Approximation Analysis for Routing with Clue in Mesh TCP/IP Network

Transcription

1 64 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.4, NO.1 FEBRUARY 2006 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network Piboonlit Viriyaphol and Chanintorn Jittawiriyanukoon, Non-members ABSTRACT Transmission Control Protocol/ Internet Protocol (TCP/IP) network is widely used as the source of information and medium of communication. An Internet Protocol (IP) also becomes the most important core protocol used in the world s largest network. The larger IP network size it becomes the longer IP addressing delay it endures, so many techniques are invented to increase the performance of the IP lookup process. One of the most interesting ideas is Routing with a Clue (RC) which introduces the distribution of IP lookup process to all nodes along the route/path. This paper compares the performance of the distributed IP lookup with conventional IP lookup process by applying to expandable meshed network. We simulated up to three meshed nodes network. Then, the performance matrices such as throughput (THRU), mean queue length (MQL), mean waiting time (MWT), and utilization factor (ρ), are collected in order to explain the effect of expanding network (scalability) versus the performance of both networks. Results indicate that RC network outperforms vis-a-vis the conventional IP network in terms of expanding the network size. Moreover, the performance of the RC network is not dropping much compared to those of the IP network. As the data rates are increased, simulations show that throughputs from both RC and IP network also increased, however the throughputs as of RC network outperform in all data rates. The input traffic fluctuates into the first mesh causing higher burden for nodes in the first mesh than ones in the next adjacent mesh, so performance parameters for nodes in the first mesh is found to be lower than those in the next meshes. Results from nodes in the higher mesh indicate that the nodes will handle little low traffic, in other words they experience fewer packets waiting in the queue. Especially in RC network, MWT for nodes in the last mesh is next to zero. The reason is that over RC network, IP lookup process is distributed to all nodes along the path, so packet holding (check for address) is reduced reflecting all performance parameters, such as throughputs, MQL, MWT, and utilization factor to be better than the conventional IP network. Once Manuscript received on September 21, 2005 ; revised on May 3, The authors are with Department of Telecommunications Science, Faculty of Science and Technology, Assumption University, Bangkok 10240, Thailand. p @au.edu, pct2526@gmail.com the mesh network is increased, RC network can still stabilize throughputs while the conventional IP networks cannot be maintained. This can be proven by extending the O notation as of a packet holding time, applying for both RC network and IP network. From mathematical point of view, the O notation as of time in packet holding for both networks will be derived. The calculations obtained from the notation are relevant to the simulation results. That is, the performance of ERC network depends solely on the address length existing in the RC packets, but the performance of IP network depends on both address length as well as number of prefixes utilized in the table. Over IP network, as mesh number increases, giving nodes increment, the number of prefixes in the hash table also increases. Network size in general will affect directly the performance of IP network rather than ERC network. This will apparently worsen the IP network s throughputs whenever the network size grows. Furthermore an approximation method is introduced. Results from the approximation method are close to results from simulation. Keywords: TCP/IP, IP routing, routing with a clue, distributed IP lookup, meshed networks. 1. INTRODUCTION Routing with a clue[1] is the newly evolving routing technology introduced in the new millennium. Applying the distributed IP lookup process, the technique can reduce the excessive time used in redundant IP lookup for each node. Routing with a Clue utilizes a small overhead unit called a clue to transmit the IP lookup parameters from the current node to the next-hop node. The next-hop node learned from the clue shows where to start its lookup processes. Distributed IP lookup was already compared with the label switching process in Multiprotocol Label Switching (MPLS) [2], [15]. The two techniques share similar concept in adding a small unit, a label in MPLS and a clue in distributed IP lookup, onto the packet header to help routing the packet to the destination. The experimental results showed that distributed IP lookup process is better than label switching process in terms of network throughput. In this paper, we try to compare the distributed IP lookup process with the conventional IP lookup process by changing the network topology to be more complex. We apply mesh topology to the simula-

