWITCH wsnb vs m1; WSW2(4, p, r, n, n), and mmax= n. . . 90

6.11 p3sVarSWITCH wsnb vs m2for selected values of m1; WSW2(4, p, r, 160, k), and mmax = n. . . . 91

6.12 p3sFixSWITCH wsnb versus m1 for selected values of n; WSW2(4, p, r, n, n), and mmax = n. . . 92

6.13 p2sVarSWITCH wsnb and p3sVarSWITCH wsnb versus mmax; WSW2(4, p, r, 350, 350), 2 6 mmax6 20. . . 92

6.14 Relationship between pssnb, pwsnb and 2 6 m^max 6 n under 2sVarSWITCH, 3sFixSWITCH and 3sVarSWITCH control algorithms: (a) WSW2(4, p, r, 20, 20), (b) WSW2(4, p, r, 80, 80), (c) WSW2(4, p, r, 320, 320). . . 93

6.15 CXsVarSWITCH p vs mmax; WSW2(4, p, r, 20, 20). . . 94

6.17 The effect of higher X on the CXsVarSWITCH p of mmaxvalues around ⁿ₂. . . 96

6.18 The effect of different splitting points on CXsVarSWITCH p ; WSW2(4, p, r, 40, 40), X = 2. . . . 97

6.19 CXsVarSWITCH p vs mmax; WSW2(4, p, r, 160, 160). . . . 97

7.1 The internal components of WSW1(r, n, k) architecture. . . 100

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7.2 The influence of WSW1(r, n, k) input parameters on the required numbers of TSCs. . . 101 7.3 The influence of WSW1(r, n, k) input parameters on the required numbers of

BV-WSSs. . . 101 7.4 The internal components of the WSW2(q, p, r, n, k) architecture. . . 102 7.5 The effect of q on the total number of TSCs for WSW2 operating with

2sVarSWITCH; N = 16, and mmax= 5. . . 104 7.6 The effect of q on the total number of BW-WSSs for WSW2 operating with

2sVarSWITCH; N = 16, and mmax= 5. . . 104 7.7 The effect of mmax on the total number of TSCs for WSW2(1, p, 8, n, k)

architecture operating with 2sVarSWITCH; N = 8. . . 107 7.8 The effect of mmax on the total number of TSCs for WSW2(1, p, 16, n, k)

architecture operating with 2sVarSWITCH; N = 16. . . 107 7.9 The effect of mmaxon SSNB and WSNB in terms of required TSCs; WSW2(1,

p, 8, 20, k). . . 109 7.10 The effect of mmax on SSNB and WSNB in terms of required BV-WSSs;

WSW2(1, p, 8, 20, k). . . 109 7.11 Implementing 1 × 400 BV-WSS using multiple 1 × 20 BV-WSSs . . . 111

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List of Tables

3.1 Number of FSUs required in different connections. . . . 27

3.2 Theoretical maximum number of DWDM channels in the C-band depending on the channel spacing. . . 30

5.1 The set of events which leads to the blocking state when kssnb< 2(n − m)m + m. 53 5.2 The set of events which lead to the blocking state in F2when k^3sFixFSU₂ is lower than given by eq. (5.18) . . . 64

5.3 Values of kssnbin WSW1 with different n; mmax= n . . . 65

5.4 Values of kssnband k^3sFixFSU_wsnb in WSW1 with different n; mmax= n . . . . 67

6.1 C2sVarSWITCH p for different values of mmax; WSW2(4, p, r, n, n), n = 20, 40, and 80. . . . 91

6.2 CXsVarSWITCH p for different values of mmax; WSW2(4, p, r, 40, 40). . . 95

7.1 W-S-W switching fabrics with the lowest number of TSCs and BV-WSSs for mmax= 11 . . . 106

7.2 Number of BV-WSSs in WSW2(1, p, r, n, k) switching fabrics under 2sVarSWITCH algorithm. . . 108

7.3 General comparison of resources requirements for WSW1(r, n, k) and WSW2(1, p, r, n, k) with different configurations; mmax= 11, no limitation on BV-WSSs sizes . . . 108

7.4 Comparison between SSNB and WSNB in terms of BV-WSSs and TSCs for WSW2(1, p, r, 20, k); mmax= 11. . . 110

7.5 General comparison of resources requirements for WSW1 and WSW2 with different configurations; mmax= 11, BV-WSS size is limited to 1 × 20. . . 111

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List of Abbreviations

BSE Basic Switching Element

BV-R Bandwidth-Variable Receiver

BV-T Bandwidth-Variable Transmitters

BV-WBCS Bandwidth-Variable Waveband Converting Switch BV-WBSSS Bandwidth-Variable Waveband Selective Space Switch BV-WSS Bandwidth-Variable Waveband Space Switch

CDM Code-Division Multiplexing

CO-OFDM Coherent Optical Orthogonal Frequency-Division Multiplexing

CS Converting Switch

CWDM Coarse Wavelength-Division Multiplexing

DCN Data Center Network

DSDM Dense Space-Division Multiplexing DWDM Dense Wavelength-Division Multiplexing

