List of Figures

(``Optical Communication Networks''
by Biswanath Mukherjee)

	Number	Table Caption	Page
	1.1	The low-attenuation regions of an optical fiber.	6
	1.2	A four-channel point-to-point WDM transmission system with amplifiers.	10
	1.3	A Wavelength Add/Drop Multiplexer (WADM).	11
	1.4	A 4 x 4 passive star.	12
	1.5	A 4 x 4 passive router (four wavelengths).	12
	1.6	A 4 x 4 active switch (four wavelengths).	13
	1.7	A passive-star-based local optical WDM network.	14
	1.8	A wavelength-routed (wide-area) optical WDM network.	16
	1.9	A wavelength-routed WDM network.	22
	2.1	The low-attenuation regions of an optical fiber.	24
	2.2	Single-mode and multimode optical fibers.	26
	2.3	Light traveling via total internal reflection within a fiber.	27
	2.4	Graded-index fiber.	28
	2.5	Numerical aperture of a fiber.	28
	2.6	Splitter, combiner, and coupler.	35
	2.7	A 16 x 16 passive-star coupler.	36
	2.8	The general structure of a laser.	38
	2.9	Structure of a semiconductor diode laser.	39
	2.10	Free spectral range and finesse of a tunable filter capable of tuning to N different channels.	47
	2.11	Cascading filters with different FSRs.	48
	2.12	Structure of a Mach-Zehnder interferometer.	49
	2.13	A semiconductor optical amplifier.	54
	2.14	Erbium-doped fiber amplifier.	55
	2.15	The gain spectrum of an erbium-doped fiber amplifier with input power = - 40 dBm.	56
	2.16	2 x 2 crossconnect elements in the cross state and bar state.	58
	2.17	Schematic of optical crosspoint elements.	60
	2.18	A 2 x 2 amplifier gate switch.	62
	2.19	A 4 x 4 nonreconfigurable wavelength router.	63
	2.20	The waveguide grating router (WGR).	64
	2.21	A P x P reconfigurable wavelength-routing switch with M wavelengths.	67
	2.22	The staggering switch architecture.	68
	2.23	The CORD architecture.	69
	2.24	The HLAN architecture.	70
	2.25	An all-optical wavelength-routed network.	70
	2.26	Wavelength-continuity constraint in a wavelength-routed network.	71
	2.27	Functionality of a wavelength converter.	72
	2.28	An opto-electronic wavelength converter.	73
	2.29	A wavelength converter based on nonlinear wave-mixing effects.	74
	2.30	A wavelength converter using co-propagation based on XGM in an SOA.	76
	2.31	An interferometric wavelength converter based on XPM in SOAs.	76
	2.32	Conversion using saturable absorption in a laser.	77
	2.33	A switch which has dedicated converters at each output port for each wavelength.	79
	2.34	Switches which allow sharing of converters.	80
	2.35	The share-with-local wavelength-convertible switch architecture.	81
	2.36	Architecture which supports electronic wavelength conversion.	81
	2.37	Broadcast-and-select WDM local optical network with a passive-star coupler network medium.	86
	2.38	Lightpath routing in a WDM WAN.	90
	2.39	MONET New Jersey Area Network.	93
	2.40	ONTC testbed.	95
	2.41	The AT&T/MIT-LL/DEC AON testbed architecture.	96
	2.42	Critical angle in a step index fiber.	98
	2.43	Critical angle in a graded index fiber.	98
	2.44	Two architectures for wavelength convertible routers: (a) share-per-node, (b) share-per-link.	103
	2.45	T=Transmitter, R=Receiver. All connections begin at transmitters and end at receivers	105
	3.1	A broadcast-and-select WDM network.	110
	3.2	Alternative physical topologies for a WDM local lightwave network.	111
	3.3	Architecture of the PAC optical packet network (the dashed lines are used to detect energy on the various channels from the ``main" star).	124
	3.4	The ALOHA/ALOHA protocol.	125
	3.5	Bimodal throughput characteristics of the slotted-ALOHA/ delayed-ALOHA protocol for L = 10 slots per data packet and N = number of data channels.	127
	3.6	Nonmonotonic delay characteristics of the slotted-ALOHA/ delayed-ALOHA protocol for L=10 slots per data packet, N=3 data channels, zero propagation delay, and different values of the backoff parameter K.	128
3.7	The extended slotted-ALOHA protocols: (a) simple case, (b) higher concurrency to reduce channel wastage. Note: $\lambda_0$ is the control channel and $\lambda_1, \lambda_2, ... , \lambda_N$ are data channels.	130
3.8	The dynamic time-wavelength division multiple access (DT-WDMA) protocol.	135
3.9	The multichannel bus network: (a) network structure with tunable transmitters and fixed receivers, and (b) a cycle in AMTRAC for N=4 and M=4.	140
