Design of Virtual Optical Bus Networks: A Heuristic Approach

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Design of Virtual Optical Bus Networks: A Heuristic Approach Ahmad Rostami and Sandeep Kumar Singh Telecommunication Networks Group (TKN) Technical University of Berlin, Germany Email: {rostami, singh}@tkn.tu-berlin.de

Abstract— We study the design of virtual optical bus (VOB) network, which has been recently proposed as a packet-oriented all-optical solution for transport networks. Design of a VOB network consists of grouping all edge-to-edge flows in the network into clusters called VOBs and that has to be done with the objective of minimizing packet collision rate in the optical network. We present an efficient heuristic algorithm, which can be utilized in networks with both ring and arbitrary meshed topology to find near optimal solutions to the VOB network design problem. Several design examples are presented and the results are compared to those obtained by applying a linearprogramming-based design method. The comparisons show that the algorithm can find comparable solutions–in terms of network performance–in a much less amount of time.

I. I NTRODUCTION The exponential growth of traffic in the Internet has turned optics into the technology of choice for transmission in the metro/core networks. In addition, it has created some concerns over the scalability of electronic switching, thereby pushing towards all-optical networks. Nonetheless, optics does not provide good support for packet switching, due to the fact that there is no equivalent to random-access-memories (RAMs) in the optical domain. In fact, buffers play a crucial role in controlling the packet contentions in packet-switched networks. To address this issue, in our earlier work in [1], we presented the virtual optical bus (VOB) as a novel evolutionary networking architecture based on the optical burst switching (OBS) [2]. In developing the VOB architecture we have utilized the fact that in an all-optical packet-based transport network, traffic shaping at the entrance edge of the network offers high potential for bufferless contention resolution. In the VOB architecture, flows of traffic between nodes in the network are grouped into clusters and within each of the clusters a special form of coordination on packet transmission is introduced. This coordination ensures collision-free packet transmission within each cluster. Additionally, clustering of flows and selection of paths for clusters are done in a way that the interaction among routes of clusters in the network is minimized. This leads to a reduction of packet collisions in the network and also an increase in the network throughput. In [1] we evaluated and discussed the issues related to the VOB architecture including its corresponding medium access control (MAC) protocol. In addition to that, we presented the design of VOB networks as an integer linear programming

(ILP) formulation. Although the ILP formulation can be solved for rather small-size networks under the static demands, finding a solution for a more realistic sets of assumptions regarding network size and dynamic traffic requires considerable processing power and time. To address this issue, in this paper we focus on the design of an efficient heuristic for the VOB network design. The presented heuristic can be utilized in networks with both ring and arbitrary meshed topology to find near optimal solutions to the VOB network design problem. The rest of this paper is organized as follows. In Section II, the architecture of VOB is reviewed. In Section III, we present our heuristics and discuss its features. Several numerical examples are presented in Section IV to demonstrate the merits of the developed heuristic in the network design. Finally, we conclude in Section V by summarizing the achieved results and discussing future works. II. VOB A RCHITECTURE The basic concept of VOB is to avoid or minimize collisions among data packets in the optical layer through traffic shaping at ingress edges of all-optical packet-switched networks, where we still have the chance to use inexpensive electrical buffers. To achieve this, a connection-oriented approach is adopted for transporting data packets in the network. In this approach, a virtual circuit is established in the network, and several edgeto-edge traffic flows are associated with it. The virtual circuit is unidirectional and should cover the entire routes of associated edge-to-edge flows. That is, it operates like an optical bus, where selected sources and destinations on the bus can use it to transmit data, and hence it is named virtual optical bus. Once a VOB is formed, ingress nodes of the flows associated with the VOB inject their data packets into the VOB in a coordinated manner and in such a way that burst collision within a VOB is avoided. By doing that, the collision among data-packets will be limited to the packets belonging to different VOBs. Therefore, if VOBs are routed in the network with the minimum interaction among them, then it can be expected that the collision rate in the network is greatly reduced or even completely eliminated if enough resources (i.e. wavelength channels) are assigned to VOBs. A VOB can be formally expressed with the following properties [1]. • A VOB is defined over a specified sequence of connected links, i.e., it is a directed simple path with a single origin and destination.