2 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network 65 tion because the topology is the most complex topology with every node connected together. Each node in the meshed network can transmit frames to each other by only one hop. We begin the simulation from one mesh up to three cascaded meshes of nodes. As the number of meshes increased, the network size is enlarged by the increasing numbers of nodes. We also varied the input data rates from 500 kbps to 2 Mbps to see whether the data rates affected the performance parameters in both meshed networks. We retrieve the network throughput parameter, and network management parameters such as Mean Queue Length, Mean Waiting Time, and utilization factor from the simulations. We concentrate on how numbers of meshes affect the parameters, and on why distributed IP lookup process is better than conventional IP lookup while the packets are communicating in this circumstance. In this paper, an overview will be firstly introduced in section II. The simulation will be briefly cited in section III. Results from simulation are shown in section IV. An approximation method and the calculation are discussed in section V. Section VI will focus on the comparison between results from approximation and results from simulation. Conclusion is written in section VII. 2. BACKGROUND There are several directions to improve the throughput of routing packets from source to destination. For example, new hardware may be developed to increase forwarding interval [11] and IP lookup process [14], [16], parallel processing may be applied to process IP forwarding [10], new data structures may be used to store and manipulate the IP prefixes [6], [7], [9], [12], and new searching methodology [13] and algorithms [17] may be invented in order to process the packet faster. However, IP network is widely used and accepted worldwide. The new technique invented must be compatible with the conventional IP network. Distributed IP lookup [1] is the extension of IP routing by adding 5 bits overhead into IPv4 packet [3]. The 5-bit clue is the encoded prefix of the packet destination address. The clue is used to acknowledge the next hop router where the router should begin searching. All prefixes are stored in a Trie [1] or Patricia data structure. The root of the tree represents the empty string. Each edge going to the left from a vertex represents 0, and an edge going to the right represents 1. Not all the vertices in the tree represent prefixes. The ones that represent prefix are specially marked. All the leaves of a trie are marked because those leaves that are not marked to be the prefix must be removed from the system. Traditional IP lookup is performed by scanning the destination address bit by bit and matching it along the path of a trie. The worst case of IP lookup is O(L) where L is the length of an IP address. Applying binary search can improve the worst case of IP lookup to O(log L).The problem on traditional IP lookup is the redundancy of lookup process cost in each hop. After the router receives the packet from the previous router, it has to perform IP lookup from the beginning until it retrieves the best matching prefix from the trie [4],[5]. Mesh topology is the network that every node is connected with every other node in the network. Implementing the mesh network is very expensive because redundancy may not be avoided. In contrast, redundancy helps increasing availability in the network. If some link in the network is down, any other alternate route will always be available for the node to redirect the traffic to the new path. Because mesh topology is usually used as a backbone network, we applied the topology in our experiments in order to study the performance of the two different IP lookup processes in the same backbone network environment. In this paper, distributed and conventional IP lookup processes are firstly introduced then compared in the three different mesh networks. We applied a mesh network of 4 nodes, then, we cascaded another mesh network with an additional mesh consisting of 2 nodes each. 3. SIMULATION MODEL In this paper, we simulate Routing with a Clue network and conventional IP network by utilizing the model as shown in figure 1. Only the first mesh consists of four nodes then another two meshes (consisting 2 nodes each) are attached to the first mesh. Each link has the maximum capacity limit to 1 Mbps. As the traditional RC network, at each node the packet holding time is next to zero and can be neglected. An extended RC (ERC) network with inclusive packet holding time will be discussed in section IV. A. Input Traffic We varied the input data rates for the simulation into several rates ranging from 500 kbps to 2 Mbps. The arrival process of the input traffic follows Poisson distribution. [2], [6]. B. Queue All queues in front of each node found in this paper are assumed to be of First-In-First-Out (FIFO) discipline. Both queue capacity and the waiting time in queue are set to be unlimited (infinity). C. Packet Holding Time The binary search is applied to the IP lookup [4] process resulting in the cost of O(log L) steps where L is the address length. In order to strengthen binary search, technique of breaking the prefixes into several hash tables is necessary. This will cost O(N log L) instead, while N is total number of prefixes used in the forwarding table. However, in distributed IP lookup, the processes are distributed to each node along the path, so each node requires only TRUE or FALSE

