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  12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses.

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  12.1 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 12.4.2Performance 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  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. 12.1 Basic 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 Figure 12-1(a). Linear bus topology used for fiber optic networks. 12.1 Basic 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  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. 12.1 Basic 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 Figure 12-1(b). Ring topology for fiber optic networks. 12.1 Basic 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 Figure 12-1(c). Star topology for fiber optic networks. 12.1 Basic 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  Over an optical fiber of length x (in km), the ratio A o of received power P(x) to transmitted power P(0) is given by A o = P(x)/P(0) = 10 -  x/10 (12-1) where  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. 12.1.2 Performance of Passive Linear Buses

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 Figure 12-2. Losses in a passive linear-bus coupler consisting of cascaded directional couplers. 12.1.2 Performance of Passive Linear Buses

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  If a fraction F c of optical power is lost at each port of the coupler, then the connecting loss L c is L c = -10 log(1-F c ) (12-2)  For example, if we take this fraction to be 20%, then L c is about 1 dB; that is, the optical power gets reduced by 1 dB at any coupling junction. 12.1.2 Performance of Passive Linear Buses

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  Let C T 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 L tap = 10 log C T (12-3)  For a symmetric coupler, C T is also the fraction of power that is coupled from the transmitting input port to the bus.  If P o is the optical power launched from a source flylead, the power coupled to the bus is C T P o. The throughput coupling loss L thru is then given by L thru = -10 log(1 - C T ) 2 = -20 log(1 - C T ) (12-4) 12.1.2 Performance of Passive Linear Buses

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  In addition to connection and tapping losses, there is an intrinsic transmission loss L i associated with each bus coupler.  If the fraction of power lost in the coupler is F i, then the intrinsic transmission loss L i is L i = -10 log(1 - F i ) (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 L fiber = -10 logA o  =  L (12-6)

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 Figure 12-3. Topology of a simplex linear bus consisting of N uniformly spaced stations. 12.1.2 Performance of Passive Linear Buses

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  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 P o is the optical power launched from a source at station 1, then the power detected at station 2 is P 1,2 = A o C T 2 (1-F c ) 4 (1–F i ) 2 P o (12-7) 12.1.2 Performance of Passive Linear Buses

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  The optical power flow encounters the following loss-inducing mechanisms: One fiber path with attenuation A o. Tap points at both the transmitter and the receiver, each with coupling efficiencies C T. Four connecting points, each of which passes a fraction (1 - F c ) of the power entering them. Two couplers which pass only the fraction (1 – F i ) 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(P o /P 1,2 ) =  L+2L tap +4L c +2L i. (12-8) 12.1.2 Performance of Passive Linear Buses

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  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 F 1 = (1-F c ) 2 C T (1–F i ) (12-9a) At station N the fraction of power from the bus- coupler input port that emerges from the detector port is F N = (1-F c ) 2 C T (1–F i ) (12-9b) 12.1.2 Performance of Passive Linear Buses

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  For each of the (N - 2) intermediate stations, the fraction of power passing through each coupling module (shown in Fig. 12-2) is F coup = (1-F c ) 2 (1-C T ) 2 (1–F i ), (12-10) since the power flow encounters two connector losses, two tap losses, and one intrinsic loss. 12.1.2 Performance of Passive Linear Buses

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  Combining the expressions from Eqs. (12-9a), (12- 9b), 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 P 1,N = A o N-1 F 1 F coup N-1 F N P o = A o N-1 (1-F c ) 2N (1-C T ) 2(N-2) C T 2 (1-F i ) N P o (12-11) 12.1.2 Performance of Passive Linear Buses

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  Using Eqs. (12-2) ~ (12-6), the power budget for this link is 10.log(P o /P 1,N ) = (N-1)  L +2NL c +(N-2)L thru +2L tap +Nl i = N(  L +2L c +L thru +L i ) –  L -2L thru +2L tap (12-12)  The losses of the linear bus increase linearly with the number of stations N. 12.1.2 Performance of Passive Linear Buses

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 Example 12-1 :  Compare the power budgets of three linear buses, having 5, 10, and 50 stations, respectively.  Assume that C T = 10 %, so that L tap = 10 dB and L thru = 0.9 dB. Let L i = 0.5 dB and L c = 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. 12.1.2 Performance of Passive Linear Buses

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 Table 12-1. Comparison of the power budgets of three linear buses that have 5, 10, and 50 stations, repectively. 12.1.2 Performance of Passive Linear Buses

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 Figure 12-4. Total loss as a function of the number of attached stations for linear-bus and star architectures. 12.1.2 Performance of Passive Linear Buses

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 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. 12.1.2 Performance of Passive Linear Buses

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 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., P 1,2 = P N-1,N ). 12.1.2 Performance of Passive Linear Buses

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 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. 12.1.2 Performance of Passive Linear Buses