3.10	Classification of single-hop network architectures.	142
4.1	Passive-star topology for Rainbow.	150
4.2	State diagram for the Rainbow model.	154
4.3	Timing for connection setup.	156
4.4	Throughput vs. arrival rate. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau$ = 1 ms, $1/\rho$ = 100 ms.	160
4.5	Throughput vs. message size. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau$ = 1 ms, $\sigma = 0.0001 msg/slot, $\phi = 10$ ms.	161
4.6	Throughput vs. timeout duration. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau = 1$ ms, $1/\rho=100$ ms.	161
4.7	Timeout probability vs. timeout duration. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau = 1$ ms, $1/\rho=100$ ms.	162
4.8	Throughput vs. timeout duration for different message lengths. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau = 1$ ms, $\sigma = 0.0001 msg/slot.	163
4.9	Delay vs. throughput with parameter $\phi $. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau = 1$ ms, $\sigma = 0.0001 msg/slot, $1/\rho= 100$ ms.	164
4.10	Delay vs. throughput with parameter $\sigma $. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau = 1$ ms, $1/\rho= 100$ ms, $\phi = 10$ ms.	165
4.11	Delay vs. throughput for varying message size. Slot = 1 microsecond, N=32, R=50 microsecond, $\tau = 1$ ms, $\sigma = 0.0001 msg/slot, $\phi = 10$ ms.	165
4.12	Throughput vs. timeout duration for different number of stations. Slot = 1 microsecond, R=50 microsecond, $\tau = 1$ ms, $\sigma = 0.0001 msg/slot, $1/\rho= 100$ ms.	166
5.1	An example four-node multihop network: (a) physical topology, (b) logical topology.	172
5.2	A (2,2) ShuffleNet.	177
5.3	A (2,3) de Bruijn graph.	182
5.4	A 4 x 6 Manhattan Street Network (MSN) with unidirectional links.	184
5.5	A (2,4) ShuffleNet.	185
5.6	An eight-node binary hypercube.	187
5.7	A linear dual-bus network.	189
5.8	Classification of multihop network architectures.	196
5.9	The (10-node) Peterson graph.	199
5.10	A bidirectional ring network.	199
6.1	A 10-node (2,5,2) GEMNET.	205
6.2	Bounds and average hop distance for a P=2, 64-node GEMNET with different values of K.	212
6.3	Growing a (1,6,2) GEMNET by one node.	216
7.1	Delay behavior of a shared-channel, WDM, multihop network with changes in load $\lambda$ and number of available wavelengths w.	221
7.2	Logical assignment of wavelengths in an eight-node network arranged as a ShuffleNet with K=2 and P=2: (a) nonshared case where w=2N=16; (b) shared case where w=8 < 2N.	223
7.3	Twelve-node SC_GEMNETs, along with corresponding timing diagrams, for various values of w: (a) w=12; (b) w=6; (c) w=4; (d) w=3; and (e) w=2. (Note: unless otherwise shown, all links are directed from left to right.)	228
7.4	A (3,2) complete Moore graph.	233
7.5	Effects of sharing on multicasting in a (3,2) complete, Moore graph. The source node is node 1 and the destination nodes are nodes 2, 3, 6, and 7: (a) nonshared case; (b) shared-channel case.	234
7.6	Various delay components vs. number of wavelengths in a 12-node network with R=2 and $\lambda$ = 0.05.	239
7.7	Average delay vs. number of wavelengths in a 12-node network with R=2 and various load values. Marked points indicate values of admitting equal sharing of the available bandwidth among the 12 nodes when each node has a single transmitter-receiver pair.	241
7.8	Upper (w_H) and lower (w_L) bounds on the number of channels admitting stability and optimal number of channels (w*) vs. the load in a 12-node network. Note that the curves for R=1 and R=0 are identical; therefore only one of them is shown.	242
7.9	Average delay, T, vs. number of wavelengths, w, for various values of propagation delay in a 120-node network: (a) $\lambda$ = 0.001; (b) $\lambda$ = 0.005; (c) $\lambda$ = 0.01; (d) $\lambda$ = 0.05.	244
7.10	Average delay, T, vs. number of wavelengths, w, for various values of load in a 120-node network: (a) R=0; (b) R=1; (c) R=10; (d) R=100.	245
7.11	Upper (w_H) and lower (w_L) bounds on the number of channels admitting stability and optimal number of channels (w*) vs. load in a 120-node network.	246
7.12	Delay vs. load for Systems A through F: (a) m=1; (b) m=5; (c) m=20; (d) m=36.	251
