rogerkuo13@gmail.com switching performed on the bottom level and wavelength routing on all upper levels. This network retains the efficiency of packet-switched net-works and the simplicity of wavelength-routed netnet-works. Switching op-erations are concentrated at some special nodes in the multilevel net-work, significantly simplifying the node configuration and wavelength routing. Moreover, the idea of bands is applied to unify wavelength management on all network levels. Network analysis is performed to assess the feasibility of our approach. A queueing model using the qual-ity of service enhanced optical burst switching protocol is employed to analyze the blocking performance of the proposed network. Also, the numerical results based on the queueing model are provided. © 2010 Society of Photo-Optical Instrumentation Engineers. 关DOI: 10.1117/1.3309456兴
Subject terms: wavelength-division multiplexing optical network; dual-ring network; self-similarity;-band; optical burst switching; blocking probability. Paper 090436R received Jun. 15, 2009; revised manuscript received Nov. 25, 2009; accepted for publication Dec. 10, 2009; published online Feb. 19, 2010.
1 Introduction
Continuous improvements to optical components and sys-tem technologies have allowed fibers to deliver several Tbits/sec data via wavelength-division multiplexing 共WDM兲. The introduction of WDM has dramatically in-creased point-to-point transmission capacity and generated considerable potential to realize broadband all-optical networks.1–5 The numerous wavelength carriers simulta-neously transmitted along a fiber are valuable resources of photonic networks. Indeed, the ability to transmit hundreds of wavelengths along a single-mode fiber makes a high-capacity WDM network feasible.
In principle, the function of WDM optical networks is simple: to route specific wavelength carriers from source nodes to appropriate destinations. In practice, however, WDM optical networks are rather complicated. A large communication network is generally a hierarchical struc-ture consisting of multiple network levels; the unique mer-its of different network levels should be considered in net-work design. This net-work proposes a multilevel WDM network architecture using the concept of self-similarity. Our idea stems from the fact that if a simple structure can be reproduced horizontally on the same level and vertically on different levels, it eventually becomes a complex struc-ture that can accommodate related complexities, as is the case in the field of fractal geometry in mathematics6 or cellular automata in computer science.7 This idea of
self-similarity enables us to integrate different network levels via the same approach to construct a simple and efficient multilevel WDM network. Note that this work intends to propose an idea that will likely be of interest in future wide-area WDM network designs, while the details in-volved in practical situations are not discussed.
To implement the proposed network architecture, basic issues associated with WDM optical networks must be con-sidered. First, the principal function of WDM networks, as mentioned, is to route wavelengths along lightpaths offered by optical fibers. Thus, the network topology defined by fiber interconnections is a critical issue in network design. Second, an efficient wavelength management scheme is needed to route wavelengths adequately and efficiently in the network. Therefore, wavelength management 共includ-ing wavelength assignment, wavelength rout共includ-ing, wave-length reuse, and wavewave-length conversion兲 is another issue that must be addressed.8–10Hence, this work is focused on designing a simple network topology and an efficient wave-length management scheme that can be applied to all net-work levels and can accommodate the varied requirements of different levels.
The remainder of this paper is organized as follows. Section 2 introduces the network hierarchy and operation principle. Next, for brevity sake, Sec. 3 presents a design example to illustrate the proposed wavelength management scheme. Section 4 demonstrates a bufferless approach for priority switching in source and destination switch fabrics, and their blocking performance is analyzed. Section 5 dis-0091-3286/2010/$25.00 © 2010 SPIE
cusses some interesting features of the conceptual WDM network. Finally, conclusions are given in Sec. 6.
2 Network Hierarchy and Operation Principle
2.1 The Cell
On the physical layer, a WDM optical network is composed of many fibers with a number of wavelength carriers propa-gating along them. The interconnection of fibers, i.e., the network topology, defines the lightpaths through which wavelength carriers can propagate. Thus, the first step in our design was to find a network topology that could be applied to all network levels. Owing to the simplicity we desired, we did not consider some complicated topologies
such as Shufflenet and Manhattan street network
共MSN兲.11,12
Instead, simple topologies like ring, star, bus, and tree topologies were considered. The star topology has been intensively studied,13,14 but its inherent weakness in survivability makes it unsuitable for high-capacity net-works. Also, it is difficult to practically implement a star network covering a wide area. Both the bus and tree topolo-gies have been employed in local-area networks and sub-scriber loops, but they are also not suitable for wide-area networks. In contrast, the ring topology can cover a wide area, and the loop-back protection for it can be performed easily.15–18Therefore, we chose the ring topology.
To accommodate the varied requirements of different network levels, the special ring topology shown in Fig. 1
was designed with all the nodes within the dual-ring struc-ture connected by an inner ring and an outer ring. We call such a dual-ring network a “cell.” The idea of a cell was adopted from wireless communications, in which a cell uses a specific frequency band to deliver messages.19 As will become clear in this paper, a dual-ring network in our approach uses specific wavelength bands共named bands兲 to deliver packets, and the dual-ring network is named a cell to distinguish it from common ring networks.
We considered a multilevel wide-area WDM network and applied the cell topology to all network levels. As shown in Fig.1, a node in a cell can be a physical node or a virtual node. A physical node is a real node while a virtual node is actually a cell of the lower network level. On the bottom level, a cell consists of physical nodes only. On upper levels, a cell is generally composed of virtual nodes and/or physical nodes.
The neighboring nodes within the inner and outer rings of a cell have two connections between them that are named the “logic connections”共see Fig.1兲. The logic
con-nections can be specially implemented on different network levels. For example, depending on actual traffic and surviv-ability requirements, two logic connections between neigh-boring nodes can be implemented by different fibers within a cable or by separate fiber cables. The introduction of vir-tual nodes and logic connections is aimed at providing a uniform topology while accommodating the varied require-ments of different network levels. This idea will be clarified later.
Special nodes in each cell deliver wavelength carriers to and from the upper levels. We call these special nodes “edge nodes,” and the others are “inner nodes.” Edge nodes serve as bridges between adjacent network levels.
2.2 Network Hierarchy
We applied the idea of self-similarity to construct the mul-tilevel optical network shown in Fig.2. The network con-sists of k levels in which the first level is the bottom level and the k’th level is the top level. On the bottom level, a cell is composed of several physical nodes with logic con-nections between them. The logic concon-nections provide lightpaths for packet transfer. There are many peer cells on this level共named “bottom cells”兲 that form the basis of this wide-area network. A bottom cell is a basic unit in the network, and specific bands are assigned to each cell to deliver packets. A band is composed of a group of trans-mitting wavelengths of the corresponding cell. Each band is managed as a sole unit in the upper network levels, i.e., all wavelengths in a band are routed together and simul-taneously. The detailed wavelength assignment and routing will be explained later.
The second level contains many level-2 cells that each consist of several nodes. A node on this level could be a virtual node or a physical node. A virtual node is actually a bottom cell. In reality, a physical node is a bigger node
Fig. 1 Dual-ring network topology.
Fig. 2 Multilevel optical network consisting of k levels. The dual-ring topology is applied to all levels.
The concept of virtual nodes and logic connections ac-comodates the varied requirements of different levels. For example, the coexistence of virtual nodes and physical nodes makes it easy to accommodate a single high-capacity node and the output of a group of low-capacity nodes to-gether on the same level. To fulfill varied survivability and traffic demands, logic connections can be specially de-signed on different levels. Also, the number of nodes in every cell and the number of cells on different levels are specified by actual circumstances without special con-straint.
2.3 Network Operation
Before proceeding further, we will clarify whether the pro-posed network is a wavelength-routed network, a packet-switched network, or another network. A wavelength-routed network provides fixed lightpaths between source and destination pairs. The operation of wavelength-routed networks is simple, but a large number of wavelength car-riers is required at each node, and the transmitter/receiver efficiency is poor. A packet-switched network is more effi-cient than a wavelength-routed network, but it requires high-speed photonic switches, optical delay lines for buff-ering, and overhead for routing processing, so its construc-tion is more complicated.
Both packet-switched and wavelength-routed networks have their inherent advantages and drawbacks, so we adopted a compound scheme in our network by applying packet switching on the bottom level and simple wave-length routing on all upper levels. The use of packet switching significantly reduces the number of transmitters/ receivers 共TXs/RXs兲 needed at each node, while wave-length routing simplifies the operation of the upper levels. Figure 3 depicts the operation of this optical network. On the bottom level, each node has several transmitters that send packets to all the other nodes in the whole network. The destination address is carried by the packet header. The optical packets generated by the nodes within a bottom cell are sent to edge nodes of this cell. At the edge nodes, those packets heading to destination nodes located at the same bottom cell are merged together by a switching system, then wavelength converted and grouped to be a band 共named the level-1 band兲. Consequently, a bottom cell generates many level-1 bands, with each band carrying packets addressed to a specific bottom cell共including the mother cell itself兲. The level-1 band destined for the mother cell is delivered directly to the destination nodes, and the others are transferred to the second level. Each
level-1 band is managed as a sole unit, which dramati-cally simplifies wavelength routing on the upper levels.
On the second level, a cell may consist of virtual nodes and physical nodes. A virtual node is actually a bottom cell whose outputs are level-1 bands. The outputs of a physi-cal node are level-1 bands generated by itself. All the nodes within a cell deliver their outputs to edge nodes first, and then those level-1 bands destined for nodes in the same level-2 cell are merged as a level-2 band. Except for the particular level-2 band heading to the mother cell, the others are delivered to the third level and are individually managed as a sole unit on the upper levels.
The same operation as that of the second level is per-formed repeatedly on the third and other upper levels, which is the core idea of self-similarity. In general, a cell on the j’th level generates qj level-j bands, where qj is the total number of cells on this level. Each level-j band carries packets destined for a particular level-j cell. Except the level-j band addressed to the mother cell, the others are sent to the共j+1兲’th level.
The typical trip that a packet would experience in such a network is shown in Fig.4. A packet Z is generated by a source node共ns兲 inside a bottom cell 共Cs兲 and delivered to a destination node共nd兲 located at another bottom cell 共Cd兲. Packet Z starts the trip on the bottom level, being sent from the node ns to an edge node of Cs. At the edge node, all packets heading to destination nodes inside Cdare switched together, wavelength converted, and then grouped to be a level-1 band. Afterward, the level-1 band containing packet Z is sent to the second level.
On the second level, the bottom cell Cs is treated as a virtual node belonging to a particular level-2 cell. The
Fig. 3 Construction of bands on different levels. A level-j band is constructed on the j’th level and is delivered to the共j+1兲’th level.
level-1 band of interest is delivered to an edge node of this level-2 cell and merged with other level-1 bands destined for the level-2 cell containing Cd as a level-2 band. Next, this level-2 band is transferred to the third level, and the operation is repeated. Eventually packet Z arrives at the top level共the k’th level兲 and is contained by a specific level-共k−1兲 band.
On the top level, the level-共k−1兲 band with packet Z is sent directly from the 共virtual兲 node containing Cs to the node containing Cd. Afterward, the level-共k−1兲 band is transferred to the 共k−1兲’th level, then decomposed into several level-共k−2兲 bands. The level-共k−2兲 band with packet Z would be dropped by a node that includes Cd. Afterward, this level-共k−2兲 band is delivered to the 共k − 2兲’th level and decomposed into several level-共k−3兲 bands. The same process is repeated all the way to the bottom level.
On the bottom level, the level-1 band containing packet Z is accepted by an edge node of Cd. At the edge node, packet Z is switched and wavelength converted to be the receiving wavelength of nd. Finally, packet Z is carried by the corresponding receiving wavelength and eventually accepted by nd.
In the above description of our network, a packet is switched twice in the network. The switching operation in the source cell makes a node able to use few transmitters to send packets to all the nodes in the network. It achieves the same transmitter efficiency as a packet-switched network. The switching operation in the destination cell enables a node to use few receivers to accept packets coming from all the nodes in the network, and it also has the same receiver efficiency as a packet-switched network. These two switch-ing operations take full advantage of the benefits of packet switching, but unlike common packet-switched networks, the packet-switching operations are concentrated at some edge nodes in our network and are absent elsewhere.
An implicit advantage of our design is that a blocking problem can occur only on the bottom level, which ensures an excellent quality of service 共QoS兲. The blocking prob-lem for the proposed network will be studied in detail in Sec. 4.
