# Improved Connection Establishment of Dynamic Traffic with Queue in WDM Optical Networks

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## Abstract

Proper route selection between source and destination \((s-d)\) connection leads to efficient resource utilization which leads to the availability of resources for future call arrivals. Various choices are available for Routing and Wavelength Assignment (RWA) and every network demands a particular set of RWA to face least call blocking. Call blocking is an important issue in WDM network since it decides the provision of efficient service. In this paper, we have proposed the solution for RWA problem, efficient Wavelength Assignment Technique (WAT) and effect of call queuing in the network. We have studied and compared all sets of RWA over 14 nodes NSF network and found out that our proposed WAT works better in every set. Call blocking is a function of time and a slight change in time shows noticeable effects. We have shown the effect of call contention on WDM network and hence proposed the optimum value of it. Our simulation results for dynamic traffic show that optimal selection of RWA and contention window improve blocking of connections.

## Keywords

Adaptive wavelength assignment Blocking performance RWA Wavelength assignment Resource allocation## 1 Introduction

Wavelength division multiplexing (WDM) technology in optical fiber networks has gained great acceptance as a means to full-fill the ever increasing bandwidth demands of network users. It is clear that as calls arrive in the network. Route for every call arrival is computed along with a wavelength getting assigned to carry the information [1]. Hence, RWA to one call request affects the resource allocation to the upcoming call request [2]. Resource allocation in the network takes place by RWA. Efficient RWA selection leads to lesser call request blocking [3]. In addition, dynamic traffic grooming with the use of call queuing techniques resolves the problems of connection establishment in the network and is found to be NP-complete [4].

In this paper, traffic in the network is used as a key element for analysis of route between any two nodes [5, 6]. Static Least Weight Routing (SLWR) and Static Least Hop Routing (SLHR) are used for analysis of the network. We have proposed *Adaptive WAT* and wavelength continuity constraint is handled with classical and proposed methods. Comparison between route selection methods and WAT has been done to estimate the best solution to reach lower bounds of blocking probability. We have studied and compared two different types of routing for call establishment along with *Adaptive WAT* and standard classical WATs viz. *Most Used*, *Least Used* and *Random Fit*.

This paper proposes an algorithm to study the effects of different routing and WATs on 14 nodes NSFNET optical network. The proposed algorithm also works for any other random network with same efficiency and correctness. The rest of the paper is organized as follows: Sect. 2 explains the mathematical analysis of the connection requests. Section 4 explains the results and discussion of the performance of several routing and WATs and concluded in Sect. 5.

## 2 Mathematical Analysis

In WDM network during the connection request arrival, it searches for the available shortest paths and latter assigns the free wavelengths available in the path and the connection gets established. As the establishment of a connection consumes a wavelength on a route, future call arrival can not be established on the same path with the same wavelength. Hence, modifying the RWA can improve the connection establishment. Therefore establishing the connection through least congested path (in terms of traffic or hops) allows future call establishment easier thereby reducing the blocking of future calls [7]. This situation of blocking the connections due to wavelength unavailability can thus be avoided by proper selection of RWA.

The procedure of connection establishment is implemented for standard network (14 node NSFNET mentioned in Fig. 1). However, it performs well on any random network. Each link in the network is considered to be unidirectional for simplicity purpose, which can latter be considered bidirectional. Call requests arrival is dynamic in nature and follows Poisson’s distribution. In the computation of route, we can choose hops or traffic to be the key parameter which is followed by the WA for data transfer [8, 9]. The number of wavelengths in the network are predefined (based on the link capacity with the assumption that link capacity is same throughout the network) and can be utilized only once per call until the call duration is completed [10]. Every wavelength has equivalent importance in a wavelength selective network because wavelength continuity constraint dominates the call establishment process. Hence, wavelength utility is also an important parameter which is to be taken care during the connection establishment. The procedure of wavelength selection for present call request affects the availability of wavelength(s) for future call arrivals which can further affect the blocking of future call requests. Due to the wavelength continuity constraint, it may happen that wavelengths are unused in some of the intermediate links of the path thereby leading to poor resource utilization.

### 2.1 Call Request Arrival

The first step of our analysis is on the arrival of call requests between the nodes. The real time traffic arrival follows Poisson’s process [11, 12]. Hence, dynamic call requests that arrive in 14 node NSF network shown in Fig. 1 is according to Poisson’s process in real time scenario. The mean call arrival rate is defined by \(\lambda (t)\) which is not always necessary that the call requests arrive at same instances between every node pair. As the call arrival is Poisson in nature, it also affects the blocking probability and hence traffic is one of the key parameters to be considered [13, 14]. The call duration depends on its holding time. Therefore, the connections with larger holding time reflects wavelengths to be busy always. At the end of the holding time, the assigned wavelengths are released and are updated as free wavelengths available for future connections that are to arrived.