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 P in and N output powers, the excess loss is given by Excess Loss = L excess = 10.log(P in /  N i=1 P outi ) (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 = L split = -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: P S is the fiber-coupled output power from a source in dBm. P R is the minimum optical power in dBm required at the receiver to achieve a specific BER.  is the fiber attenuation. All stations are located at the same distance L from the star coupler. L c 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 P S - P R = L excess +  (2L) + 2L c + L split = L excess +  (2L) + 2L c + 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 Figure 12-4. Total loss as a function of the number of attached stations for linear-bus and star architectures. 12.1.3 Performance of 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 P S - P R = [0.75 + 0.4(1.0) + 2(1.0)10log10] dB  For N = 50, the power margin is P S - P R = [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  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. 12.3.1 Broadcast-and-Select Single-Hop 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 12.3.1 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  Figure 12-15 illustrates the concept of multicast or broadcast for a star network.  Workstations at nodes 4 and 2 communicate using 2, whereas a user at node 1 broadcasts information to workstations at nodes 3 and 5 using 1.  The same concepts are applicable to bus structures, although the losses encountered in the star and bus architectures are different. 12.3.1 Broadcast-and-Select Single-Hop 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 Figure 12-15. A single-hop broadcast-and-select network. 12.3.1 Broadcast-and-Select Single-Hop 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  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. 12.3.1 Broadcast-and-Select Single-Hop 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 12.3.2 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 Figure 12-16. Architecture and traffic flow of a multihop broadcast-and-select network. 12.3.2 Broadcast-and-Select Multihop 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  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. 12.3.2 Broadcast-and-Select Multihop 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 Figure 12-17. Representation of the fields contained in a data packet. 12.3.2 Broadcast-and-Select Multihop 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  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 1.  Then node 3 forwards the message to node 2 using 6.  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. 12.3.2 Broadcast-and-Select Multihop 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 12.3.3 ShuffleNet Multihop Network  The extension of perfect shuffle to optical networks consists of a cylindrical arrangement of k columns, each having p k nodes, where p is the number of transceiver pairs per node.  The total number of nodes is then N = kp k (12-17) 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  Given that each node requires p wavelengths to transmit information, the total number of wavelengths N needed in the network is N = pN = kp k+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. 12.3.3 ShuffleNet Multihop 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 Figure 12-18. Logical interconnection pattern and wavelength assignment of a (p,k) = (2,2) ShuffleNet. 12.3.3 ShuffleNet Multihop 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  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, p 2 additional nodes can be reached in two hops, and so on, until all the (p k -1) other nodes are visited.  The maximum number of hops is H max = 2k -1 (12-19) 12.3.3 ShuffleNet Multihop 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  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) 12.3.3 ShuffleNet Multihop 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  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 = kp k+1 links, the total network capacity C is C = kp k+1 /H (12-21) and the per-user throughput S is S = C/N = p/H (12-22) 12.3.3 ShuffleNet Multihop 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  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. 12.3.3 ShuffleNet Multihop 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 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, wavelength- conversion, 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 1, whereas the connection between nodes 4 and 5 requires a different wavelength 2.

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 2 on input fiber 1 needs to be switched to output fiber 2 and that 1 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  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  be the probability that a wavelength is used on any fiber link.  Since  F is the expected number of busy wavelengths on any link,  is a measure of the fiber utilization along the path. 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  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 P b ’ 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 P b ’ = 1 - (1 -  F ) H (12-23) 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  Let q be the achievable utilization for a given blocking probability in a network with wavelength conversion, q = [1 - (1 - P b ’) 1/H ] 1/F = (P b ’/H) 1/F (12-24) where the approximation holds for small values of P b ’/H.  Figure 12-22 shows the achievable utilization q for P b ’ = 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. 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 Figure 12-22. Achievable wavelength utilization as a function of the # of wavelengths for a 10 -3 blocking probability in a network using -conversion. 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  The probability P b 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 P b = [1 - (1 -  ) 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 - P b 1/F ) 1/H = -(1/H).ln(1 - P b 1/F ) (12-26)  The achievable utilization is inversely proportional to the length of the path H between A and B. 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 Figure 12-23. Achievable wavelength utilization as a function of the # of wavelengths for a 10 -3 blocking probability in a network not using -conversion.  Figure 12-23 depicts the achievable utilization p for P b =10 -3 as a function of the number of wavelengths for H = 5, 10, and 20 hops. 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  Define the gain G=q/p to be the increase in fiber or wavelength utilization for the same blocking probability.  Setting P b ’=P b 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 P b =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. 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 Figure 12-24. Increase in network utilization as a function of the # of wavelengths for a 10 -3 blocking probability when -conversion is used. 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 Chapter 12 Basic Optical Network  12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses.

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Presentation on theme: "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  12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses."— Presentation transcript:

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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  12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses.

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Presentation on theme: "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  12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses."— Presentation transcript:

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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  12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses.

Presentation on theme: "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  12.1 Basic Networks 12.1.1 Network Topologies 12.1.2 Performance of Passive Linear Buses."— Presentation transcript: