15th International Conference on Advanced Computing and Communications
WDM Network Topologies -A Probabilistic Model Virendra Singh Shekhawat*, Dinesh Kumar Tyagi* and V.K. Chaubey** *CSIS Group, **EEE Group Birla Institute of Technology & Science, Pilani 333031 (Rajasthan) India E-mail:
[email protected],
[email protected],
[email protected] Abstract Thus it is essential for a network developer to optimize the network performance for the least crosstalk, minimum delay and best throughput suitable for most of the network topologies. Optical packet switching combined with WDM technology has changed the static usage of WDM network into an intelligent optical network capable of guaranteeing an efficient routing and switching [15-17]. The need for fixed or variable packet length with full optical synchronization has added a new feature in such networks [18-21] to support the data traffic. Architectural study and analysis of such intelligent nodes has been less emphasized in the recent past and thus requires an attention to model a proper optical node. Node architecture for such networks involves multiple delay lines, output queuing, and wavelength encoding and control blocks. The performance model for a high-speed data through such network becomes tedious and time consuming as the number of wavelength and nodes increases. A novel method for achieving such intelligent routing at a fast speed is attained through mapping the optical network onto a reserve signaling channels and updating the node status table to implement the routing algorithm for better traffic handling. This proper online update may lead to implement the decision through activating the wavelength converters to maintain the light path even any single channel is available between the source and destination. The large the number of nodes and wavelength converters degrade the multiplexed WDM signal to be acceptable for a given quality of service. This may provide a simpler way to achieve an optimal path between source and destination without going for time consuming recursive algorithms for evaluating all possible path combination. In the present paper an appropriate model of an optical node is proposed estimate the routing performance of an optical node receiving erlang B traffic. The proposed router is used to optimize the path on the basis of applied algorithms to process the WDM traffic in general.
This paper presents a simple generic network model to evaluate the network performance of an optical network. A probabilistic traffic model for a WDM optical network employing a ring and a star topology has been developed to investigate the call connection probability and router performances respectively. The numerical results show a huge data transmission through the router with a least dependence on the routing time upto a significant data rate. Key Words: All Optical Networks, WDM, Intelligent Routing, Call Blocking Probability.
1. Introduction Optical Networks employing routers embedded with efficient routing algorithms on intelligent nodes have opened the path of next generation internet. The performance of a circuit switched Wavelength Division Multiplexed (WDM) networks critically depends on the active and passive circuit components utilized at the nodes in such a way that each subscriber is assigned a separate wavelength channel to be routed through routing devices with a minimum loss and cross talk [1-4]. However, the performance of packet switched optical networks are characterized by the strategy involved in handling the packet blocking either through utilizing buffering or wavelength conversion [5-7]. This traffic management requires optical logic processing and data buffering to implement optical burst switching or optical label switching [8-9] in WDM networks. Thus, the network node architecture require a dynamic reconfigurable switch fabric to sustain the demand of resource allocation and a series of provisioning requirement to support traffic fluctuation and scalability. An emphasis has also been made to put more intelligence onto the WDM nodes to implement distributive or online traffic control [10-14] to achieve a better network management.
0-7695-3059-1/07 $25.00 © 2007 IEEE DOI 10.1109/ADCOM.2007.38
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This traffic (ρ) can be expressed as:
2. Node Architecture Model
ρ = nλ Cµ
(1) This traffic equation can be used to evaluate the performance of the node structure in the WDM network.
The algorithm proposed in an earlier paper [10], aims to gain the property of ‘look ahead’. It determines whether a signal can be sent to the destination from the first node itself. If it is not possible, then the signal is blocked in the initial nodes. This in turn saves a lot of time and resources, especially in the cases where the signals get blocked after traveling for some part of the path. The concept of ‘look ahead’ is introduced by reserving a wavelength wz for online routing. This wavelength is separate from the main set of wavelengths and is used only for communicating the status of the channels originating from the other nodes. Based on the concept of intelligent routing, we have proposed the model for a new router that is capable of routing the signal over different wavelengths in the various links such that the path of minimum propagation loss and crosstalk effects in the WDM network is taken up. We may consider a physical architecture of an optical node having routing and conversion capability as shown in Fig.1. In this model the traffic arrival follows a poisson process and the node process the traffic within the service time. However in practice to capture the burst nature of the network having finite population, the model is limited and needs appropriate modifications [22-23]. In the present analysis we have considered a general case with large number of packets to analyze the proposed node architecture. The node requires some time to read the address or scan the entire wavelength and to take decision to either to convert or to download at the node involving switching fabric (GSF). This node can upload data on a given wavelength by switching on the respective source for a given time slot duration (τp) through the encoder block as shown in Fig.1. Encoder is capable to encode serial data on different wavelengths by switching them alternatively and through the circulator and delay combination these encoded data can be brought in the same time at different wavelengths. It is obvious to note that the node is capable to stack the data at different wavelength and time slot as per the control algorithm using on the node. The model assumes the node performance in an ideal situation; however the nonlinearity of the subcomponent and jittering of the encoding block limits the performance by incorporating some additional delay. These node components can be modeled as delay components with some random noise adder. This in turn governs the value of data processing time µ and the total number of packets that can be processed by the router. The effective traffic (ρ) at the node depends on the capacity of the channel link (C), packet arrival rate (λ) and the number of nodes (n) in the network involved.
Fig.1. Node Architecture
3. Performance Evaluations and Discussion In the case of our simulated router, we consider it as a single server model that allows for w waiting slot for each of the channels and serves the request on the first come first serve basis. Here λ is the data packet arrival rate at each node from its adjacent nodes and assuming the node itself adds 1/m fraction of incoming traffic and thus creating a total packet processing rate as nλ/m for n node network. We can develop mathematical expression for the call connection probability in two different cases viz. ring and start topology.
3.1. Ring Network The performance of a network may be evaluated on the basis of its ability to process the arriving packets efficiently. This can be better represented by the parameter ρ, given as nλ/mµ. Now, the dropping probability of incoming packets can be written as:
(
Pring = ρ w +1 (1 − ρ ) 1 − ρ w + 2
)
(2)
The probability that an incoming packet at any node to be served by router is given as: Pservice = 1 − Pring (3) Now at each node, every wavelength can be thought of as a server and µ’ is the time to transmit a data packet between two nodes over a link. Assuming that in each
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link the number of wavelength is ‘w’, providing the total number of buffering slots as ‘w’. Therefore, the effective service rate for the entire network is:
λ ′ = λ {1 − [ρ w+1 (1 − ρ ) (1 − ρ w+2 )]} m
w+2
( n−1) 2
w−1 ×∑ ρ k k! P0 k=0
{1−[ρ (1−ρ) (1−ρ )]} w+1
(
)
(6)
where
(4) For the traffic congestion model, the performance parameter ρ’ becomes λ/µ’. Thus the total number of data packets arriving at a node would become λ(1+1/m), which is illustrated in Fig.2. The figure shows the number of packets delivered at a node is equal to number of packets routed at each node and similarly the number of packets outgoing from a node is equal to the number of packets arriving at a node from its adjacent nodes.
P0 =
1 w + 1 w ρ ′ 1 − {ρ ′ w!} 1 + w −1 k (1 − ρ ′ w )w!+ ∑ ρ ′ k ! k =0
(
)
(7)
These equations are used to evaluate the call connection probability and the blocking probability of the router for a given number of nodes and link parameters. The plots of the numerical evaluations have been presented in Fig. 3 and Fig. 4.
Fig.2. Network node of a ring topology The probability that atleast 1 server is free in a link is given as w−1
∑ (ρ
k
k =0
)
k! P0
Fig.3. Call connection probability for a ring topology.
So for the entire Ring network, the probability that atleast 1 wavelength is free in all (n/2) links for routing is
Equation (5) has been used to find the call connection probability for a ring network having 20 nodes each separated by 20 km with service rates µ and µ’ as 107 and 104 respectively. This graph shows the call connection probability of the entire ring network for different number of available wavelengths. It is to be seen that the limiting supported data packets in the channel heavily depends on number of wavelengths and providing a scope for the decision of optimized data rate for a required connection probability. The blocking probability at the router for six wavelengths involved in 20 node network has been shown in Fig. 4. The router demonstrates an impressive performance, as it is capable of routing huge number of data packets in the network. The blocking probability is very low up to a significant data packet in each link. Thus the router is capable of taking correct routing decision for huge number of data packets; the connection is only limited
n2
w−1 P2ring = ∑ ρ k k! P0 , for n being even k =0
(
)
and
(n−1) 2
w−1 k = P2ring ∑ ρ k! P0 k=0
(
)
, for n being odd
The total call connection probability for ring is
Pnet −ring = (1 − Pring )P2 ring
This makes Pnet-ring for a ring with even number of nodes as w+2
n/ 2
× ∑ ρ k k! P0
{1− [ρ (1− ρ ) (1− ρ )]} w+1
(
)
(5)
and Pnet-ring for a ring with odd number of nodes as
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by the number of such virtual circuits that can be formed with the given network parameters.
P2 star
w−1 = ∑ ρ k k! P0 k =0
(
)
2
(9)
Net probability for the star topology can be written as Pnet − star = (1 − Pstar )P2 star (10) The graphs for the performance evaluation of the star network node in this case and the call connection probability are shown in Fig.6 and Fig.7 respectively. In this case also, the superior performance of the router is noteworthy. The router has the ability to route several more data packets than the amount limited by the network parameters like the number of wavelengths etc. The remarkable routing property shows that since µ’ can be of the order of 108 data packets of size 1500 bytes, this router can be suitable for taking routing decisions in Gigabit networks. The router performance for a star network with 20 nodes and 6 wavelengths is shown in Fig.7. It may be inferred that blocking probability is insignificant for data packet intensity upto a critical rate and increases exponentially for a given network parameters.
Fig. 4. Router performance of a ring topology
3.2. Star Network In order to evaluate the performance of a star network, we need to derive in a similar manner, the expressions for a probabilistic evaluation of a star network. The present star topology contains ‘n’ edge nodes connected via a central hub having λ calls generated at each node as shown in Fig. 5.
Fig.6. Router performance of a star network.
Fig.5. Traffic distribution of a star topology The blocking probability for the star will be given by
Pstar = (nλ µ )
w+1
[1 − (nλ µ )] [1 − (nλ µ )w+2 ]
(8) The probability that a packet coming at any edge node will be serviced by star node is 1-Pstar. This makes the effective number of data packets being routed at each node as λ (1-Pstar) and marked as λ ′′ in the Fig.5. The performance parameter ρ for the star topology shown in Fig.5 can be written as
ρ = 2λ (1 − Pstar ) µ ′
Fig.7. Call connection probability of a star network
and
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The performance for the entire network having 20 nodes and link length of 20 km is presented in Fig. 6 for different available wavelengths. These curves are qualitatively similar to the case of a ring topology but with a quantitative difference. The graphs clearly illustrates that the router performance is very high, but the limitation in connection is just a function of some network parameters. If proper design is maintained, the router is capable of high speed efficient routing in networks where very large number of data packets is getting routed.
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4. Conclusions The present discussion has mainly focused on the development of the mathematical models to evaluate the call blocking in a WDM optical network; in general based on different network node architecture for different data arrival rates. The proposed architectural node was found to be very efficient in making the routing decision upto a significant data rates. The connection probability of a WDM routed network was solely limited by the network parameters like the number of wavelengths; the routing capability of the router, link delay and traffic intensity. The router can achieve a capability of achieving as many as 107 to 108 data packets in a second as governed by the design of the chip and speed of the processor. This in turn shows the enormous potential of the router in developing base don such model for high-speed optical networks. The rapid development in the field of integrated circuit design further provides a promising ground for exploring the possible development of high speed mixed computing based on the proposed model in optical networks.
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