EDFA Erbium Doped Fiber Amplifier

EON Elastic Optical Network

EPS Electronic Packet Switching

ESS Electronic Switching System

FDM Frequency-Division Multiplexing

FM-MCFs Few Mode Multi-Core Fibers FRSC Full Range Spectrum Converter

FSU Frequency Slot Unit

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I/O Input/Output

ITU International Telecommunication Union

LC Liquid Crystal

LCoS Liquid Crystal on Silicon

LRSC Limited Range Spectrum Converter

MDM Mode-Division Multiplexing

MEMS Microelectromechanical System

M-R-M MEMS-Ring-MEMS

O/E/O Optical-Electrical-Optical

OCS Optical Circuit Switching

OFDM Orthogonal Frequency-Division Multiplexing

OXC Optical Cross Connect

PC Passive Combiner

PCM Pulse-Code Modulation

PDM QPSK Polarization-Division Multiplexing QPSK

PNB Repackably Nonblocking

PM QPSK Polarization Multiplexing QPSK

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase Shift Keying

RF Radio Frequency

RNB Rearrangably Nonblocking

R-M-R Ring-MEMS-Ring

SDH Synchronous Digital Hierarchy

SDM Space-Division Multiplexing

SF Switching Fabric

SONET Synchronous Optical Networking

SS Space Switch

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SSNB Strict-sense Nonblocking

S-W-S Space-Wavelength-Space

TDM Time-Division Multiplexing

ToR Top of Rack

TSC Tunable Spectrum Converter

T-S-T Time-Space-Time

T-T-T Time-Time-Time

VLSI Very Large Scale Integration

WBC Waveband Conversion

WDM Wavelength-Division Multiplexing

WSNB Wide-sense Nonblocking

WSS Wavelength Selective Switch

W-S-W Wavelength-Space-Wavelength

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List of Symbols

a_e Number of stages with fully occupied outputs

b Minimum weight of a connection

be Number of elements in the fully occupied stages

b_B Number of inputs/outputs in the switching elements of banyan switching fabric

B Maximum weight of a connection

C(q, p, r) 3-stage Clos switching fabric with configuration of q, p, and r

C_FSUs^Algorithm The saving in FSUs for each WSW1 algorithm as compared to SSNB C_p^Algorithm The saving in middle stage switches for each WSW2 algorithm as compared

to SSNB

f Nominal central frequency

Fⁱ Subset i of FSUs in interstage fibers

g Maximum number of converted connections allowed for each output link in architectures NA-III, and NA-IV

I_i Input switch i

k Number of FSUs in each interstage fiber k^j_i Number of FSUs in set Fⁱ of algorithm j m Number of FSUs required by a connection

m_i The splitting point (border rate) between two subsets of FSUs in WSW1, the splitting point (border rate) between two groups of middle stage switches in WSW2

Mwss Number of input ports in a WSS

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m_max Maximum number of FSUs could be occupied by a connection n Number of FSUs in each input and output fiber

N Capacity of a switching fabric, total number of input links N_wss Number of output ports in a WSS

O_j Output switch j

p Number of switches in the second stage

Pⁱ Set i of switches in the second stage of WSW2 architecture p^j_i Number of switches in set Pi of algorithm j

q Number of input fibers in each first stage switch, number of output fibers from each third stage switch

r Number of switches in the first and third stages T_e Total number of elements in a BV-WSS switch

w Number of TSCs per direction in architectures NA-I, NA-II, and NA-III.

WSW1(r, n, k) Architecture WSW1 with configuration of r, n, and k WSW2(q, p, r, n, k) Architecture WSW2 with configuration of q, p, r, n, and k x_e Number of outputs in one BV-WSSs element

y_e The number of outputs in one BV-WSS switch

(I_i, O_j, m) m-slot connection from input switch number i to output switch number j

|x| The cardinality of set X of FSUs/switches bxc The highest integer lower than or equal to x dxe The highest integer higher than or equal to x

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A

^BSTRACT

In this thesis, the combinatorial properties of elastic optical switching fabrics are addressed.

Two elastic optical switching fabrics are investigated in details, namely WSW1(r, n, k) and WSW2(q, p, r, n, k). Both architectures are of special design derived from Clos switching fabrics, hence, both consist of three stages. First and last stages have wavelength conversion capabilities while switching in second stage is merely in space domain. For the first architecture, WSW1, strict-sense nonblocking and wide-sense nonblocking conditions are derived and proved.

Five control algorithms based on functional decomposition of frequency slot units (FSUs) in interstage links are proposed. The results show that the algorithms reduce the required number of FSUs to up to almost 84% of the FSUs required in the strict-sense nonblocking switching fabrics.

As for the second architecture, WSW2, wide-sense nonblocking conditions are also derived and proved. Five control algorithms are proposed. These algorithms are based also on functional decomposition, but this time switches of the second stage are decomposed instead of FSUs.