3 Wavelength Management Scheme
In this section, the wavelength management scheme for our proposed network is investigated. For WDM optical net-works, wavelengths are precious resources, so an efficient wavelength management scheme is necessary and it is criti-cal to best use those available wavelengths. A limit on the number of wavelengths co-propagating along a single-mode fiber must be taken into account because it sets a practical constraint on wavelength management. The other issues that should be considered are wavelength reuse and wavelength conversion. The aim of an efficient wavelength management scheme is to maximize wavelength reuse while minimizing wavelength conversion.
For illustrative purposes, the example shown in Fig. 5
considers a WDM network consisting of three levels. For simplicity, we assume that the cells on the same level have an equal number of nodes. On the top level, there is only one cell with four virtual nodes inside. On the second level, there are four cells that each consist of five virtual/physical nodes. On the bottom level, there are 20 cells that each have 10 nodes. As shown in the figure, a physical node on the second level is treated as a virtual cell on the bottom level. In the following discussion, this example is used to illustrate the network construction and wavelength manage-ment.
3.1 Bottom Level
As shown in Fig.6, the physical nodes in a bottom cell are connected with a fiber cable. Since the effect of fiber failure on the bottom level is less critical, one fiber cable is used to implement logic connections in the bottom cell. There are eight inner nodes and two edge nodes in the cell, and the traffic of this cell is managed by two edge nodes.
For the purpose of illustration we assume the traffic be-tween any two bottom nodes is identical. Although this
Fig. 4 Typical trip a packet will experience in the multilevel network from a source node nslocated at a bottom cell Csto a destination
node ndlocated at the other bottom cell Cd.
simplified assumption is made here, the derived results can be easily applied to practical networks with suitable modi-fications.
Let aᐉ,ibe the number of nodes in the cell Cion theᐉ’th level. The number of cells on theᐉ’th level, denoted as Nᐉ, is given by
Nl= al+1,1+ al+1,2+ ¯ + al+1,Nl+1=
兺
i=1 Nl+1al+1,i. 共1兲
Let Fbe the capacity of a wavelength carrier, and Tnbe the node-to-node traffic on the bottom level. Due to the varied sizes of bottom cells on this level, the traffic be-tween cell Ci and cell Cj on the bottom level, denoted as Ti,j, is calculated by
Ti,j= Tn· a1,i· a1,j, i⫽ j. 共2兲
The intra-traffic of a bottom cell Cican be obtained from Eq.共2兲 using the following modification:
Ti,i= Tn·共a1,i− 1兲 · a1,i. 共3兲
Here we assume the traffic between Ci and Cj on the bottom level is an integer multiplier of the capacity of a wavelength carrier, i.e.,
Ti,j⬇ Zi,j· F, 共4兲
where Zi,j is an integer. The total number of wavelengths required in a bottom cell Cican be calculated as
W1,i= Zi,1+ Zi,2+ ¯ ¯ + Zi,i+ ¯ ¯ + Zi,N1=
兺
j=1 N1Zi,j. 共5兲 A bottom cell Cineeds共W1,i− Zi,i兲 wavelength carriers to communicate with the other bottom cells and Zi,i wave-length carriers for intra-cell traffic, respectively. Because of the varied scales of bottom cells, the total number of wave-lengths needed in each cell is different.
If the required wavelength carriers are generated equally by all the nodes within a bottom cell Ci, the number of transmitters needed at each node is given by
m1,i=W1,i/a1,i, 共6兲
where “x” denotes the minimum integer equal to or greater than a real number x.
We can assign m1,idifferent wavelengths to each node in a physical bottom cell Ci. The m1,i wavelengths appointed to a particular node will be served as transmitting wave-lengths as well as receiving ones because they are the iden-tity wavelengths of this node. Consequently, the total num-ber of wavelength carriers assigned to a bottom cell Ci is evaluated as
X1,i= a1,i· m1,i. 共7兲
As will be clear soon, the same set of X1,iwavelength car-riers can be reused in the other bottom cells without wave-length conflict, which unifies the optical components used in all the bottom cells.