*dt*, number of arrival occurred is unpredictable. In time interval

*dt*number of arrival occurred with the probability \(\lambda \dot{d}t\) and independent of arrivals outside the time interval

*dt*. The number of arrivals

*N*(

*t*) in a finite interval

*t*follows the Poisson’s arrivals given by,

#### 2.1.1 Inter Arrival Time Distribution

*X*denotes the inter arrival time between two consecutive lightpath request. Let

*n*lightpaths are established in such a way that the inter arrival time between lightpath

*i*and lightpath \(i+1\) is \(x_i\) where, \(i=1, 2, 3, \ldots , n-1\) assuming all \(x_i\)’s are mutually independent random variables. Let \(f(x_i)\) denotes the continuous probability density function of the inter arrival time between two consecutive established lightpath requests. Probability density function for an inter arrival time \(x_i\) is given by negative exponential distribution \(f(x_i)=\lambda e^{-\lambda x_i}\) , where \(\lambda\) is connection request arrival rate. Let the distribution of the sum of all inter arrival times \(x=x_1+x_2+x_3+\cdots +x_n\) between lightpaths \(i=1\) and \(i=n+1\) is denoted by

*j*(

*x*). The variable

*x*itself is the sum of

*n*variables. The variable

*x*denotes the time to \((n+1)\)th connection request arrival. The sum of probability density functions of individual inter arrival time is not equal to the probability density function of the sum because the sum of n probability densities is not even a density, since the area exceeds more than one. Let \(x=x_1+x_2+x_3+\cdots +x_n\) have probability density \(f_1(x)\) and cumulative density

*F*(

*x*). Then \(F_1(x)\) = Prob\((x < y)\) = Prob\((x=x_1+x_2+x_3+\cdots +x_n < y)\). Now, we compute the probability distribution of sum of first two inter arrival time. Next we apply the same analogy to rest of inter arrival time. Let the cumulative distributions of first two inter arrival time be \(F_2\), \(F_3\) and \(z=x_1+x_2\) have probability density

*h*and cumulative density

*H*. Then

*H*(

*z*) = Prob\((z < u)\) = Prob \((x_1+x_2 \le u)\).

*f*i.e. \(h=f*f\). Here, it is seen from the above result that the probability density of sum of two inter arrival time density is equal to convolution of their individual inter arrival time densities. Further, we expand the same computation for sum of three time gap densities. Let \(v=x_1+x_2+x_3\) have probability density

*g*and cumulative density

*G*. Then

*G*(

*v*)= prob\((z+x_3<w)\) as \(z=x_1+x_2\). Repeating computation process for densities

*h*and

*g*, we have got the following result.

*h*is given as,

*u*is a time parameter,

*j*(

*u*) shows the probability density function of summation of

*n*inter arrival time.

#### 2.1.2 Expected Arrival Time

#### 2.1.3 Standard Deviation of Arrival Time

## 3 RWA Strategy Analysis

The procedure of connection establishment is implemented for the standard network (14 node NSFNET mentioned in Fig. 1). Each link in the network is considered to be bidirectional.

### 3.1 Routing

Route Selection (RS) problem is to compute the routes available between source and destination nodes according to the weight of the links or hop distance. Standard weight functions are utilized for every link. Solving RS problem using standard weight function is referred to as SLWR. In SLWR the path with least distance ration which refers to the least weight function is selected. Distance ratio between any two nodes is the ratio of the distance between respective nodes and the maximum possible distance between two nodes in the network. The routing algorithm for SLWR is shown in Algorithm 1.

Hop count can be defined as the number of nodes in the path between the source to destination nodes. When the hop count is minimum, the number of links between source and destination nodes are minimum. This ensures the least utilization of resources and hence leave more resources for future calls making future call blocking lesser. Such routing is referred to as SLHR. The Algorithm for SLHR is shown in algorithm 2.

In this paper, we used dijkstra’s algorithm to find the shortest path between the source and destination nodes. The complexity of dijkstra’s algorithm is less (\(O[n_2]\)) and hence it is used to find out the least traffic part. The optical paths here are considered to be bidirectional in nature.

