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Chapter 12 Basic Optical Network 12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses 12.1.3 Performance of Star Architectures 12.3 Broadcast-and-Select WDM Networks 12.3.1 Broadcast-and-Select Single-Hop Networks 12.3.2 Broadcast-and-Select Multihop Networks 12.3.3 The ShuffleNet Multihop Network 8.3 Demodulation Schemes 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 Chapter 12 Basic Optical Network 12.4 Wavelength-Routed Networks 12.4.1 Optical Cross-Connects 12.4.2 Performance of Wavelength Conversion 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1 Basic Networks Figure 12-1 shows the three common topologies used for fiber optic networks: the linear-bus, ring, and star configurations. Access to an optical data bus is achieved by means of a coupling element. An active coupler converts the optical signal on the data bus (Fig. 12-1(a)) to its electric baseband counterpart before any data processing is carried out. A passive coupler employs no electronic elements. It is used passively to tap off a portion of the optical power from the bus. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1 Basic Networks Figure 12-1(a). Linear bus topology used for fiber optic networks. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1 Basic Networks In a ring topology, consecutive nodes are connected by point-to-point links that are arranged to form a single closed path. Information in the form of data packets is transmitted from node to node around the ring. The interface at each node is an active device that has the ability to recognize its own address in a data packet in order to accept messages. The active node forwards those messages that are not addressed to itself on to its next neighbor. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1 Basic Networks Figure 12-1(b). Ring topology for fiber optic networks. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1 Basic Networks In a star architecture, all nodes are joined at a single point called the central node or hub. Using an active hub, one can control all routing of messages in the network from the central node. In a star network with a passive central node, a power splitter is used at the hub to divide the incoming optical signals among all the outgoing lines to the attached stations. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1 Basic Networks Figure 12-1(c). Star topology for fiber optic networks. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Over an optical fiber of length x (in km), the ratio Ao of received power P(x) to transmitted power P(0) is given by Ao = P(x)/P(0) = 10-ax/10 (12-1) where a is the fiber attenuation in units of dB/km. The losses encountered in a passive coupler in a linear bus are shown in Fig. 12-2. The coupler has four functioning ports: two for connecting the coupler onto the fiber bus, one for receiving tapped-off light, and one for inserting optical signal onto the line after the tap-off to keep the signal out of the local receiver. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Figure 12-2. Losses in a passive linear-bus coupler consisting of cascaded directional couplers. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses If a fraction Fc of optical power is lost at each port of the coupler, then the connecting loss Lc is Lc = -10 log(1-Fc) (12-2) For example, if we take this fraction to be 20%, then Lc is about 1 dB; that is, the optical power gets reduced by 1 dB at any coupling junction. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Let CT represent the fraction of power that is removed from the bus and delivered to the detector port. The power extracted from the bus is called a tap loss and is given by Ltap = 10 log CT (12-3) For a symmetric coupler, CT is also the fraction of power that is coupled from the transmitting input port to the bus. If Po is the optical power launched from a source flylead, the power coupled to the bus is CTPo. The throughput coupling loss Lthru is then given by Lthru = -10 log(1 - CT)2 = -20 log(1 - CT) 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-4) 12.1.2 Performance of Passive Linear Buses In addition to connection and tapping losses, there is an intrinsic transmission loss Li associated with each bus coupler. If the fraction of power lost in the coupler is Fi, then the intrinsic transmission loss Li is Li = -10 log(1 - Fi ) (12-5) Consider a simplex linear bus of N stations uniformly separated by a distance L, as shown in Fig. 12-3. From Eq. (12-1) the fiber attenuation between any two adjacent stations is Lfiber = -10 logAo = aL 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-6) 12.1.2 Performance of Passive Linear Buses Figure 12-3. Topology of a simplex linear bus consisting of N uniformly spaced stations. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses NEAREST-NEIGHBOR POWER BUDGET. The smallest distance in transmitted and received power occurs for adjacent stations, such as between stations 1 and 2 in Fig. 12-3. If Po is the optical power launched from a source at station 1, then the power detected at station 2 is P1,2 = AoCT2(1-Fc)4(1–Fi)2Po 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-7) 12.1.2 Performance of Passive Linear Buses The optical power flow encounters the following loss-inducing mechanisms: One fiber path with attenuation Ao. Tap points at both the transmitter and the receiver, each with coupling efficiencies CT. Four connecting points, each of which passes a fraction (1 - Fc) of the power entering them. Two couplers which pass only the fraction (1 – Fi) of the incident power owing to intrinsic losses. Using Eqs. (12-2) ~ (12-4) and Eq. (12-6), the losses between stations 1 and 2 can be expressed as 10 log(Po/P1,2) = aL+2Ltap+4Lc+2Li. (12-8) 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses LARGEST-DISTANCE POWER BUDGET. The largest distance occurs between stations 1 and N. The fractional power level coupled into the cable from the bus coupler at station 1 is F1 = (1-Fc)2 CT (1–Fi) (12-9a) At station N the fraction of power from the buscoupler input port that emerges from the detector port is FN = (1-Fc)2 CT (1–Fi) 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-9b) 12.1.2 Performance of Passive Linear Buses For each of the (N - 2) intermediate stations, the fraction of power passing through each coupling module (shown in Fig. 12-2) is Fcoup = (1-Fc)2(1-CT)2(1–Fi), (12-10) since the power flow encounters two connector losses, two tap losses, and one intrinsic loss. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Combining the expressions from Eqs. (12-9a), (129b), and (12-10), and the transmission losses of the N – 1 intervening fibers, we find that the power received at station N from station 1 is P1,N = AoN-1F1FcoupN-1FNPo = AoN-1(1-Fc)2N(1-CT)2(N-2)CT2(1-Fi)NPo (12-11) 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Using Eqs. (12-2) ~ (12-6), the power budget for this link is 10.log(Po/P1,N) = (N-1)aL +2NLc +(N-2)Lthru +2Ltap +Nli = N(aL +2Lc +Lthru+Li) –aL -2Lthru +2Ltap (12-12) The losses of the linear bus increase linearly with the number of stations N. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Example 12-1 : Compare the power budgets of three linear buses, having 5, 10, and 50 stations, respectively. Assume that CT = 10 %, so that Ltap = 10 dB and Lthru = 0.9 dB. Let Li = 0.5 dB and Lc = 1.0 dB. If the stations are relatively close together say 500 m, then for an attenuation of 0.4 dB/km at 1300 nm the fiber loss is 0.2 dB. Using Eq. (12-12), the power budgets for these three cases can be calculated as shown in Table 12-1. The total loss values given in Table 12-1 are plotted in Fig. 12-4, which shows that the loss increases linearly with the number of stations. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Table 12-1. Comparison of the power budgets of three linear buses that have 5, 10, and 50 stations, repectively. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Figure 12-4. Total loss as a function of the number of attached stations for linear-bus and star architectures. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Example 12-2 : For the Example 12-1, suppose that for implementing a 10-Mb/s bus we gave a choice of an LED that emits -10 dBm or a LD capable of emitting +3 dBm of optical power. APD receiver with sensitivity of -48 dBm is used at the destination. In the LED case, the power loss allowed up to 5 stations on the bus. For the LD, we gave an additional 13 dB of margin, so we can have a maximum of 8 stations connected to the bus. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses DYNAMIC RANGE: System dynamic range is the maximum optical power range to which any detector must be able to respond. The worst-case dynamic range (DR) is found from the ratio of Eq. (12-7) to Eq. (12-11): (12-13) This could be the difference in power levels received at station N from station (N - 1) and from station 1 (i.e., P1,2 = PN-1,N). 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.2 Performance of Passive Linear Buses Example 12-3 : Consider the linear buses described in Example 12-1. For N = 5 stations, from Eq. (12-13) the dynamic range is DR = 3[0.2 + 2(l.0) + 0.9 + 0.5] dB = 10.8 dB. For N = 10 stations, DR = 8[0.2 + 2(l.0) + 0.9 + 0.5] dB = 28.8 dB. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.3 Performance of Star Architectures From Eq. (10-25), for a single input power Pin and N output powers, the excess loss is given by Excess Loss = Lexcess = 10.log(Pin/SNi=1Pouti) (12-14) The total loss of the device consists of its splitting loss plus the excess loss in each path through the star. The splitting loss is given by Splitting Loss = Lsplit = -10.log(1/N) = 10.logN (12-15) 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.3 Performance of Star Architectures For power-balance equation, the following parameters are used: • PS is the fiber-coupled output power from a source in dBm. • PR is the minimum optical power in dBm required at the receiver to achieve a specific BER. • a is the fiber attenuation. • All stations are located at the same distance L from the star coupler. • Lc is the connector loss in decibels. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.3 Performance of Star Architectures The power-balance equation for a particular link between two stations in a star network is PS - PR = Lexcess + a(2L) + 2Lc + Lsplit = Lexcess + a(2L) + 2Lc + 10.logN. (12-16) In contrast to a passive linear bus, for a star network the loss increases much slower as logN. Figure 12-4 compares the performance of the two architectures. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.3 Performance of Star Architectures Figure 12-4. Total loss as a function of the number of attached stations for linear-bus and star architectures. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.3 Performance of Star Architectures Example 12-4 : Consider two star networks that have 10 and 50 stations, respectively. Assume each station is located 500 m from the star coupler and that the fiber attenuation is 0.4 dB/km. Assume that the excess loss is 0.75 dB for the 10-station network and 1.25 dB for the 50-station network. Let the connector loss be 1.0 dB. For N = 10, from Eq. (12-16) the power margin between the transmitter and the receiver is PS - PR = [0.75 + 0.4(1.0) + 2(1.0)10log10] dB For N = 50, the power margin is PS - PR = [1.25 + 0.4(1.0) + 2(1.0)10log50] dB 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.1.3 Performance of Star Architectures Using the transmitter output and receiver sensitivity values given in Example 12-2, we see that an LED transmitter can easily accommodate the losses in this 50-station star network. In comparison, a laser transmitter could not even meet the 10-station design in a passive linear bus. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3 Broadcast-and-Select WDM Networks Broadcast-and-select techniques employing passive optical stars, buses, or wavelength routers are used for LAN applications. Active optical components form the basis for constructing wide-area wavelength-routing networks. Single-hop refers to broadcast-and-select networks where information transmitted without O/E conversions at any intermediate point. Intermediate E/O conversion can occur in a multihop broadcast-and-select network. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.1 Broadcast-and-Select Single-Hop Networks Figure 12-14 shows N sets of transmitters and receivers being attached to a star coupler or a passive bus. Each transmitter sends its information at different wavelength. All transmissions from various nodes are combined in a passive star coupler or coupled onto a bus and the result is sent out to all receivers. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.1 Broadcast-and-Select Single-Hop Networks Figure 12-14. Alternate physical architectures for a WDM-based local network : (a) star, (b) bus. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.1 Broadcast-and-Select Single-Hop Networks Figure 12-15 illustrates the concept of multicast or broadcast for a star network. Workstations at nodes 4 and 2 communicate using l2, whereas a user at node 1 broadcasts information to workstations at nodes 3 and 5 using l1. The same concepts are applicable to bus structures, although the losses encountered in the star and bus architectures are different. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.1 Broadcast-and-Select Single-Hop Networks Figure 12-15. A single-hop broadcast-and-select network. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.1 Broadcast-and-Select Single-Hop Networks The WDM setup in Fig. 12-15 is protocol transparent. This means that different sets of communicating nodes can use different information-exchange rules (protocols) without affecting the other nodes in the network. This is analogous to TDM telephone lines in which voice, data, or facsimile services are sent in different time slots without interfering with each other. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.2 Broadcast-and-Select Multihop Networks Figure 12-16 shows an example of a four-node broadcast-and-select multihop network where each node transmits on one set of two fixed wavelengths and receives on another set of two fixed wavelengths. Stations can send information directly only to those nodes that have a receiver tuned to one of the two transmit wavelengths. Information destined for other nodes will have to be routed through intermediate stations. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.2 Broadcast-and-Select Multihop Networks Figure 12-16. Architecture and traffic flow of a multihop broadcast-and-select network. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.2 Broadcast-and-Select Multihop Networks As shown in Fig. 12-17, at each intermediate node, the address header is decoded to examine the routing information field. Using this routing information, the packet is switched electronically to the specific optical transmitter. The specific optical transmitter will appropriately direct the packet to the next node in the logical path toward its final destination. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.2 Broadcast-and-Select Multihop Networks Figure 12-17. Representation of the fields contained in a data packet. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.2 Broadcast-and-Select Multihop Networks The flow of traffic can be seen from Fig. 12-16. If node 1 wants to send a message to node 2, it first transmits the message to node 3 using l1. Then node 3 forwards the message to node 2 using l6. With this scheme there are no destination conflicts or packet collisions in the network, since each wavelength channel is dedicated to a particular source-destination link. For H hops between nodes, there is a network throughput penalty of at least 1/H. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.3 ShuffleNet Multihop Network The extension of perfect shuffle to optical networks consists of a cylindrical arrangement of k columns, each having pk nodes, where p is the number of transceiver pairs per node. The total number of nodes is then N = kpk with k = 1, 2, 3, ... and p = 1, 2, 3, .… 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-17) 12.3.3 ShuffleNet Multihop Network Given that each node requires p wavelengths to transmit information, the total number of wavelengths Nl needed in the network is Nl = pN = kpk+1 (12-18) Figure 12-18 illustrates a (p, k) = (2, 2) ShuffleNet, where the (k+1)-th column represents the completion of a trip around the cylinder back to the 1st column, as indicated by the return arrow. In this example, there are eight nodes and sixteen wavelengths. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.3 ShuffleNet Multihop Network Figure 12-18. Logical interconnection pattern and wavelength assignment of a (p,k) = (2,2) ShuffleNet. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.3 ShuffleNet Multihop Network An important performance parameter for the ShuffleNet is the average number of hops between any two randomly chosen nodes. Since all nodes have p output wavelengths, p nodes can be reached from any node in one hop, p2 additional nodes can be reached in two hops, and so on, until all the (pk-1) other nodes are visited. The maximum number of hops is Hmax = 2k -1 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-19) 12.3.3 ShuffleNet Multihop Network In Fig. 12-18, consider the connections between nodes 1 and 5 and between nodes 1 and 7. In the first case, the hop number is one. In the second case, three hops are needed with the routes being either 1-6-4-7 or 1-5-2-7. The average number of hops of a ShuffleNet is (12-20) 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.3.3 ShuffleNet Multihop Network As a result of multi-hopping, only part of the capacity of a particular link directly connecting two nodes is actually utilized for carrying traffic between them. The rest of the link capacity is used to forward messages from other nodes. Since the system has Np = kpk+1 links, the total network capacity C is C = kpk+1/H (12-21) and the per-user throughput S is S = C/N = p/H 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-22) 12.3.3 ShuffleNet Multihop Network Different (p, k) combinations result in different throughputs, so one can make some tradeoffs among the variables to get a better network performance. For example, given that the number of nodes is fixed at N, one can reduce the average number of hops by increasing p (which decreases k) to boost the capacity and the throughput. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4 Wavelength-Routed Networks Two problems in Broadcast-and-Select networks : 1). More wavelengths are needed as the number of nodes in the network grows. 2). Without optical booster amplifiers, a large number of users spread over a wide area cannot be interconnected. Wavelength-routed networks can overcome these limitations through wavelength-reuse, wavelengthconversion, optical-switching. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4 Wavelength-Routed Networks Wavelength-routed network consists of optical wavelength routers interconnected by pairs of point-to-point fiber links in a mesh configuration, as illustrated in Fig. 12-19. In Fig. 12-19 the connection from node 1 to node 2 and from node 2 to node 3 can both be on l1, whereas the connection between nodes 4 and 5 requires a different wavelength l2. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4 Wavelength-Routed Networks Figure 12-19. Wavelength reuse on a mesh network. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.1 Optical Cross-Connects Consider the OXC architecture shown in Fig. 12-20 that uses space switching without wavelength conversion. The space switches can be cascaded electronically controlled optical directional-coupler elements or semiconductor-optical-amplifier switching gates. Each of the input fibers carries M wavelengths, any of which could be added or dropped at a node. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.1 Optical Cross-Connects Figure 12-20. Optical cross-connect architecture using optical space switches and no wavelength converters. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.1 Optical Cross-Connects At the input, the arriving signal wavelengths is amplified and passively divided into N streams by a power splitter or AWG demultiplexer. Tunable filters then select individual wavelengths, which are directed to an optical space-switching matrix. The switch matrix directs the channels either to one of the eight output lines if it is a through-traveling signal, or to a particular receiver attached to the OXC at output ports 9 through 12 if it has to be dropped to a user at that node. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.1 Optical Cross-Connects Signals that are generated locally by a user get connected electrically via the DXC to an optical transmitter. The switch matrix directs them to the appropriate output line. The M output lines, each carrying separate wavelengths, are fed into a wavelength multiplexer to form a single aggregate output stream. Contentions arise in the architecture shown in Fig. 12-20 when channels having the same wavelength but traveling on different input fibers enter the OXC and need to be switched simultaneously to the same output fiber. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.1 Optical Cross-Connects The contentions could be resolved by assigning a fixed wavelength to each optical path throughout the network, or by dropping one of the channels and retransmitting it at another wavelength. In the first case, wavelength reuse and network scalability are reduced. In the second case, the add/drop flexibility of the OXC is lost. These blocking characteristics can be eliminated by using wavelength conversion at any output of the OXC. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.1 Optical Cross-Connects Example 12-5 : Consider the 4 x 4 OXC shown in Fig.12-21. The OXC consists of three 2 x 2 switch elements. Suppose that l2 on input fiber 1 needs to be switched to output fiber 2 and that l1 on input fiber 2 needs to be switched to output fiber 1. This is achieved by having the 1st two switch elements set in the bar-state and the 3rd elements set in the cross-state, as indicated in Fig. 12-21. Obviously, without wavelength conversion there would be wavelength contention at both mux output ports. By using wavelength converters ahead of the multiplexer, the cross-connected wavelengths can be converted to noncontending wavelengths. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.1 Optical Cross-Connects Figure 12-21. Example of a simple 4x4 OXC architecture using optical space switches and wavelength converters. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.2 Performance of Wavelength Conversion Assume that there are H links (or hops) between nodes A and B. Take the number of available wavelengths per fiber link to be F, and let r be the probability that a wavelength is used on any fiber link. Since rF is the expected number of busy wavelengths on any link, r is a measure of the fiber utilization along the path. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.2 Performance of Wavelength Conversion In the case of wavelength conversion, a connection request between nodes A and B is blocked if one of the H intervening fibers is full. The probability Pb’ that the connection request from A to B is blocked is the probability that there is a fiber link in this path with all F wavelengths in use, so that Pb’ = 1 - (1 - rF)H 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 (12-23) 12.4.2 Performance of Wavelength Conversion Let q be the achievable utilization for a given blocking probability in a network with wavelength conversion, q = [1 - (1 - Pb’)1/H]1/F = (Pb’/H)1/F (12-24) where the approximation holds for small values of Pb’/H. Figure 12-22 shows the achievable utilization q for Pb’ = 10-3 as a function of the number of wavelengths for H = 5, 10, and 20 hops. The effect of path length is small, and q rapidly approaches 1 as F becomes large. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.2 Performance of Wavelength Conversion Figure 12-22. Achievable wavelength utilization as a function of the # of wavelengths for a 10-3 blocking probability in a network using l-conversion. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.2 Performance of Wavelength Conversion The probability Pb that the connection request from A to B is blocked is the probability that each wavelength is used on at least one of the H links, so that Pb = [1 - (1 - r)H]F (12-25) Letting p be the achievable utilization for a given blocking probability in a network without wavelength conversion, then p = 1 - (1 - Pb1/F)1/H = -(1/H).ln(1 - Pb1/F) (12-26) The achievable utilization is inversely proportional to the length of the path H between A and B. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.2 Performance of Wavelength Conversion Figure 12-23 depicts the achievable utilization p for Pb=10-3 as a function of the number of wavelengths for H = 5, 10, and 20 hops. Figure 12-23. Achievable wavelength utilization as a function of the # of wavelengths for a 10-3 blocking probability in a network not using l-conversion. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.2 Performance of Wavelength Conversion Define the gain G=q/p to be the increase in fiber or wavelength utilization for the same blocking probability. Setting Pb’=Pb in Eqs. (12-23) and (12-25), we have (12-27) Figure 12-24 shows G as a function of H = 5, 10, and 20 links for a blocking probability of Pb=10-3. The figure shows that as F increases, the gain increases, and peaks at about H/2. The gain then slowly decreases, since large trunking networks are more efficient than small ones. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 12.4.2 Performance of Wavelength Conversion Figure 12-24. Increase in network utilization as a function of the # of wavelengths for a 10-3 blocking probability when l-conversion is used. 國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