To become familiar with the operation of a bottom cell, we must first consider the particular inner node ni in a bottom cell Cishown in Fig.6. Let the output traffic of ni be 80 Gbps and assume each TX can carry 10 Gbps infor-mation. Hence, eight transmitters共i.e., m1,i= 8兲 with differ-ent output wavelengths are equipped to deliver the traffic of ni. These transmitters are divided into two groups, with each consisting of four transmitters. Since there are 20 bot-tom cells共including Ciitself兲 in the network example, each transmitter group of ni will carry packets destined for 10 bottom cells. The outputs of two transmitter groups are separately sent to two edge nodes.
The configuration of niis shown in Fig.7. All transmit-ting wavelengths are added to the transmittransmit-ting fiber 共fT兲, and all receiving wavelengths are dropped from the receiv-ing fiber 共fR兲 via the wavelength cross-connect 共WXC兲. The structure and operation of the inner node are quite simple, which can be easily implemented in practice.
The configuration of the edge node is shown in Fig.8. As described above, an edge node will receive four wave-lengths coming from each of the other nine nodes of this cell共eight inner nodes and one edge node兲 plus four lengths locally generated by itself. Thus, a total of 40 wave-lengths destined for 10 bottom cells will be managed by it. Without loss of generality, these 40 wavelengths are
de-Fig. 6 Construction of a physical bottom cell in the example. The edge nodes are further connected to fiber cables of the second level.
noted as共1−40兲, in which wavelengths 共1−4兲 are lo-cally generated and wavelengths 共5−40兲 are delivered from the other nine nodes of this cell.
As shown in Fig.8, wavelengths共5−40兲 are dropped from the transmitting fiber via a WXC and then decom-posed into individual wavelengths by a WDM demulti-plexer. The 36 incoming wavelengths plus four local wave-lengths are sent to a photonic switching system A. The switching system has 40 ingress and 40 egress ports. Recall that the packets destined for the 10 bottom cells are carried by these 40 wavelengths, so the 40 output ports are divided into 10 groups. Each group consists of four egress ports that correspond to a particular destination bottom cell. Ac-cording to the addresses carried by the packet headers, those packets destined for the same bottom cell are switched together to the corresponding egress group. A wavelength converter共WC兲 is placed at each egress port to convert the output packets to a particular wavelength. The four wavelengths of each output group are further merged to be a level-1 band. Thereafter, 10 level-1 bands are constructed with each consisting of four different wave-lengths, so a total of 40 wavelengths共1
⬘
−40⬘
兲 is generated. Each level-1 band carries packets heading to a specific bottom cell.The edge node shown in Fig.8also accepts 10 level-1 bands coming from the second level that carry packets des-tined for this bottom cell, so a total of 40 wavelengths 共1
⬙
−40⬙
兲 is received. These received level-1 bands are first decomposed into individual wavelengths and then sent to a photonic switching system B. This switching system also has 40 ingress and 40 egress ports. Since the receiving wavelengths carry packets destined for 10 nodes in this cell, the 40 egress ports are divided into 10 groups. Each group consists of four ports, that correspond to a particular node in the bottom cell. Those packets heading to a particu-lar node will be switched to the four egress ports assigned to this node. A WC is placed at each egress port to convert the output into a specific wavelength.Although the structure of an edge node is more
compli-cated, just two edge nodes are needed in a bottom cell. Moreover, switching and wavelength conversion are per-formed only at edge nodes and therefore are absent at inner nodes on the bottom level.
Each level-1 band is composed of wavelengths des-tined for a particular bottom cell. Moreover, a specific level-1 band destined for the intracell traffic within the mother bottom cell is generated in a physical bottom cell but will not be created in a virtual bottom cell. Assume that b1,i,j is the number of wavelengths in a level-1 band dedicated to cell Cito cell Cjtraffic. According to the pre-ceding description, we can obtain b1,i,jby
b1,i,j= Zi,j=
Tn· a1,i· a1,jF
. 共8兲All the level-1 bands generated in a bottom cell will be delivered to the second level except the one carrying packets destined for those nodes within the mother cell. This specific level-1 band heading to the mother cell will be sent directly to destination nodes. Therefore, for a bot-tom cell, a total of共N1− 1兲 level-1 bands are transferred to the second level.
3.2 Second Level
A typical level-2 cell is shown in Fig.9. The inner ring and outer ring of this cell are implemented by two separate fiber cables. There are two edge nodes in the cell that deal with wavelengths carried by the inner ring and outer ring fiber cables, respectively. As was the case on the bottom level, the number of edge nodes in a level-2 cell also depends on the amount of traffic within this cell.