These algorithms can reduce the number of required middle stage switches by almost 94% as compared to the number required under strict-sense conditions. These two architectures are also optimized in terms of numbers of required switching elements. Switching fabric architectures of different capacities are investigated using the full search, i.e., for each architecture and capacity, all possible configurations are checked. These architectures can be utilized as a center of an elastic optical switching node or as optical circuit switching in data center networks.

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S

TRESZCZENIE

W niniejszej rozprawie dokonano analizy wła´sciwo´sci kombinatorycznych pól komutacyjnych dla elastycznych sieci optycznych. Rozwa˙zone zostały dwie architektury, które nazwano WSW1(r, n, k) oraz WSW2(q, p, r, n, k). Obie s ˛a rozszerzeniem trzysekcyjnego pola Closa, st ˛ad te˙z obie posiadaj ˛a trzy sekcje elementów komutacyjnych. W obu przypadkach, pierwsza i ostatnia sekcja zawiera elementy z mo˙zliwo´sci ˛a konwersji długo´sci fali, natomiast w drugiej sekcji znajduj ˛a si˛e wył ˛acznie elementy stanowi ˛ace komutatory przestrzenne. Dla pierwszej architektury (WSW1) zostały wyprowadzone i udowodnione warunki nieblokowalno´sci w w ˛askim i szerokim sensie. Zaproponowano pi˛eć algorytmów sterowania takim polem, wykorzystuj ˛a one funkcjonaln ˛a dekompozycj˛e szczelin cz˛estotliwo´sciowych w ł ˛aczach mi˛edzysekcyjnych. Rezultaty analizy pracy algorytmów pokazuj ˛a, ˙ze wykorzystanie tych algorytmów mo˙ze prowadzić do nawet 84 procentowej redukcji wykorzystania szczelin cz˛estotliwo´sciowych w stosunku do pól nieblokowalnych w w ˛askim sensie. Równie˙z dla architektury WSW2 analogiczne warunki zostały wyprowadzone i udowodnione. W tym przypadku równie˙z zaproponowano pi˛eć algorytmów sterowania zestawianiem poł ˛aczeń bazuj ˛acych na funkcjonalnej dekompozycji, jednak w tym przypadku dekompozycji podlegały komutatory sekcji drugiej, a nie szczeliny cz˛estotliwo´sciowe. Zaproponowane algorytmy pozwalaj ˛a o 94 procent zredukować liczb˛e wymaganych komutatorów w stosunku do pól nieblokowalnych w w ˛askim sensie. Obie architektury zostały przeanalizowane pod k ˛atem optymalnej liczby elementów komutacyjnych. Pola o ró˙znych pojemno´sciach zostały przeanalizowane metod ˛a pełnego przegl ˛adu, tzn. ka˙zda mo˙zliwa kombinacja parametrów została sprawdzona. Przedstawione architektury mog ˛a być wykorzystane w w˛ezłach dla optycznych sieci elastycznych oraz centrach danych.

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1

CHAPTER

Introduction

The sustained growth of data traffic volume requires links with higher and higher transmission rates. Optical networks can provide optical paths of more than 100 Gb/s between end users.

Current and future applications and services will probably generate data flows of required transmission rate varying from several Gb/s up to Tb/s. Therefore, network operators will need cost-effective and scalable solutions to transport such variety of traffic streams. One of the solutions is to use elastic optical networks (EONs) [44].

The elastic optical networking is a new networking paradigm that is capable of assigning bandwidth to optical paths flexibly, this is why they are called “elastic optical networks” (EON) or

“flexible optical networks”. In EONs, the bandwidth is assigned to an optical channel depending on the required transmission speed, distance to be covered, path quality, and/or the modulation scheme used [25].

In current wavelength-routed optical networks, full wavelength capacity is assigned to an optical path even when the traffic is lower. To use bandwidth available in optical links efficiently, traffic grooming was proposed [15]. Another approach is to divide bandwidth into smaller parts (sub-wavelengths) and make it also possible to aggregate these smaller parts into larger parts (super-wavelengths), and allocate bandwidth to optical paths flexibly. The International Telecommunication Union (ITU) proposed a 50 GHz grid, which divides the relevant optical spectrum range of 1530–1565 nm (the so-called C-band) into fixed 50 GHz spectrum slots, but it is likely that bit rates greater than 100 Gb/s will not fit into this scheme [40].

100-Gb/s-based transmission systems have been commercialized in the last few years. Since they are compatible with the 50 GHz ITU grid already deployed, the need for replacing the grid did not arise. The standard transmission data rate beyond 100 Gb/s, and 400 Gb/s is receiving a lot of attention from both the telecom and datacom industries. Unfortunately, the spectral width occupied by 400 Gb/s at standard modulation formats is too broad to fit in the 50 GHz ITU grid,

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Chapter 1

and forcing it to fit by adopting a higher spectral efficiency modulation format would only allow short transmission distances [25]. So, ITU proposed a standard of the flexible frequency grid to support flexibility of spectrum assignment in the Dense Wavelength-Division Multiplexing (DWDM) networks. Fig. 1.1 shows both ITU grids, fixed and flexible. The fixed grid does not support bit rates of 400 Gb/s and 1 Tb/s at standard modulation formats, as they overlap with at least one 50 GHz grid boundary. Since 100 Gb/s and higher bit rates must be supported by the same network, it makes sense to “properly size” the spectrum for each demand based on its bit rate and the transmission distance, instead of forcing all demands to use more spectrum.