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Each VOB is piecewise associated with a specific wavelength channel. On a multichannel link with wavelength converters available, a VOB can use any channel on that link; however, flows associated with that VOB may not use more than one channel at any given time. • Each edge-to-edge flow must be associated with one and only one VOB. The second property expresses that the capacity assigned to a VOB on any associated link must be limited to that of a single wavelength. Nevertheless, the aggregated capacity of flows associated with a VOB may exceed the capacity of a single wavelength, since different flows can be supported on disjoint parts of a VOB (i.e., spatial reuse). Also, the third property implies that both the origin and destination of a given flow should be associated with the same VOB, meaning that the traffic of an edge-to-edge flow will not be split/switched over multiple VOBs. An integral part of the VOB architecture is the coordination among different ingress nodes in injecting traffic into a single VOB. For this purpose the VOB utilizes a modified version of the well-known buffer-insertion protocol. The buffer-insertion MAC ensures that packets belonging to a VOB do not overlap in space–neither completely nor partially–during their journey in the network. This is achieved by giving the transit traffic the priority over the local traffic. Specifically, if at any point in time a given node i needs to inject a packet from its local transmission queue over the VOB v, it first checks the status of transit packets at the same node i over the same VOB v. If there is any transit packet being currently in transmission, then the node delays the transmission of local packet until the transit packet transmission is complete (shaping at the ingress). Alternatively, if a transit packet arrives at the node i on the VOB v and finds a packet from a local queue in transmission on the same VOB, then the transit packet is sent through a small fiber delay line (FDL) based insertion buffer. The insertion buffer in this case will delay the packet for the time equal for transmission of a maximum packet size. This approach requires an insertion buffer per VOB per any active intermediate node–an intermediate node that injects traffic into the bus–being part of that VOB. The details of operation and performance of the MAC protocol has been studied in [1]. •

III. A H EURISTIC FOR VOB N ETWORK D ESIGN Design of a VOB network consists of grouping all edgeto-edge flows into VOBs and that has to be done with the objective of minimizing packet collision rate in the network. We refer to this step as VOB layout design, which can formally be stated as follows. Consider we have a network with given resources, including the number of wavelength division multiplexing (WDM) links and transceivers, and an edge-to-edge traffic matrix. Then the VOB layout design is how to cover the traffic matrix by a set of VOBs, with respect to the limitations imposed by the topology and the resources available within each node and link, in such a way that the packet collision in the network is minimized. The VOB layout design should give us complete information about the beginning, the end and the route of all VOBs

as well as identities of flows to be covered by each VOB. It should be noted that VOB layout design involves assigning edge-to-edge flows to VOBs and that, in turn, implies routing of edge-to-edge flows in the network. As explained in Section II, by applying the traffic shaping at each source node the collision among the flows within each VOB is completely eliminated, and the packet collision rate in the network is merely limited to inter-VOB collisions. Nevertheless, the minimization of inter-VOB collisions cannot be solved explicitly and in a straightforward manner, if at all possible, since it depends on many factors such as traffic characteristics and routing. As a result, we resort to the implicit minimization of the collision rate in the network by minimizing the VOB interactions in the network. On this basis, in [1] the path-based method [3] has been applied to present the VOB layout design as an ILP formulation that minimizes the maximum number of VOBs that are multiplexed to any link in the network. It has been shown that this implicit formulation can indeed eliminate or greatly reduce the collision rate in the network. Nevertheless, solving this ILP formulation for network topologies with a large number of nodes and links should require a large amount of processing power or finding a solution should take a large amount of time on conventional PCs. This is because the problem of routing VOBs and assigning flows to VOBs is very similar in nature to the routing and wavelength assignment problem in classical IP-over-WDM networks, which has been shown to be N P hard [4]. Therefore, here we present a heuristic algorithm that can solve the VOB layout design problem. A. Assumptions •

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Between each two nodes in the network there will be at most one VOB in each direction. All nodes support full wavelength conversion. Although this is not mandatory for the VOB design framework, this assumption will simplify the layout design process.