From the preceding discussion, a node on this level will output共N1− 1兲 level-1 bands. The function of this level is to merge those level-1 bands destined for the same level-2 cell as a level-2 band and deliver them either to the upper levels or directly to destination nodes in the mother cell. Since the node-to-node traffic on this level is equivalent to a level-1 band, the number of wavelength carriers contained in a level-2 band can be calculated.
Let a2,pbe the number of nodes in cell Cpon the second level. In general, the number of wavelengths in a level-2 band can be formulated as
Fig. 8 Configuration of edge node.
Fig. 9 Construction of a level-2 cell in the example. The edge nodes are further connected to fiber cables of the third level.
b2,x,y=
兺
i=1 a2,x兺
j=1 a2,y b1,i,j, 共9兲where b1,i,jis the number of wavelengths in the level-1 band used for the traffic from node niin cell Cxto node nj in cell Cyon the second level. For the particular level-2 band addressed to nodes in the mother cell, the number of wavelengths within it is evaluated as
b2,x,x=
兺
i=1 a2,x兺
j=1 j⫽i a2,x b1,i,j. 共10兲From Eqs. 共9兲 and 共10兲, we obtain the total number of transmitting wavelengths to be delivered by cell Cxas
W2,x=
兺
y=1 N2b2,x,y. 共11兲
The level-2 cell shown in Fig.9illustrates the operation inside the cell. The cell of interest is named C2,x and its outer ring is considered first. There are a2,x nodes within C2,xand each node outputs r共=10 in this example兲 level-1 bands to the outer ring, so a total of 共a2,x· r兲 level-1 bands will be carried. These level-1 bands will be sent to an edge node and be managed by it. At the edge node, those level-1 bands destined for the same level-2 cell are merged as a level-2 band. With deliberate wavelength assignment, those level-1 bands heading to K 共=2 here兲 particular level-2 cells can be carried by the outer fiber cable of C2,x. The number of wavelength carriers contained in each of the level-2 bands separately delivered to the K level-2 cells can be obtained by Eq.共9兲.
The wavelengths belonging to K level-2 bands are separately carried by K fibers, and those level-1 bands heading to the same level-2 cell are naturally merged as a level-2 band in the transmitting fiber cable. The construc-tion of the edge node is shown in Fig. 10. Here, a fiber cross-connect 共FXC兲 instead of a WXC is used, thereby
second level is performed.
From the above discussion, we see that as the network level increases, the number of wavelengths contained in a band increases, whereas the number of bands to be pro-cessed decreases. A band is managed as a sole unit, which implies that the higher the network level, the fewer the number of bands that are managed and the simpler the routing operation becomes.
4 Performance Analysis
In the proposed multilevel WDM network, a transmitting packet may be dropped in the switching systems during its delivery. This section describes the just-enough-time共JET兲 based optical burst switching共OBS兲 model we used to ana-lyze the blocking performance of the switching systems on a packet path from a source cell to a destination cell.20–22In principle, the OBS system works as follows. Arriving data packets are assembled into much larger bursts in advance and then fed into the switching entity. Under the reservation mechanism of JET, each burst is preceded by a correspond-ing control packet in the time domain, and their respective transmission instants at the source node are separated by a time interval called an offset. The control packet is elec-tronically processed at the switching system in its source and destination cells but the burst is not, so the offset time between them compensates for the processing delay of the control packet. A control packet contains information about the length of its corresponding burst, the value of the offset time between them, and the routing scheme. When it ar-rives at a switching system in the source/destination cell, it would request resource allocation in the switch for its cor-responding burst. If the requested bandwidth resource is available, it is reserved from the time the burst is expected to arrive until the time the burst leaves the switch, which makes the burst transparently pass through the switch fab-ric. Otherwise, the burst would be blocked and dropped.