50 GHz

10 Gb/s 50 Gb/s 100 Gb/s

400 Gb/s 1 Tb/s

Fixed Grid

Flexible Grid

Figure 1.1: ITU fixed and flexible grids.

To support EONs, elastic optical switches are needed. Flexible optical switches are used to switch flexible connections between fibers. The issue of optical switching and switching fabrics was considered in many books and papers [17, 47, 81]. Proposed switches for EON differ in design, capacity and blocking characteristics. Some researchers considered switches that depend only on Bandwidth-Variable Waveband Space Switch (BV-WSS), which is a device that separate wavelengths multiplexed in a single fiber and forward them into different directions [20, 31, 118].

The BV-WSSs elements are further explained in Chapter 3. Since the results of BV-WSS were not satisfactory in terms of the blocking probability, researchers had to come out with another solution. The widely accepted solution is to adapt the principle of staging, where a switching fabric is implemented by means of switching elements organized in stages. When we talk about multi-stage switching fabrics, we have to consider Charles Clos and his well-known paper [9].

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Chapter 1

Clos published a paper in 1953 that defined the basics of what is known today as Clos switching fabrics [9]. In 1953, switching systems were purely electro-mechanical that depended on the principle of space-division, which can be simply defined as separation of switching paths merely in space. The separation of switching paths is further explained in Chapter 2. Clos defined in his paper the number of second stage switches required so that any connecting request from any free input to any free output could be established successfully. V. E. Beneš extended the theory of Clos by introducing the notion "nonblocking in the wide-sense" (WSNB) and refereed to the conditions proposed by Clos as "nonblocking in the strict-sense" (SSNB) [5, 42]. SSNB and WSNB concepts are further extended in Chapter 2. The well-known results of space-division Clos switching fabrics are not valid when we consider a system that operate in slots, such as Time-Division Multiplexing (TDM) or Wavelength-Division Multiplexing (WDM), where each slot in the interstage links is considered as a connecting path. When we compare slot-operating systems with the original principle of Clos, each of the links connecting two consecutive stages in Clos original design corresponds to a single slot in TDM or WDM systems. The definition of the term "free link" in WDM is also different than Clos. In WDM systems, a free input link to an m-slot connection can be defined as a link that has free adjacent slots, and their sum is> m.

The adjacency constraint is not an obligation in TDM, as it will be explained later in this section.

Many researchers considered the combinatorial properties of 3-stage Clos switching fabrics that operate in the time domain. However, due to the slot-assignment algorithms, the conditions derived for TDM systems cannot be applied on WDM. Slots assignment is an important issue in multi-slot switching systems. Assignment defines how idle slots are assigned to a new connection. Slots may be assigned using either the floating or the flexible assignments. In the floating assignment, any m slots contiguous to each other can be assigned to the m-slot connection, while in the flexible assignment, the selected slots no longer need to be contiguous.

There are other assignment algorithms, such as fixed and periodic, these algorithms are just mentioned because they are irrelevant to the proposed work. An example of these different assignments is shown in Fig. 1.2. In the floating assignment, a multi-slot connection has to use slots contiguous to each other, but the first slot used by this connection may by any slot in the link. The two connections considered in the example (Fig. 1.2(a)) uses slots 1-6 and 7-12. On the other hand, flexible assignment would utilize any free slots in the link, no matter adjacent they were or not. The flexible assignment is presented in Fig. 1.2(b), where these two 6-slot connections occupy sets of slots, which are spread and not contiguous [47].

The difference between TDM and WDM systems is in the assignment algorithms. In TDM, connections in most cases may occupy any slots in a link (flexible assignment), while in the WDM, a connection must spread over adjacent slots (floating assignment). If we use the results derived for TDM in WDM, the switching fabric will be blocking and new results are needed for WDM switching fabrics. There is another reason why known results are not valid for the

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Chapter 1

3 4 5 6 7 8 9¹⁰

1 2 ^{11 12}13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 (a)

3 4 5 6 7 8 9¹⁰

1 2 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

6-slot connection 1 6-slot connection 2

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Figure 1.2: Assignment of time slots for two 6-slot connections in 32 Pulse-Code Modulation (PCM) link using: (a) floating and (b) flexible assignment.

switching fabric architectures considered in this thesis. The considered architectures are called the W-S-W, which stands for Wavelength-Space-Wavelength. First and last stages are referred to with the term (Wavelength) because they contain the Tunable Spectrum Converter (TSC) elements, which allow them to convert the spectrum utilized by the request. The middle stage switches lack such capability and forward the requests in the space. Most of the known results for TDM systems are derived based on switching fabrics that have conversion capability provided for all the stages. Even if we ignore the assignment constraint, the W-S-W switching fabrics will be blocking when TDM results are used, due to less switches available in the middle stage, which lead us again to the same fact, that new results are needed for W-S-W switching architectures, as it will be further explained in Chapter 4.