3 66 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.4, NO.1 FEBRUARY 2006 Fig.1: Simulation model. Fig.4: MWT for 1 mesh (input data rate = 2 criterion when consulting the hash table. Therefore, only O(log L) steps are cost in RC network. In the extended RC (ERC) network, this packet holding time O(log L) is included in the account. 4. SIMULATION RESULTS A. One Mesh Fig.5: Utilization factor for 1 mesh (input data rate = 2 Fig.2: Throughputs for 1 mesh. Fig.6: MQL for 1 mesh (input data rate = 1.5 Fig.3: MQL for 1 mesh (input data rate = 2 From Fig. 2, the throughput of RC network is outnumbered by that of the conventional IP network in every input data rate. This is because the IP lookup process has been distributed to every node along the path and has to be repeatedly performed at every single node. Since this IP process repetition will not af- Fig.7: MWT for 1 mesh (input data rate = 1.5

4 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network 67 Fig.8: Utilization factor for 1 mesh (input data rate = 1.5 Fig.11: Utilization factor for 1 mesh (input data rate = 1 Fig.9: MQL for 1 mesh (input data rate = 1 Fig.12: MQL for 1 mesh (input data rate = 500 kbps). Fig.10: MWT for 1 mesh (input data rate = 1 Fig.13: MWT for 1 mesh (input data rate = 500 kbps). fect throughputs of both networks much, there will be no significant differences while the number of nodes is small as well as at low input data rates. We obviously see that the queue length of every node in RC network is lower than that of IP network in every data rate as appeared in Fig. 3, 6, 9 and 12, especially the MQL of RC can be negligible when the low input data rate becomes. However, MQL will increase as the input data rate becomes higher. From Fig. 4, 7, 10 and 13, mean waiting time of nodes in RC network is less than that of IP network because packet processing time at each node in RC network is reduced compared to IP network. At low data rates, fewer jobs enter the system resulting Fig.14: Utilization factor for 1 mesh (input data rate = 500 kbps).

5 68 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.4, NO.1 FEBRUARY 2006 smaller utilization factor compared to at any higher data rates. From Fig. 5, 8, 11 and 14, we can observe that RC network nodes have smaller utilization factor. B. Two Meshes Fig.18: Utilization factor for 2 meshes (input data rate = 2 Fig.15: Throughputs for 2 meshes. Fig.19: MQL for 2 meshes (input data rate = 1.5 Fig.16: MQL for 2 meshes (input data rate = 2 Fig.20: MWT for 2 meshes (input data rate = 1.5 Fig.17: MWT for 2 meshes (input data rate = 2 In the two-mesh network, the difference between the throughputs of RC and IP networks can be observed more obviously than in one mesh network as shown in figure 13. As the node is increased, the throughput of IP network dropped, but RC network still maintained the level of its throughput to remain unchanged from the one mesh network. The reason is because RC network s performance relies only on address length, but for conventional IP network s per- Fig.21: Utilization factor for 2 meshes (input data rate = 1.5