B. Notations, Definitions and Parameters •

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G = (V, E) is the graph of the network consisting of nodes in V and links in E F is set of all edge-to-edge traffic flows in the network and |F | is the total number of flows Λ = [λf ] is the given demand matrix, where λf denotes the intensity of the edge-to-edge flow f ∈ F (normalized to a single wavelength capacity) Amax is the maximum allowable load on a single WDM channel in the network normalized to capacity of a single wavelength. This is a design parameters that is used to control the VOBs access delays of traffic flows [1] W is the total number of available channels on any link in the network

C. VOB Design Algorithm Our heuristic for designing VOB networks is presented in Algorithm 1. The concept of our algorithm is as follows. We first use the k-shortest path algorithm [5] to find the first and

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second shortest paths for all flows in the network and assign the first shortest paths to the flows in STEP 2. Then, in STEP3 we sort the flows in a non-increasing order of number of hops using the assigned paths. After sorting the flows, the algorithm creates a set of potential VOB candidates VOBini in STEP 4. In doing so, we ensure that each flow is assigned to at least one VOB candidate and the path of flows assigned to each VOB are fully supported on the path of the longest flow belonging to the same VOB candidate. At this stage, each traffic flow is usually assigned to several VOB candidates in VOBini . STEP 5 is a call to VOB selection and flow assignment (VSFA) function that is presented in Algorithm 2. VSFA function takes as input the list of all VOB candidates (VOBini ), routing matrix and design parameter Amax and produces the first list of selected VOBs (VOB) together with the flows assigned to each VOB. Each flow is assigned to one and only one VOB in VOB. In selecting VOBs the list of VOB candidates (VOBini ) is used, which is already sorted in a decreasing order of number of hops. That is, we start with the longest VOBs and try to pack as many flows to each VOB as possible. The main criterion here is that the aggregate demands assigned to a VOB on any link should not exceed Amax . The function returns the first set of designed network layout in VOB, together with the maximum number of VOBs per link and a set ρV OB , which contains per VOB a vector of aggregate loads on each link in the network due to that VOB. If the maximum number of VOBs per link (Bmax ) is equal or smaller than the number of channels on links, then the algorithm is terminated and we can expect to have a loss-free network operation with the designed layout. Otherwise we try to reduce the Bmax by merging the selected VOBs (STEP 6) and/or redesign the network layout based on the second shortest path of some flows (STEP 7). The VOB merging function (Merge-VOB) is presented in Algorithm 3. The function goes through all pairs of VOBs and try to merge them, and thereby reducing the number of VOBs in network. There are two criteria for merging VOBs. First, the load on any link of the merged VOB still cannot exceed Amax . Second, two flows can only be merged if the path of one is fully supported by the other one or one of the VOBs shares some of the first or last hops of the other one. If after applying the VOB merging Bmax is still larger than number of channels on links, we go through the rerouting in STEP 7. In this step, all traffic flows that traverse the links having Bmax VOBs are assigned new routes based on the second shortest path. The rerouting is done flow by flow and after each reroute the VOB layout is redesigned. This process is repeated until either the Bmax is reduced to the desired value or there is no more flow to reroute. IV. N ETWORK D ESIGN E XAMPLES In this section we use two examples of VOB network design to demonstrate the effectiveness of the presented heuristic algorithm and compare them with the results obtained from solving the ILP formulation presented in [1]. We also present the performance results of the networks designed using both ILP and heuristic algorithm. To make the results comparable,