To provide service differentiation in OBS, one feasible approach is to assign different offset values for different burst traffic classes. As described in Refs.20–22, a longer offset allows higher-priority traffic to reserve resources prior to lower-priority traffic with a shorter offset, which gives the better QoS to higher-priority burst traffic. Such a mechanism of service differentiation for separate traffic classes was applied to our OBS model. For the sake of brevity, our analyses are conducted in accordance with the network example demonstrated in Sec. 3, whose focus is on the blocking performance of the switching systems A and B shown in Fig. 8. Since an OBS burst is an aggregation of
many data packets, the packet loss probability of our OBS model can be inferred from its burst loss probability.
A JET-based, service-differentiation-supporting OBS model for the switching system A/B is investigated and depicted in Fig.11. No buffering is provided. In this model, we consider two service priority classes, i.e., class 1 and class 2, where the bursts of class 1 have preemptive priority over those of class 2. The N output ports of this switch are divided into M groups according to the number of bottom cells/nodes being managed. Those output ports in each group are further multiplexed to an output link. The param-eter Xzdenotes the number of output ports in the group z, where z = 1 , 2 ,¯ , M, which is the number of wavelengths in a band carried by their attached output link. We as-sume that the class-mixed burst arrivals for a concerned output link follow a Poisson process.
In the following analyses, we first focus on a specific 共i.e., tagged兲 output link of the switching system A, which serves an output group z. We assume that the class m arrival rate for the tagged output link is␣mand its service rate is
m, where m = 1 , 2. Because the bursts of class 1 have strict priority over those of class 2, the blocking probability of class 1 bursts for the tagged output link can be calculated by using the well-known Erlang B formula, as addressed in Refs.20and21, given by
P1A= 1 Xz/X z!
兺
k=0 Xz 1 k/k! , 共12兲where1共=␣1/1兲 is the traffic load of class 1.
The mixed traffic of classes 1 and 2 is possessed of absolute service priority in this two-class OBS system; therefore, the blocking probability of the mixed traffic for the tagged output link can be obtained, independent of ser-vice differentiation, as PmixedA = Xz/X z!
兺
k=0 Xz k/k! , 共13兲where=1+2=共␣1/1兲+共␣2/2兲. Note that we have as-sumed the mean burst lengths of class 1 and class 2 are equal for the equality in Eq.共13兲.
Using P1A and PmixedA , we can acquire the burst blocking probability of class 2, P2A, by solving the following equal-ity: 共␣1+␣2兲 · Pmixed A =␣1· P1A+␣2· P2A. 共14兲 It is formulated as follows: P2A=␣1+␣2 ␣2 PmixedA −␣1 ␣2 P1A, 共15兲
where␣1 and ␣2 represent the class 1 and class 2 arrival rates for the tagged output link of switching system A, re-spectively.
The process to estimate the blocking performance for switching system B is similar to that for switching system A; however, the effective arrival rates of class 1 and class 2 at the switching system B, ␣1
⬘
and ␣2⬘
, are reduced to ␣1⬘
=共1− P1A兲␣1 and ␣2⬘
=共1− P2A兲␣
2, respectively, due to the blocking impact at the switching system A. Let m
⬘
be the class m service rate of switching system B and assumem
⬘
=m, where m = 1 , 2. Since ␣m⬘
=共1− Pm A兲␣ m, we have m⬘
=共␣m⬘
/m⬘
兲=共1− Pm A兲 m.Using the effective traffic loads and above assumption, the blocking probabilities of class 1 and mixed traffic, on a considered output link of the switching system B, can be calculated as P1B= 共1
⬘
兲 Xz/X z!兺
k=0 Xz 共1⬘
兲 k/k! = 关共1 − P1 A兲 1兴Xz/Xz!兺
k=0 Xz 关共1 − P1 A兲 1兴k/k! 共16兲 and PmixedB = 共⬘
兲 Xz/X z!兺
k=0 Xz 共⬘
兲k/k! , 共17兲 where ⬘
=1⬘
+⬘
2=共1− P1A兲1+共1− P2 A兲2. Then the block-ing probability of class 2 bursts is
P2B=␣1
⬘
+␣2⬘
␣2⬘
PmixedB −␣1⬘
␣2⬘
P1B =共1 − P1 A兲␣ 1+共1 − P2 A兲␣ 2 共1 − P2 A兲␣ 2 PmixedB −共1 − P1 A兲␣ 1 共1 − P2 A兲␣ 2 P1B. 共18兲 While delivering a class m burst toward the destination cell in this network example, its overall blocking probabil-ity is obtained as PBL,m= 1 −共1 − Pm A兲共1 − P m B兲 = P m A + Pm B − Pm A · Pm B , m = 1,2. 共19兲Two simulation results based on the network example for the overall blocking probabilities of class 1 and class 2 versus the normalized utilization with different values of
␥共2/1兲 are plotted in Figs.12and13, respectively. In the simulation, the parameter Xz is set to be 4, and 1 =2=1