### 3.2 WA Problem

Wavelength Assignment (WA) problem is heuristics in nature and standard algorithms (or mathematical formulations) are used to decide the wavelength(s) for call establishment. In this paper, we have focused on mathematical calculations which helped us to select wavelength for establishment dynamically and adaptively and thereby reducing blocking probability. Wavelength selection and WA is done for all the connection requests after route computation. A dynamic WAT is proposed in this paper and is compared with the classical WATs.

Wavelength for assignment is selected from Wavelength Utilization Factor (WUF). Traffic in the network, information about node pairs involved in call establishment and wavelength(s) utilized for every link are observed. WUF is calculated for every wavelength in the network and wavelength with highest WUF is selected for call establishment. The mathematical formulation for WUF is shown in Eq. 5. With every call establishment, WUF for each wavelength is updated thereby making WA adaptive.

*n*, \(m\ (m \le n)\) and \(k\ (k > n)\). In wavelength selective network, for route between \((s-d)\) pair, \(AF_{RL} = AF_1 \times AF_2 \cdots \times AF_n\). In cluster, AF is calculated for links which are part of cluster but not of route i.e. \(k-n\) links. Free wavelengths on

*p*th link is shown by \((\lambda _{free})_p\) and total wavelength per link by \(\lambda\). WUF for every wavelength is updated every-time any the call is getting established. Updated values save time for WUF calculation every time when the wavelength is required to be chosen.

The concept of WUF is applicable to classical WATs also, but the computation of WUF will be different. For example, in *Most Used WAT* WUF will be the number of times wavelength is used in the network and wavelengths will be arranged in decreasing order of WUF. In *Least Used WAT* wavelengths will be arranged in increasing order of WUFs. In *Random Used WAT* random arrangements will be done so WUF is not significant. The algorithm for routing and WA is explained in Algorithm 3. The non-established calls are considered to be automatically added into queue according to allowed contention window.

### 3.3 Connection Request Queuing

*T*is the maximum time limit for call arrival. When the call requests arrive at any time instant \(t_1\ (0 \le t_1 \le T)\) the calls are queued according to nodes sequence with least route length to highest route length. As the routes for every node pair has been already computed, it becomes easier and faster to decide the route on every call arriving and temporary queuing sequence. The previously queued calls are given first preference over new arrivals. Therefore, the call gets queued once before it gets blocked [15]. The time window can not be taken larger as it increases the congestion for upcoming calls. The sequencing of calls plays an important role since the call with long route requirement if established first would utilize maximum resources and eventually increases the probability of blocking for remaining calls. Therefore, routing and blocking probability are interdependent parameters. Therefore such calls are established at the cost of other call establishments.

There is direct comparison between blocking probability and contention window size in the network as shown in Figs. 3 and 4. When traffic in the network is kept same for *Adaptive WAT*, the optimum window size for 20 wavelengths is 5 time units and while for 16 wavelengths it is 4 time units. We can infer from this result that for same traffic the window size reduces by one time unit when wavelengths are increased by 4. Furthermore, this analysis puts light on the dependence of window size over traffic (in Erlang units) and the number of link-node structure of the network.

## 4 Results and Discussion

### 4.1 Simulation Parameters

For simulation, we have considered 14 nodes NSFNET backbone WDM networks consisting of 21 bidirectional links with different link capacity. The wavelength continuity constraint is enforced here for the wavelength selective networks. Each node in the network is assumed to have the sufficient number of transmitters and receivers. The connection requests for the lightpaths arrive at each node according to a Poisson’s process along with the assumption of network wide inter-arrival time of 10 time units and mean holding time of each call request is 60 time units. An arriving request is equally likely to be destined to any node in the network. After the establishment of the lightpath, it is discarded/tear down after the holding time.

### 4.2 Results

*Adaptive*,

*Most Used*,

*Least Used*and

*Random Used WATs*for SLWR in NSF network. The call arrival and destruction is dynamic in nature and follows Poisson’s distribution. For dynamic traffic

*Adaptive WAT*is better than all other WATs.

*Least Used WAT*gives the highest blocking for same call arrival requests than any other techniques. It is important to note that same call request arrivals and routing are used for analysis of different WATs. The blocking probability increases from

*Adaptive*to

*Most Used*to

*Random Used*to

*Least Used WAT*. The pattern is similar for all the wavelengths from 1 to 40. Blocking probability gives the measure to distinguish the techniques.