The switching fabrics which are nonblocking in the strict-sense require usually a big number of middle stage switches. This might be the reason why Beneš proposed the notion of wide-sense nonblocking in the first place. In WSNB, the switching fabric depends on a certain control algorithm to achieve the nonblocking. What is important in WSNB, the number of middle stage switches is reduced or in some cases is equal to SSNB, where number of middle stage switches (p) is the min {pssnb; pwsnb}. In [46, 47, 48, 67, 77], it was shown that, when the middle stage switches of a TDM switching fabric are divided into two groups, each serves certain connections, the switching fabric required less number of middle stage switches to maintain the nonblocking operation. Mentioned technique was an inspiration for the possibility of using a similar decomposition in the W-S-W switching fabrics, with considering the differences in the assignment and conversion capability provided by the stages. To my knowledge, algorithms that decompose the middle stage switches into more than two groups are not investigated till now.

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Chapter 1 Thesis and Aim of the Work

1.1 Thesis and Aim of the Work

This thesis deals with topics related to combinatorial properties of Clos switching fabrics. These fabrics were first introduced by Charles Clos in his well known paper [9]. There, the structure for such fabrics were defined. Different implementations of these fabrics were introduced based on many switching technologies, such as space and time [13, 80, 116]. Nowadays, fabrics of this type are widely used in telecommunications, especially in optical networks [23, 69, 117, 124, 126].

The aim of the work is to elaborate the combinatorial properties of the 3-stage EON switching fabrics. Two elastic optical switching architectures are considered in this thesis. The combinatorial properties of both architectures are analyzed in order to maintain a nonblocking operation under both SSNB and WSNB. For each of these architectures, multiple control algorithms are proposed. These algorithms depend on decomposing the resources of the second stage, in a way less resources are needed and the nonblocking operation is ensured under all circumstances. Both architectures are optimized in terms of numbers of required switching elements, as an effort to reduce the total implementation costs.

Thesis of the work: The considered switching fabrics can have a nonblocking operation when the number of switches/slots in the middle stage is properly assigned and this number of resources can be reduced when the decomposition algorithms are utilized while the number of switching elements required to implement the switching fabrics can be further reduced when the design parameters are optimized.

1.2 Overview of the Thesis

This thesis is structured into two background chapters, the general introduction to switching fabrics (Chapter 2) and the principle of elastic optical networks (Chapter 3), one chapter concerning the considered architectures and state of the art (Chapter 4), two chapters that present nonblocking conditions for the proposed architectures (Chapter 5 and 6). Both architectures are optimized in (Chapter 7). Chapter 8 summarizes the contents of this thesis.

Chapter 2, entitled Switching Fabrics, explores the definition of switching along with brief description of historical and current switching techniques and provide an introduction to multi-stage switching fabrics and two most popular topologies, Clos and Banyan. This chapter also describes how data is transfered in different domains.

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Chapter 1 Overview of the Thesis

Chapter 3, entitled Elastic Optical Networks, offers an overview on the evolution of optical networks. The value proposition of optical transport networks as well as their critical network elements and their enabling technologies is discussed.

Chapter 4, entitled Considered Architectures and Limits of Known Results, presents in details the architectures considered in this thesis and discusses up to data advances in switching fabrics related to the ones considered in this thesis and shows how current propositions are not applicable on the considered architectures.

Chapters 5 and 6, entitled The WSW1(r, n, k) Architecture: Conditions and Analysis and The WSW2(q, p, r, n, k) Architecture: Conditions and Analysis, respectively, describe the strict-sense nonblocking conditions and the wide-sense nonblocking conditions of ten control algorithms, five for each architecture along with a numerical analysis and comparisons.

Chapter 7, entitled Optimization of Architectures, considers the optimization of proposed architectures in terms of numbers of required switching elements. The information provided by this chapter can help us understand the effect of different implementation parameters, and draw a more general conclusions about the parameters of optimal switching fabrics.

Chapter 8, entitled Conclusions and Future Work, summarizes the results of research proposed in this thesis and presents a new idea for future work.

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2

CHAPTER

Switching Fabrics

This chapter provides the basic definitions concerning switching technologies, switching fabrics and a historical review of early switching techniques. The principle of multi-stage switching fabrics is also introduced and extended with details about the widely used topologies. This chapter also presents the domains of switching and how they affect the process of switching in a switching fabric.

2.1 Switching Elements

In general, a switching function means to establish connections between a given set of terminals.

The simplest element which can realize this function is called a crosspoint. It connects one input with one output and it is usually placed in the crossing point of lines representing an input and an output. A crosspoint is represented by a circle, and the states of a crosspoint are presented in Fig. 2.1(a) and Fig. 2.1(b) [47]. Another basic element which can realize the switching function

Input

Output

Crosspoint

(a)

Input

Output

Crosspoint

(b)

Figure 2.1: Crosspoint in: (a) off and (b) on states.

is called the basic switching element (BSE). Unlike the crosspoint, BSE can connect more inputs and outputs. A directional coupler is one example of the BSE. It has two inputs and two outputs

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Chapter 2 Historical Review

and it can be also in one of two states, called cross and bar, as it is shown in Fig. 2.2 [47]. In the bar state, the upper input is connected to the upper output and the lower input is connected to the lower output. In the cross state, the upper input is connected to the lower output and the lower input connected to the upper output.

Bar state Cross state

Figure 2.2: Bar and cross states of 2 × 2 BSE.

In a crossbar switch, BSEs are arranged in a two dimensional grid, and by setting the individual elements in bar or cross states, any input can be connected to any output without internal blocking. Fig. 2.3 presents a 4 × 4 switch implemented with crosspoints and 2 × 2 BSEs.

Inputs

Outputs 0 1 2 3

0 1 2 3

(a)

Inputs

Outputs 0 1 2 3

0 1 2 3

(b)

Figure 2.3: The 4 × 4 switch implemented with: (a) crosspoints and (b) 2 × 2 BSEs.

2.2 Historical Review

One of the first to propose a telephone exchange was the Hungarian Tivadar Puskás in 1877 while he was working for Thomas Edison [6, 7]. The first experimental telephone exchange was based on the ideas of Puskás, and it was built by the Bell Telephone company in Boston in 1877.

The world’s first state-administered telephone exchange was opened on November 12, 1877 in Friedrichsberg close to Berlin under the direction of Heinrich von Stephan [16], while George W.

Coy designed and built the first commercial US telephone exchange which was opened in New

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Chapter 2 Historical Review

Haven, Connecticut in January, 1878. The switchboard was built from "carriage bolts, handles from teapot lids and bustle wire" and could handle two simultaneous conversations. In Europe, other early telephone exchanges were based in London and Manchester, both were opened under Bell patents in 1879 [75], while Belgium had its first International Bell exchange (in Antwerp) a year later.

In 1889, Almon Strowger applied for a U.S. patent (which was issued in 1891) for what would be the basis for the first practical automatic telephone switch. In the Strowger switch, pulses are generated in the subscriber telephone by moving an electromagnetic contacts in a stack of rotary contacts, thus selecting a telephone number, one digit at a time, without operator intervention. As the switch had a 10 × 10 bank of contacts, the earliest switch could handle only 100telephones. The development of multilevel switching greatly increased the switch capacity, initially to 6, 000 and ultimately 10, 000 telephones [70]. The successor of Strowger switches was the panel switch. It was an extremely complex device, with tall panels covered with 500 rows of terminals. Each panel had an electric motor, which drives its (usually sixty) selectors with electromagnetically controlled clutches. The selector moved continuously rather than in steps, and the selectors could move a considerable distance. Separate frames were used for the several parts of the telephone-calling process. AT&T began to work on an alternative to the panel switch even before the first panel switch was installed. In 1913, J.N. Reynolds of Western Electric invented the crossbar selector, in which a small number of magnets operated a large number of relay contacts in a coordinate array. This means that there were only small mechanical motions and none of the large sliding movements, which were required in the panel and Strowger switches. However, the crossbar selector was too expensive at that time to be put into use. Bell Labs also redesigned the crossbar as a smaller switch for use in suburban and other non-urban exchanges, where it replaced step-by-step switches. This new switch, which was known as the

#5 crossbar, first went into service in Media, Pennsylvania in 1948.

Europe was not far away from the telecoms revolution, where L.M. Ericsson was the first company to present an electronic trial exchange, the EMAX (Electronic Multiplex Automatic Exchange) in 1954. EMAX was a laboratory module made of diodes and cold-cathode tubes and was the first to apply time-division switching principle [36]. The beginning of electronic switching studies in France can be dated to 1957, with the establishment of Electronic Machine Research Department (RME). After one year, Socotel (Société mixte pour le développment de la technique de la Commutation dans le domaine des Télecommunications) was founded.

The members of Socotel were administration and its main suppliers of switching equipment.

Socotel divided the research work so that the RME worked on full electronic exchanges and the research departments of the manufacturers on semi-electronic switching elements.

RME produced two entirely different electronic switching prototypes, known as Aristotle and Socrate. Aristotle ( Appareillage Réalisant Intégralement et Systématiquement Tout Opération

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Chapter 2 Switching Technologies

de Téléphonie Électronique) was a model to be used in setting up a high-capacity system organized around one central processor and a number of peripheral secondary processors under the exclusive use of electronic components. Its central processor, known as Ramses, was an original achievement of RME. Aristotle was developed in 1963 and put into operation first by CNET at Issy-les-Moulineux and then transferred to Lannion, where it handled the internal telephone service of the CNET sites up to 1969 [28].

The Socrate ( Systéme Original de Commutation Rapide Automatiqe á Traitement Électronique) project was carried out in close cooperation with the French manufacturers.