⬘
=2⬘
. In these two figures, note that for a given␥, Fig. 11 QoS-enhanced OBS model for the switching system A/B.the lower-priority traffic 共i.e., class 2 burst traffic herein兲 has the higher blocking probability, as expected. Because the service priority of class 1 is always higher than that of class 2, and for a given the traffic load of class 1 de-creases as ␥ increases, the blocking probability of class 1 bursts reduces significantly when ␥ is large. Thus, the variation of ␥ would result in greater influence on PBL,1 than on PBL,2. To operate the network at a high utilization with low blocking probabilities of class 1 and class 2, the ratio of2to1, i.e.,␥, should be large; however, it implies that limited high-priority traffic is allowed in the network. Therefore, a tradeoff exists between the amount of high-priority traffic and the blocking performance when design-ing such a multilevel WDM network.
5 Discussion
The concept underlying self-similarity is a simple geomet-ric structure enabled by a recursive algorithm. By repeat-edly expanding共or shrinking兲 the geometric structure using the recursive algorithm, a complicated object can be
ob-• It is self-similar in bands. A level-j band consists of several level-共j−1兲 bands. If we look into a level-共j−1兲 -band, it is similarly composed of sev-eral level-共j−2兲 bands. Sevsev-eral level- j bands can be merged to become a level-共j+1兲 band. Owing to the self-similarity property of bands, wavelength routing is simplified, which requires us to simply merge or decompose bands on each level without addressing individual wavelengths.
• It is a compound packet-switched and wavelength-routed network. In the proposed optical network, packet switching is performed on the bottom level, which can much enhance the TX/RX efficiency. The switching of transmitting wavelengths involves merg-ing the transmitted packets together to construct level-1 bands. The switching of receiving wave-lengths involves merging the incoming packets ad-dressed to the same destination node together. Without these switching operations, a large number of transmitters/receivers will be required in each node. Meanwhile, simple wavelength routing is carried out on all upper levels, which significantly simplifies net-work operations.
6 Conclusions
In this paper, we have proposed a novel network architec-ture based on self-similarity for multilevel wide-area WDM networks. We developed special dual-ring topology and an efficient wavelength management scheme that can be ap-plied to all network levels. The dual-ring structure offers great flexibility and assures good survivability in the event of fiber failure. The idea of bands is introduced to effi-ciently manage wavelength carriers. In the proposed optical network, packet switching is performed at edge nodes of the bottom level, while simple wavelength routing on bands is carried out on upper levels. Therefore, the pro-posed architecture retains the efficiency of packet-switched networks and the simplicity of wavelength-routed net-works. The performance analysis of the proposed multi-level WDM optical network showed that, according to our numerical results, the parameters for designing such a WDM network can be appropriately determined.
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Shu-Tsung Kuo received BS and MS degrees in electrical engi-neering from Yuan-Ze University, Taiwan, R.O.C., in 1996 and 1999, respectively. He is currently working toward his PhD degree in the Department of Communication Engineering, National Chiao-Tung University, Hsinchu, Taiwan. His main research interest is in high-speed optical networks.
Ming-Seng Kao received his BSEE degree from National Taiwan University in 1982, his MS degree in optoelectronics from National Chiao-Tung University in 1986, and his PhD degree in electrical engineering from National Taiwan University in 1990. From 1986 to 1987 he was an assistant researcher at the Telecommunications Laboratories, Chung-Li, Taiwan. In 1990, he joined the faculty of National Chiao-Tung University, Hsinchu, Taiwan, where he is now a professor in the Communication Engineering Department. From 1993 to 1994, he was a visiting professor at the Swiss Federal In-stitute of Technology共ETH兲, Zurich, Switzerland, where he worked in the area of optical communications. He is currently interested in high-speed optical networks and wireless communications.