*Adaptive WA*,

*Most Used*,

*Least Used*and

*Random Used*wavelength assignment techniques for SLHR in NSF network. Here, similar to SLWR,

*Adaptive WA*is better compared to the other WATs. The queuing of calls show the significant effect on the call blocking. It has been seen that call requests queuing is less for

*Adaptive WA*because most of the links and routes are free. The call requests are being queued and hence blocking of connections are significantly similar to each other. Here, call requests queuing and call blocking differ only by the time window. Time window gives the opportunity to some calls to wait for few routes to become free and hence these calls get the chance for connections to get established thereby reducing the blocking probability.

*PRD*= percentage rate of decrements in blocking probability,

*LBP*= least blocking probability, \(K_P\) = LBP for ‘P’ wavelengths, \(K_1\) = LBP for 1 wavelength.

*Adaptive WA*shows the higher and consistently increasing PRD. The PRD is higher for the range of 16 to 24 wavelengths and then the increment is slow.

*Adaptive WA*is better WAT as PRD is higher than the other.

*Most Used WAT*also shows the similar PRD as

*Adaptive WA*. So, both can be preferred for the network.

From the above mentioned results it is found that *Adaptive WAT* is better than others and hence the comparison between SLWR and SLHR is done on the basis. It is seen after comparing results of *Adaptive WAT* for both routing techniques, SLHR provides minimum blocking as compared to SLWR for the same WAT because of the cumulative effect of path selection. The route between any \((s-d)\) pair can be short or long or of similar length in both the techniques and hence, it can give higher or lesser blocking probability. But when all calls are established, maximum number of shorter paths yields least call blocking in the network because use of shortest path in present time thereby allowing future calls to have more free links with respect to the availability of wavelengths for connection establishment.

The comparison can be better on comparing PRDs of both routing techniques. After comparing results of *Adaptive WAT* for both routing techniques, it is clear that the PRD of *Adaptive WAT* with SLHR is higher than SLWR for same lightpath provisioning. Rate of decrement in blocking probability directly suggests for the better one as it compares the present call blocking with the first call blocking scenario. It is very easy to understand that value of blocking probability may be higher or lesser but when the rate of decrement is higher then it becomes the better solution in network implementation.

*Adaptive WA*is better for SLHR as compared to other WATs irrespective of increasing traffic demand.

From Figs. 9 and 10, we see that the performance of *Adaptive WA* is better on comparing the performance metrics between SLWR and SLHR for different traffic for link capacity of 20 wavelengths. In addition, when we compare blocking performance of *Adaptive WAT* for SLWR and SLHR, we found that SLHR is better than SLWR.

In blocking analysis, we have found that the SLHR is better than SLWR. The single call establishment provides different result and blocking also differ for both the techniques. But on considering the overall call arrivals in the NSF network, we see that SLHR is better. The queue formation has the significant effect on call blocking. It reduces the number of calls blocked in the network. Similarly, *Adaptive WAT* is better than *Most Used WAT*. *Most Used WAT* is better than *Random Used WAT* and *Random Used WAT* is better than *Least Used WAT*. *Least Used WAT* provides highest blocking for same dynamic call arrival in NSF network. This shows that *Adaptive WAT* with SLHR is best for the network and is independent of traffic and lightpath provisioning.

## 5 Conclusion

In this paper, we analyzed the RWA techniques in WDM network for a different number of wavelengths with queuing of call requests. The performance of blocking probability according to selection of RWA shows that the blocking performance can be improved by selecting SLHR and *Adaptive WAT*. These two techniques provide the best desired output in almost every situation. The call queuing improves the blocking performance of the network upto certain value. This value varies with wavelength, number of nodes and traffic in the network. The dynamic traffic proves the selection of these techniques to be applicable for the practical scenario.

## Notes

### Acknowledgements

We acknowledge the thanks and support provided to us by Department of Electronics Engineering of Indian Institute of Technology (Indian School of Mines), Dhanbad, India.