Socrate was a semi-electronic exchange using the crossbar-switching network of the CP-400 system. Ferrite cores and magnetic drums were used for the memories. The control system used a new method known as load sharing between duplicated processors. The Socrate experimental exchange was in service at CNET-Lannion from early 1965 to 1972. In Germany, Siemens developed a time-division electronic switching system called EVA ( Electronische Vermittlungs Anlage; electronic switching equipment). A 1000-line prototype entered into service in early 1962 in Munich within the private network of Siemens. The EVA installation operated satisfactorily for a long time, but the time was not yet ripe for cost-competitive production of time-division switching equipment. In the U.K, research on electronic switching began very soon after World War II at Dollis Hill. The British researchers concentrated from the beginning on time–division electronic switching. In 1956, GPO labs and five British manufacturers founded the Joint Electronic Research Committee (JERC). JERC developed a time–division switch using pulse amplitude modulation (PAM), this was followed by a 600-line exchange which was installed in north London suburb of Highgate Wood. In December 1962, the world’s first public time–division switch was invented, precisely 50 years after the first British automatic telephone exchange had been installed at Epsom [36]. By the 1970s it was clear that the days of the electromechanical switch were numbered, because in 1965 AT&T had installed the first electronic switch, the #1 ESS (Electronic Switching System) in a local exchange in Succasunna, New Jersey [45].

2.3 Switching Technologies

The work of this thesis is mainly about optical switching, therefore, I will concentrate on various optical switching technologies and the concept of electrical switching is briefly explained because they are still used until today.

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2.3.1 Electronic Switching

The analog switch is an electronic component that behaves in a similar way to a relay, but has no moving parts. The switching element is normally a pair of MOSFET transistors, one is an N-channel device, the other is a P-channel device. The device can conduct analog or digital signals in either direction when on and isolates the switched terminals when off. Analogue switches are usually manufactured as integrated circuits in packages containing multiple switches (typically two, four or eight).

Analog switches are able to pass or isolate both analog and digital signals, but digital switches can only pass or isolate digital signal lines. Both are used instead of mechanical switches for convenience, reliability, and their small size as compared to mechanical switches. There are some limitations on the signals that can be carried by both types of switches. Analog switches have a frequency response limitation due to channel capacitance. (A signal-level change can be caused by parasitic capacitance at high frequencies, for example.) For digital switches, there is a maximum frequency that can be fed into the input of the digital switch, after which the output state of the switch will no longer reliably follow the input. With both types of switches, the data sheet of the switch will reveal the limitations. An example of a simple electronic crossbar is shown in Fig. 2.4, where control signals are applied to gates of transistors that connect rows to columns as desired [38].

Data In

Data Out

Configuration

Figure 2.4: Electronic 4 × 4 crossbar.

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2.3.2 Optical Switching

There have been numerous proposals to implement the light switching function between optical fibers, such as semiconductor amplifiers, liquid crystals, holographic crystals, and tiny mirrors.

In this section, we explore some of the widely used technologies for optical domain switching.

Figure 2.5: Mirrors in MEMS based optical switch.

An optical switch that is based on Microelectromechanical System (MEMS) technology, is presented in Fig. 2.5. It consists of mirrors no larger in diameter than a human hair, which are arranged on special pivots so that they can be moved in three dimensions. Several hundreds of such mirrors can be placed together on mirror arrays no larger than a few centimeters square.

Light from an input fiber is aimed at a mirror, which is directed to move the light to another mirror on a facing array. This mirror then reflects the light down towards the desired output optical fiber [30]. Since MEMS contains so many mirrors on a single chip, the cost per switching element is relatively low. However, since it involves moving parts, MEMS is fairly slow to switch, requiring milliseconds to do so. This is fine for lambda provisioning or restoration but is too slow for optical burst switching or optical packet switching applications. By applying more current, the mirror can move faster, but there is a limit to how much current can be sent into the array of mirrors. By changing the mirror design so that the angle through which light is bent is smaller, it is possible to achieve faster switching speeds. This technique is known as "fast MEMS".

There are many designs of MEMS-based optical switches, which can mainly be classified into two categories according to their working principles. The first is based on the manipulation of the propagation direction of the light by reflecting structures. Typically, such MEMS optical switches consist of an array of tiny micro-mirrors and moving parts arranged on special substrate material with CMOS-integrated circuits [3]. The micro-mirror is usually fabricated by depositing

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dielectric layers on a substrate, which is typically a single crystal or polycrystalline silicon substrate, and then etching selected material using photolithographic technology [103]. The reflector surface of the mirror is often made of thin metal coating such as aluminum or gold. By applying current on the moving parts, the mirror and the surrounding ring can rotate by a certain angle and reflect the beam of light from an input port to a specified output port. This structure can easily be batch-fabricated in the form of arrays of hundreds of mirror elements in a single chip of a few centimeter square. The second category is based on the adjusting of the phase of light through mechanical motion in MEMS to achieve switching function due to diffractive or interference effects. Examples of this are the mechanical anti-reflection switch [110] and the tunable grating structure-based switch [97]. Both categories make use of motion of micro-mirrors to realize switching and share the common features of MEMS devices, while the first category is more widespread for commercialization due to its advantage in batch fabrication. A commercial MEMS optical switch consists of MEMS arrays integrated on a single chip, driving circuits, control software, and input/output ports. MEMS arrays are usually built in two-dimensional (2D) and three-dimensional (3D) configurations [29, 86]. In 2D MEMS, shown in Fig. 2.6 [122], light beams from the input ports are steered to the desired output ports by the corresponding switching elements within a single plane. The crossbar switching fabric can be easily implemented with two-dimensional (2D) MEMS. Small switches, i.e., a 2 × 2 MEMS switches with two input and two output ports, have been available in market for a few years. The crossbar architecture can be easily extended to larger scaled N × N optical switches [92]. However, physical constraints became dominant for large-scale implementations [65].

Input Fiber

Output Fiber

Mirror Input Fiber

Input Fiber

Output Fiber

Figure 2.6: The 2D 2 × 2 MEMS crossbar optical switch.

In order to support large-scale switching, MEMS optical switches with 3D structure have been proposed [12, 114]. The architecture of a N × N 3D MEMS optical switch, which consists of a pair of two-axis (2D) tilting mirror arrays and optical fiber collimator arrays, is illustrated in Fig. 2.7 [62]. The light beams from the input ports are collimated by input collimators onto the first tilting micro-mirror array, which then reflects the light beams to the second micro-mirror array that redirects the beams to the corresponding output ports through the output collimators.

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Since the tilting range of each micro-mirror in the first array can continuously cover all the micro-mirrors of the second array, the light beams from each input port can reach any output port by precisely adjusting the tilting angles of micro-mirrors in two arrays, yielding a non-blocking switching in this structure. Compared with 2D structure, the 3D structure allows the switch to achieve even larger scalability. One of the challenges of 3D MEMS optical switch is the fact that the system requires complex control software to coordinate operations of thousands of micro-mirrors.

Figure 2.7: Cross-sectional view of a conventional 3D MEMS optical switch.

Liquid Crystals (LCs) are materials showing characteristics that are intermediate between those of a crystal and those of an isotropic liquid, thus possessing unique electric and optical properties. Even though LCs have been known for more than a century, they have become widely used in electro-optic applications only since the early 1960s. The switching function of liquid crystals is achieved by placing the material between a pair of parallel glass plates to manipulate polarization states of light. Applying voltage across the crystal layer rotates the polarization of the light passing through it [109]. With suitably arranged polarizing optics, the liquid crystal can function as a 1 × 2 switch. Voltage effect on liquid crystal states is presented in Fig. 2.8.

Figure 2.8: Liquid crystal cell without (a) and with voltage (b).

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The Agilent all-optical bubble switch uses bubbles in an organic fluid index matched to a silica planar lightwave circuit. In contrast to the inkjet bubble, the optical switch bubble is continuously on during operation [107]. The continuous operation means that the fluid flow is continuous, heaters dissipate power continuously, and inertia effects are only noticeable during turn on and turn off. The bubble is created and sustained by heaters that are deposited on an attached silicon substrate. The switch is made up of two layers: a silica bottom layer, through which optical signals travel, and a silicon top layer, containing the inkjet technology. In the bottom layer, two series of waveguides intersect each other at an angle of around 120^◦. At each crosspoint between two guides, a tiny hollow is filled in with a liquid that exhibits the same refractive index of silica, in order to allow propagation of signals in normal conditions. Thus, a light beam travels straight through the waveguide, unless the waveguide is interrupted by a bubble placed in one of the hollows at the crosspoints. In this case, light is deflected into a new waveguide crossing the path of the previous one. Bubbles are generated by means of tiny electrodes placed in the top silicon layer, which heat the liquid until it gasifies [107].

Thermo-optic switches are based on the thermo-optic effect. Such switches depend on the variation of the refractive index of a dielectric material, due to temperature variation of the material itself [10, 85]. There are two categories of thermo-optic switches: interferometric and digital optical switches. While the former need a particular value of the driving voltage to achieve the switching of signals, the latter are characterized by a threshold value of the driving voltage and a step-like response (hence, the adjective digital).

Interferometric switches are usually based on Mach-Zender interferometers [22]. These devices consist of a first 3-dB coupler, that splits the signal into two beams, which then travel through two distinct arms of the same length, and of a second 3-dB coupler which merges and finally splits the signal again. Heating one arm of the interferometer causes its refractive index to change. Consequently, a variation of the optical path of that arm is experienced. It is thus possible to vary the phase difference between the light beams by heating one arm of the interferometer.

Hence, as interference is constructive or destructive, the power on alternate outputs is minimized or maximized. The output port is thus selected. Digital optical switches exhibits a nonperiodic switching characteristic. They are based on mode sorting in adiabatic waveguide branches and crossings. Digital switches are wavelength insensitive within some limits. However, the known symmetrical designs do not yield a defined zero-voltage state. They require a driving voltage for both switching states. First digital optical switches have been realized on LiNbO3 with a symmetrical design in order to employ electro-optical push-pull operation [32].

Poznan University of Technology