Algorithm 1 Heuristic for VOB Network Layout Design 1: STEP1: Initialization of Algorithm 2: Get G, F, Λ, Amax , W 3: counter ← 1 4: STEP2: K-Shortest-Path Routing 5: Apply the k-shortest path (KSP) routing algorithm to find first two shortest paths for all flows F and put results in P1 and P2 6: P ← P1 7: STEP3: Sorting of Flows 8: Sort the flows in F in a non-increasing order of number of hops using P. For flows having equal number of hops, sort based on traffic intensity (λfi ) in a decreasing order. 9: STEP 4: Finding Potential VOB Sets 10: For each flow fi ∈ F form a set Sfi that includes flow fi and every other flow fj ∈ F if the the path of flow fj is a subset of that of fi in P. Put all Sf sets in VOBini 11: STEP 5: VOB Selection and Flow Assignment 12: (VOB, Bmax ,ρV OB ) = VSFA(VOBini , P, G, Λ, Amax ) 13: STEP 6: Merging VOBs 14: if Bmax > W then 15: (VOB,Bmax ,BAvg ,LBmax )= VMERGE(VOB,ρV OB , P,Amax ) 16: if counter == 1 then 17: Go through all links having Bmax VOBs on them and put all flows passing through them into set FBmax 18: Bmax,tmp ← Bmax 19: BAvg,tmp ← BAvg, 20: LBmax,tmp ← LBmax 21: f lowindex ← 0 22: end if 23: end if 24: STEP 7: Rerouting to Optimize 25: if Bmax > W && f lowindex ≤ |FBmax | then 26: if (Bmax < Bmax,tmp )$(Bmax == Bmax,tmp && LBmax < LBmax,tmp )$(Bmax == Bmax,tmp && LBmax == LBmax,tmp &&BAvg < BAvg,tmp ) then 27: if Bmax < Bmax,tmp then 28: f lowindex ← 0 29: update FBmax 30: end if 31: Bmax,tmp ← Bmax 32: BAvg,tmp ← BAvg 33: LBmax,tmp ← LBmax 34: else if counter ! = 1 then 35: Take flow fi ∈ FBmax (i = f lowindex ) and again replace corresponding routing in P with corresponding f irst shortest path in P1 36: end if 37: counter++, f lowindex + + 38: Take flow fi ∈ FBmax (i = f lowindex ) and again replace corresponding routing in P with corresponding second shortest path in P2 39: Goto STEP 3 40: end if 41: STEP 8: Terminate

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Algorithm 2 VSFA Function 1: Get VOBini , P, G, Λ, Amax 2: for each flow fi ∈ F (i ∈ {1, 2, . . . |F |}) do 3: if Sfi is not empty then 4: Construct a routing matrix Z (|Z| = |Sfi | × |E|) 5: initialize Z to all zero 6: for each link lj ∈ E and each flow fk ∈ Sfi do 7: if flow fk traverses link lj then 8: Z[fk , lj ] ← 1 9: end if 10: end for 11: Associate a load vector ρSfi to set Sfi (|ρSfi | = |E|) 12: ρSfi ← 0 13: for each flow fk ∈ Sfi do 14: if Maximum(ρSfi + λfk .Z[k, :]) ≤ Amax then 15: Keep flow fk in Set Sfi 16: if k &= i then 17: Delete all elements of Sfk 18: end if 19: Delete fk from all other Sf sets 20: ρSfi ← ρSfi + λfk .Z[k, :] 21: else 22: Delete fk from set Sfi 23: end if 24: end for 25: end if 26: end for 27: VOB ← VOBini 28: Bmax ← maximum number of VOBs per link in network 29: Construct a set ρV OB (|ρV OB | = |VOB|) and put all ρSf vectors in it. 30: Return VOB, Bmax and ρV OB Algorithm 3 VMERGE Function 1: Get VOB, ρV OB , P, Amax 2: for each Sfi ∈ VOB do 3: for each Sfj ∈ VOB(j! = i) do 4: if Maximum(ρSfi + ρSfj ) ≤ Amax ) && MergingCriteria* is met for (Sfj , Sfi ) then 5: Put elements of Sfj in Sfi 6: Delete Sfj from VOB 7: ρSfi ← ρSfi + ρSfj 8: end if 9: end for 10: end for 11: Bmax ← maximum number of VOBs per link in network 12: BAvg ← average number of VOBs on links in network 13: LBmax ← number of links with Bmax assigned VOB 14: Return ρV OB , Bmax , BAvg , LBmax 15: *Merging-Criteria for (V OBi and V OBj ): V OBj can be merged into V OBi if the starting and ending node of V OBj as well as the path of V OBj are all present in the path of V OBi , OR two VOBs share the common link(s) in such away that destination node of one and source node of the other are present in both the VOBs and intermediate nodes of the common path are also same.

we use the same design examples as in [1]. Specifically, we consider two network topologies as explained below. In the first example, we consider a network with 10 nodes, where nodes are connected according to a bidirectional ring topology. Each node is connected to any of the two adjacent nodes via two WDM fibers in different directions, i.e., there are 20 fiber links in the network. In the second example, the NSFNET backbone network with 14 nodes is considered [4]. The network has 42 unidirectional fiber links and the minimum and maximum nodal degree of the nodes are 2 and 4, respectively. In both networks it is assumed that each WDM link supports one control channel and four data channels, where each data channel operates at the rate of 10 Gb/s. The architecture of the nodes is the same as the one described in [1]. In the ring network, each node is equipped with 8 tunable lasers and receivers as well as 8 internal wavelength converters. For the NSFNET, the number of available tunable lasers and receivers as well as that of wavelength converters in node i (0 ≤ i ≤ 13) are both set to 4 × N Di , where N Di is the nodal degree of node i. A. Designing the VOB Layout First let us consider the ring network. We design the network layout using the heuristic algorithm for two different traffic matrices. The first one is a randomly generated traffic matrix, where the edge-to-edge demands are uniformly distributed in the range of (0, 4) Gb/s. This leads to the average demand of 1.87 Gb/s per edge-to-edge flow. In the second case we use a uniform traffic matrix, where all demands are equally set to the average value of the first matrix, i.e., 1.87 Gb/s. Figs. 1 and 2 depict summaries of the results obtained through solving the layout design problem for the random and uniform traffic matrices, respectively. The figures show the minimum, average and maximum number of VOBs required to support the demands in the network. The results are shown for designing the network with the heuristic algorithm, denoted as HST, and compared with those obtained from designing the network using the ILP optimization presented in [1], denoted as ILP. In addition to that, the results are compared in each case with the number of traffic flows per link under the shortest path routing in the classical OBS approach, denoted as OBS. We consider the classical OBS because it gives us an upperbound on the number of VOBs per link in the network. In fact, in the classical OBS there will be no VOB and therefore each edge-to-edge traffic flow can be considered as a VOB. The first observation is that the heuristic can successfully achieve its goal, which is the reduction/minimization of maximum number of VOBs multiplexed into any link in the network, as compared to the upper-bound given by the classical OBS. We recall that the packet collisions rate in a VOB network is limited to the inter-VOB collisions that can be reduced/eliminated by reducing the number of VOBs being multiplexed over links in the network. In addition to that, we observe that the maximum number of VOBs per link under the heuristic method is either the same or very close to that obtained from optimization. Specifically, with the random

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Fig. 3. No. of VOBs per link for the NSFNET at Amax = 0.7. For OBS no. of independent flows per link is shown.

minutes to hours depending on the topology and traffic matrix. This is the main gain of using heuristic over the ILP. B. Performance Evaluation of Designed Networks

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Fig. 1. No. of VOBs per link for the ring network with random traffic at different values of Amax . For OBS no. of independent flows per link is shown.

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Fig. 2. No. of VOBs per link for the ring network with uniform traffic at different values of Amax . For OBS no. of independent flows per link is shown.

traffic matrix, the value obtained with ILP is only 20% smaller than heuristic, and for the uniform traffic matrix, there is no difference between the optimization and the heuristic. In fact, in the uniform case, the range of possibilities for routing VOBs and assignment of flows to VOBs is fairly limited due to the symmetry in the traffic matrix and the network topology. As a result, the heuristic can easily find very similar solutions to the problem. Now let us turn to the design of the VOB layout for the NSFNET backbone network. For the traffic matrix, we use the estimated relative demand for the NSFNET presented in [4] and scale the edge-to-edge demands in a way that the maximum value of the demand matrix is equal to 7 Gb/s. The summary of the network design, in terms of the number of VOBs per link, is presented in Fig. 3. The results of the heuristics are compared with those of the ILP optimization and the classical OBS. For the ILP case, we have used the first 4 shortest paths per pair of nodes in the optimization. Here we observe that the results are similar to the previous example. Specifically, the heuristic algorithm achieves a fairly good results in terms of reduced number of maximum VOBs per link. When comparing the maximum VOBs per link for ILP and heuristic, we can see that the ILP achieves around 20% better results, in terms of maximum number of VOBs on any link. Finally, let us discuss the execution time of the algorithm. While the heuristic algorithm can find the solutions to the above examples on a conventional PC within second(s), finding solutions to the same examples through solving ILP required a much larger amount of time ranging from several

In this section, we consider the evaluation of the performance of the designed VOB networks and the comparison with the networks designed using the ILP optimization and with the classical OBS. For both VOB and OBS networks we assume just enough time (JET) protocol [6] is used for channel reservation. The performance metrics we consider in our evaluations include the average packet drop rate in the network due to the collisions, average network throughput, access (shaping) delay at the edge of the network averaged over all edge-to-edge flows, and maximum access delay over all flows in the network. To evaluate the metrics, we have implemented the VOB and OBS networks in the discreteevent simulator OMNeT++ [7]. In the simulations, we generate packet traffic for each edge-to-edge flow using the Poisson process with the deterministic packet size of 10 kB and at the corresponding load. The assumptions on the traffic are in line with the traffic analysis presented in [8]–[9]. Table I depicts estimated performance results for the ring network. As we could expect from the results of VOB layout design, the reduced number of VOBs per link is reflected in the great reduction of the packet drop rate in comparison to the classical OBS. For the case with the random traffic and the heuristic design this reduction is in the range of one order of magnitude. Nevertheless, in contrast to the ILP-based design, the design based on heuristic cannot completely eliminate the loss rate in the network. To figure out the reason we should note that the maximum number of VOBs per link is 4 and 5 for the ILP and heuristic solution, respectively, and the number of wavelength channels per link is also equal to 4. On the other hand, in a VOB network we would have zero drop rate only if the number of wavelength channels at any link in the network is at least equal to the number of VOBs being multiplexed on that link. For the case with the uniform traffic matrix, we observe different results based on the Amax values. At Amax =0.75, we achieve a loss-free network operation using both heuristic and ILP designs. This is because in both cases the maximum number of VOBs per link is equal to 4. At Amax =0.7 we observe some dropped packets for both design methods, which is nevertheless an order of magnitude less than that for

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TABLE I P ERFORMANCE EVALUATION RESULTS FOR THE RING NETWORK . T HE AVERAGE VALUES ARE SHOWN WITH 90% CONFIDENCE LEVEL .

ILP Random Traffic

HST

ILP Uniform Traffic

HST

VOB Amax =0.7 VOB Amax =0.75 VOB Amax =0.7 VOB Amax =0.75 OBS VOB Amax =0.7 VOB Amax =0.75 VOB Amax =0.7 VOB Amax =0.75 OBS

Avg. Packet Drop Rate 0 0 9.5 × 10−3 ±1.5 × 10−5 7.2 × 10−3 ±1.3 × 10−5 9.4 × 10−2 ±2.4 × 10−5 3.6 × 10−2 ±2.4 × 10−5 0 − 3.2 × 10−2 ±3.1 × 10−5 0 1.2 × 10−1 ±6.6 × 10−5

Avg. Network Throughput (Mb/s) 168645 ±5.02 168645 ±4.7 167039 ±21 167434 ±21 152763 ±8.9 162287 ±26.2 168329 ±32 162972 ±29 168297 ±33 148250 ±25.2

Avg. Access Delay over all flows (µs) 12.3 ±6.5 × 10−3 17.01 ±5 × 10−2 9.4 ±7.4 × 10−3 14.2 ±1.7 × 10−2 1.7 ±3.7 × 10−4 6.2 ±7.5 × 10−3 21.1 ±4.9 × 10−2 7 ±3.7 × 10−3 21 ±3.8 × 10−2 1.2 ±7.5 × 10−3

Max Access Delay over all flows (µs) 52.7 ±0.77 111 ±5.1 31.7 ±0.24 90.4 ±0.95 28 ±0.1 12.2 ±2.2 62.7 ±11.5 13.18 ±0.13 85.3 ±0.86 1.8 ±1.3

TABLE II P ERFORMANCE E VALUATION R ESULTS FOR THE NSFNET. T HE AVERAGE VALUES ARE SHOWN WITH 90% CONFIDENCE LEVEL .

VOB ILP VOB HST OBS

Avg. Packet Drop Rate 0 6.1 × 10−4 ±3.28 × 10−6 1.75 × 10−2 ±2.01 × 10−5

Avg. Network Throughput (Mb/s) 219400 ±28.19 219265 ±28.1 215567 ±17.4

classical OBS. Interestingly, the loss rate with heuristic design is slightly better than that with the ILP design. The reason lies in the fact that, although both heuristic and ILP design give us the solution with the same value for the maximum number of VOBs per link, the average number of VOBs per link is slightly smaller for the heuristic solution. In all the above cases, we can observe that, as expected, the network throughput improves when the loss rate reduces. The reduction in the loss rate and the increase in the throughput both come at a cost of the increased shaping delay at the edge of the network. The results of Table I show that there is no considerable difference between the shaping delay values for the heuristic and the ILP design. The performance results for the NSFNET network is presented in Table II. The results show trends similar to the ring network examples. Here the heuristic design achieves a quite better performance in comparison to the classical OBS, i.e., the drop rate is reduced by two orders of magnitude. Nevertheless, the heuristic design cannot completely suppress the loss rate in the network. V. C ONCLUSION We have presented and evaluated a heuristic algorithm for designing VOB networks. Through numerical design examples and simulation-based performance evaluations, it has been demonstrated that the proposed algorithm can perform quite well and achieve similar results as compared to the ILP-based optimization approach. The use of the algorithm results in

Avg. Access Delay over all flows (µs) 6.93 ±1 × 10−2 7.4 ±7.03 × 10−3 2.18 ±1.7 × 10−3

Max Access Delay over all flows (µs) 42.07 ±0.43 41.1 ±0.81 9.41 ±2.7 × 10−2

saving the required amount of time/processing for network design in the range of orders of magnitude. R EFERENCES [1] A. Rostami and A. Wolisz, ”Virtual optical bus: an efficient architecture for packet-based optical transport networks,” IEEE/OSA Journal of Optical Communications and Networking (JOCN), vol. 2, no. 11, pp. 901–914, 2010. [2] Y. Chen, C. Qiao, and X. Yu, ”Optical burst switching: A new area in optical networking research,” IEEE Network, vol. 18, no. 3, pp. 16–23, 2004. [3] M. Pi´oro and D. Medhi, Routing, flow, and capacity design in communication and computer networks. Morgan Kaufmann, 2004. [4] B. Mukherjee, Optical WDM Networks. Springer, 2006. [5] D. Eppstein, ”Finding the k shortest paths,” SIAM Journal on Computing, vol. 28, no. 2, pp. 652–673, 1999. [6] Y. Xiong, M. Vandenhoute, and H. Cankaya, ”Control architecture in optical burst-switched wdm networks,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 10, pp. 2062-2071, 2000. [7] OMNeT++ User Manual, available at: http://omnetpp.org/documentation. [8] A. Rostami and A. Wolisz, ”Modeling and synthesis of traffic in optical burst-switched networks,” IEEE/OSA Journal of Lightwave Technology (JLT), vol. 25, no. 10, pp. 2942-2952, 2007. [9] A. Rostami, A. Wolisz, and A. Feldmann, ”Traffic analysis in optical burst switching networks: a trace-based case study,” European Transactions on Telecommunications, vol. 20, no. 7, pp. 633–649, 2009.