7.13	Ratio of maximum throughput at a given m to the maximum throughput at m=1.	252
7.14	A (2,2) complete Moore graph.	255
7.15	A (4,2) incomplete Moore graph.	255
8.1	NSFNET T1 backbone, 1991. ( \copyright Merit Network, Inc. )	262
8.2	Modified physical topology.	266
8.3	A 16-node hypercube virtual topology embedded on the NSFNET physical topology.	267
8.4	Details of the Utah (UT) node.	268
8.5	The physical topology with embedded wavelengths corresponding to an optimal solution (more than one transceiver at any node can tune to the same wavelength).	269
8.6	The physical topology with embedded wavelengths corresponding to an optimal solution (all transceiver pairs at any node must be tuned to different wavelengths).	269
8.7	Delay vs. throughput (scaleup) characteristics with no WDM, i.e., physical topology as virtual topology.	283
8.8	Delay vs. throughput (scaleup) characteristics with WDM used on some links, but no WRSs, i.e., multiple point-to-point links are allowed on the physical topology.	284
8.9	Delay vs. throughput (scaleup) characteristics with full WDM on some links and a WRS at each node, i.e., arbitrary virtual topologies are allowed.	284
8.10	Delay vs. throughput (scaleup) characteristics for different virtual topologies.	285
8.11	Distributions of the number of wavelengths used in each of the 21 fiber links of the NSFNET for the virtual topology approach with nodal degree P = 4, 5, and 6.	287
9.1	NSFNET T1 backbone.	293
9.2	Optimal solution for a two-wavelength and a five-wavelength network. Each physical link consists of two unidirectional fibers carrying transmissions in opposite directions (hence, each wavelength may appear twice on any link in the diagrams; their signal propagation directions are opposite to each other in such cases). Wavelength 0 is used to embed the physical topology over the virtual topology, so the Wavelength-0 lightpaths are not shown explicitly in these diagrams to preserve clarity. Note: $\circ$ = transmitter; $\bullet$ = receiver.	294
9.3	Transport node in the RACE WDM optical network architecture.	306
9.4	Average packet hop distance for the optimal solution.	311
9.5	Average transceiver utilization for the optimal solution.	312
9.6	Average wavelength utilization for the optimal solution.	312
9.7	Comparison of heuristic algorithms for a four-wavelength network.	314
9.8	Reconfiguration statistics.	316
9.9	Physical network topology.	318
9.10	Physical network topology.	319
10.1	Lightpath routing in an all-optical network.	322
10.2	Effect of nodal degree d (for K=2 alternate paths) on wavelength routing.	335
10.3	Effect of number of connections on link congestion.	338
10.4	Connection requests.	340
11.1	An all-optical wavelength-routed network.	342
11.2	Wavelength-continuity constraint in a wavelength-routed network.	343
11.3	Functionality of a wavelength converter.	344
11.4	A switch which has dedicated converters at each output port for each wavelength.	345
11.5	Switches which allow sharing of converters.	346
11.6	Wavelength conversion for distributed network management.	350
11.7	Blocking probabilities for different loads in a 10-node optical ring with sparse nodal conversion.	358
11.8	NSFNET with the number of convertible routes shown. A number on a link indicates how many source-destination paths passed through the previous node and possibly could have been converted. A number next to a node indicates how many source-destination paths pass through the node and can possibly be wavelength converted.	359
11.9	Blocking probabilities in the NSFNET for optimal and heuristic placement of wavelength converters (30 ERLANG load).	360
11.10	Comparison of blocking probabilities in the NSFNET when using full conversion and no conversion in the network with the Best-Fit algorithm.	362
11.11	Percent gain in the NSFNET from using full-conversion at every node as opposed to no conversion in the network.	362
11.12	Distribution of the number of wavelength converters utilized at node 2 in the NSFNET (30 ERLANG load).	363
11.13	Network with uniform loading.	366
12.1	Implementation of the circuit-migration sequence.	381
12.2	Network architecture for distributed control and management.	382
12.3	The AT&T testbed architecture.	388
12.4	The Bellcore all-optical network architecture.	390
12.5	Transport node in the RACE architecture.	392
13.1	The WDDI ring network.	400
13.2	WDDI node and bridge interfaces.	403
13.3	Delay versus N characteristics for two-server traffic (W=2).	420
13.4	Delay versus N characteristics for clustered traffic, c=2, k=5 (W=2).	422
13.5	Delay versus N characteristics for pseudo-random traffic (W=2).	423
13.6	Delay versus throughput characteristics (W=2).	424
13.7	Delay vs. throughput characteristics for multiple partitions for MIN-DIFF-based algorithms.	426
13.8	Delay vs. number of partitions for MIN-DIFF-based algorithms.	426
13.9	Delay vs. throughput characteristics for multiple partitions for MIN-CROSS-based algorithms.	428
13.10	Delay vs. number of partitions for MIN-CROSS-based algorithms.	428
14.1	EDFA gain curve.	433
14.2	Wavelength routing using AOTF.	434
14.3	Wavelength-routed network with $\Lambda_0$ cycles.	436
14.4	An example five-station, five-switch subgraph of the NSFNET T3 backbone. This network is used for the example ``static'' analysis results.	437
14.5	A (random) four-station, eight-switch network generated by Module 1. Note that this network contains $\Lambda_0$ cycles (as indicated by dashed and dotted lines) when all switches are in BAR state.	438
14.6	Flow chart of modules.	439
14.7	Network after elimination of $\Lambda_0$ cycles using Module 3.	448
14.8	Network after establishing two connections -- heavy lines -- (from station 2 to station 4 and from station 4 to station 3) using Module 4. However, a new connection -- dashed heavy line -- (from station 3 to station 1) is causing a $\Lambda_k$ cycle -- dashed light line.	448
14.9	Network after elimination of $\Lambda_k$ cycles using Module 5.	449
14.10	Fraction of unblocked calls vs. M for the 5-station, 17-link network.	452
14.11	Probability of resource blocking vs. M for the 5-station, 17-link network.	452
14.12	Probability of crosstalk blocking vs. M for the 5-station, 17-link network.	453
14.13	Fraction of unblocked calls vs. M for the 14-station, 56-link network.	454
14.14	Probability of resource blocking vs. M for the 14-station, 56-link network.	454
14.15	Probability of crosstalk blocking vs. M for the 14-station, 56-link network.	455
14.16	Network for Problem 14.1.	459
14.17	Network for Problems 14.2 and 14.3.	460
14.18	Network for Problem 14.4.	461
15.1	Example of a passive-star-based optical metropolitan-area network (slightly modified version of the one used in [LTGC94]).	464
15.2	Example of a nonreflective star.	465
15.3	Two examples of powers on three wavelengths passing through a fiber.	467
15.4	Simple two-star network that needs no amplifiers to operate.	468
15.5	Original amplifier gain model approximations used in previous studies [LTGC94].	470
15.6	More-accurate amplifier gain model used in this study.	471
15.7	Mid-sized tree-based network needing no amplifiers to function.	481
15.8	A possible MAN network.	482
15.9	A scaled-up version of the MAN network in Fig. 15.8.	485
15.10	A scaled-down version of the MAN network in Fig. 15.8.	485
15.11	A sample switched network.	487
15.12	A cascade of amplifiers along a link.	489
15.13	Network for Problems 15.5 and 15.6.	490
15.14	A portion of a network.	491
15.15	A distribution network.	492
16.1	A TDM link and multiplexer.	495
16.2	Generation of the OTDM signal: packet compression.	498
16.3	Evolution of a nonhyperbolic secant pulse in a fiber.	502
16.4	Evolution of a hyperbolic secant pulse in a fiber.	502
16.5	All-optical clock recovery system (BPF = band-pass filter, PC = polarization controller) [BCHK96].	503
16.6	The HLAN architecture.	505
16.7	The staggering switch architecture.	506
16.8	The CORD architecture.	507
16.9	A pseudo-random sequence generator.	511
16.10	A CDMA receiver.	512
16.11	Original data streams and coded, transmitted streams.	513
16.12	Combined signals on data channel.	514
16.13	Decoded sequence consisting of original signal and pseudo-noise.	515
16.14	Decoded sequence with varying number of overlapping signals.	516
16.15	Implementation of a CDMA coder and decoder based on optical splitters and combiners.	517
16.16	Optical time-spreading CDMA.	519
16.17	CDMA codes.	521

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