## References

- 1.Murthy, C. S. R., & Gurusamy, M. (2002).
*WDM optical networks: Concepts, design and algorithms*(1st ed.). Upper Saddle River: Pearson Prentice Hall.Google Scholar - 2.Birman, A. & Kershenbaum, A. (1995). Routing and wavelength assignment methods in single-hop all-optical networks with blocking. In
*INFOCOM’95 fourteenth annual joint conference of the IEEE computer and communications societies, bringing information to people, proceedings, IEEE*(Vol. 2). IEEE.Google Scholar - 3.Thangaraj, J., Mankar, P. D., & Datta, Raja. (2010). Improved shared resource allocation strategy with SLA for survivability in WDM optical networks.
*Journal of Optics*,*39*(2), 57–75.CrossRefGoogle Scholar - 4.Hu, J. Q. & Leida, B. (2004). Traffic grooming, routing and wavelength assignment in optical WDM mesh networks. In
*Proc. IEEE INFOCOM*(Vol. 4, pp. 495–501).Google Scholar - 5.Xin, C. (2007). Blocking analysis of dynamic traffic grooming in mesh WDM optical networks.
*IEEE/ACM Transactions on Networking*,*15*, 721–733.CrossRefGoogle Scholar - 6.Betker, A., Gerlach, C., Hlsermann, R., Jger, M., Barry, M., Bodamer, S., Spth, J., Gauger, C., & Khn, M. (2004). Reference transport network scenarios. German Ministry of Education and Research (BMBF), MultiTeraNet project under contract numbers 01 BP 254, 01 BP 256, and 01 BP 289.Google Scholar
- 7.Barry, R. A. & Humblet, P. A. (1995). Models of blocking probability in all-optical networks with and without wavelength changers. In
*Proc. IEEE INFOCOM95*(Vol. 2, pp. 402–412).Google Scholar - 8.Tornatore, M., Baruffaldi, A., Zhu, H., Mukherjee, B., & Pattavina, A. (2007). Dynamic traffic grooming of subwavelength connections with known duration. In
*Proc. IEEE OFC/NOFC07*(Vol. 1, pp. 1–3).Google Scholar - 9.Yao, W., & Ramamurthy, B. (2005). A link bundled auxiliary graph model for constrained dynamic traffic grooming in WDM mesh networks.
*IEEE Journal on Selected Areas in Communications*,*23*, 1542–1555.CrossRefGoogle Scholar - 10.Huang, S., & Dutta, R. (2007). Dynamic traffic grooming: The changing role of traffic grooming.
*IEEE Communications Surveys & Tutorials*,*1*, 32–50.CrossRefGoogle Scholar - 11.Ramaswami, R., & Sivarajan, K. (1998).
*Optical networks: A practical perspective*. Burlington: Morgan Kaufmann Publishers.Google Scholar - 12.Shen, G., et al. (2001). Efficient heuristic algorithms for light-path routing and wavelength assignment in WDM networks under dynamically varying loads.
*Computer Communications*,*24.3*, 364–373.CrossRefGoogle Scholar - 13.Birman, A. (1996). Computing approximate blocking probabilities for a class of all-optical networks.
*IEEE Journal on Selected Areas in Communications*,*14*(5), 852–857.CrossRefGoogle Scholar - 14.Vardakas, J. S., Vassilakis, V. G., & Logothetis, M. D. (2007). Calculating blocking probabilities in single-hop WDM traffic groomed optical networks. In
*ICTON’07 9th international conference on transparent optical networks, 2007*(Vol. 4). IEEE.Google Scholar - 15.Medhi, J. (1991).
*Stochastic models in queueing theory*(2nd ed.). New York: Academic Press.zbMATHGoogle Scholar - 16.Maurya, R. K., Thangaraj, J., & Priye, V. (2016). Statistical analysis of blocking probability for dynamic traffic in WDM optical networks based on Erlang B model. In
*International conference on wireless communications, signal processing and networking (WiSPNET)*. IEEE.Google Scholar - 17.Charbonneau, N., & Vokkarane, V. M. (2012). A survey of advance reservation routing and wavelength assignment in wavelength-routed WDM networks.
*IEEE Communications Surveys & Tutorials*,*14*(4), 1037–1064.CrossRefGoogle Scholar - 18.Jukan, A. (2001).
*QoS-based wavelength routing in multi-service WDM networks*. Vienna: Springer-Verlag/Wien.CrossRefGoogle Scholar - 19.Rouskas, G. N., Zhu, Y., & Perros, H. G. (1999). Blocking in wavelength routing networks I: The single path case. In
*Proc. IEEE INFOCOM99*(Vol. 1, pp. 321–328).Google Scholar - 20.Kelly, F. P. (1986). Blocking probabilities in large circuit-switched networks.
*Advances in Applied Probability*,*18*, 473–505.MathSciNetCrossRefzbMATHGoogle Scholar - 21.Zang, H., Jue, J. P., & Mukherjee, B. (2000). A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks.
*SPIE /BALTZERS Optical Networks Magazine*,*1*, 47–60.Google Scholar