6 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network 69 Fig.22: MQL for 2 meshes (input data rate = 1 Fig.26: MWT for 2 meshes (input data rate = 500 kbps). Fig.23: MWT for 2 meshes (input data rate = 1 Fig.27: Utilization factor for 2 meshes (500 kbps). Fig.24: Utilization factor for 2 meshes (input data rate = 1 Fig.25: MQL for 2 meshes (input data rate = 500 kbps). formance relies on both the address-length and numbers of prefixes. In the two-mesh network, increase in number of nodes results the increasing of prefixes in data transmission. From figure 14, 15, 17, 18, 20 and 21, the nodes of the first mesh have more queue length, and waiting time than those in the next mesh because most traffic waits in the queue of the first mesh nodes, so traffic that passed the first mesh can enter the second mesh nodes immediately causing less queue and waiting time in the second mesh nodes. From the figures, RC nodes still outperform IP network nodes in both meshes. Especially in node 5 and 6, queue length is very low, and mean waiting time is nearly 0. From figure 16, 19, 22 and 25, node5 and 6 have fewer loads than the nodes in the first mesh, and the utilization factor for RC is distinctly less than that of IP network in every data rate, and in every node. C. Three Meshes The results from every parameter in every data rates and every node still indicate that distributed IP lookup outperforms compared to conventional IP lookup. RC throughputs are distinctly higher than IP. In the three-mesh network, the increasing number of nodes has a major impact on the performance of conventional IP network. The throughputs of IP network dropped dramatically because of the growing numbers of prefixes, while it has no effect on the RC network s performance. From Fig. 26, RC throughputs remain unchanged compared to those re-

7 70 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.4, NO.1 FEBRUARY 2006 Fig.28: Throughputs for 3 meshes. Fig.32: MQL for 3 meshes (1.5 Fig.29: MQL for 3 meshes (2 Fig.33: MWT for 3 meshes (1.5 Fig.30: MWT for 3 meshes (2 Fig.34: Utilization factor for 3 meshes (1.5 Fig.31: Utilization factor for 3 meshes (2 Fig.35: MQL for 3 meshes (1 sults from one-mesh and two-mesh networks. From Fig. 27, 30, 33 and 36, the MQL for both networks is increasing according to the increasing data rate. In lower data rate, packet interarrival time is longer than packet processing time, so fewer packets are waiting in the queue. However, with the performance of distributed IP lookup, MQL in RC network is obviously less than that of conventional IP network because RC network utilizes less packet processing time in terms of address lookup. Small numbers of

8 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network 71 Fig.36: MWT for 3 meshes (1 Fig.40: Network Utilization for 3 meshes (500kbps). Fig.37: Utilization factor for 3 meshes (1 5. APPROXIMATION ANALYSIS In the previous section, the simulation of two address lookup techniques has been investigated. The results of simulation illustrate the difference of the two techniques. Several parameters have been carried out from the simulation program. However, to develop, to use, and to learn how to use the simulation programs are time-consuming processes. As the simulation is complicated and resource-consuming process, an approximation tool can be an easy process that is less time-consuming and utilizes small numbers of calculation or computing process. The approximation method then will be introduced in this section. Each node in the model as shown in Fig. 1 will be assumed to accommodate an input as Poisson arrival process. f(x) = 1 x! λx e λ, x = 1, 2, 3. (1) Fig.38: MQL for 3 meshes (500kbps). where λ is a mean arrival time. In the simulation, input data rate λ will be ranging from 0.5 Mbps up to the capacity of the network 2 Mbps. Another assumption is based upon the service distribution in each node. Here the Erlang distribution is employed. g(x) = µn x n 1 e µx (n 1)! (2) where x=1,2,3... and n is a positive integer. In the simulation, µ will be ranging by the cost O(N log L), where N is total number of prefixes used by the forwarding table and L is the address length. From the assumption of input (equation 1) arrival process and the service rate (equation 2), mean queue length (MQL 0 ) at the very first node can be estimated by Fig.39: MWT for 3 meshes (500kbps). queue length can be found in RC network as shown in Fig. 28,29,31,32,34,35,37 and 38. MQL 0 = λ2 E [ x 2] 2(1 λe [x]). (3) Note that an output from a particular node will proceed to next node then becomes an input arrival process to next adjacent node.

9 72 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.4, NO.1 FEBRUARY 2006 MQL k = λ2 k E [ x 2] 2(1 λ k E [x]). (4) Similarly, utilization factor (ρ) at node k can be approximated by ρ k = λ k µ k. (5) Finally, throughput (THRU) at node k can be computed by T HRU k = λ k (1 E (T k )). (6) where E(T k) is an average time T k that IP frames reside in node k. The iterative computation of each node s (k=0, 1, 2,..., k-1) performance measures (MQL k, UTILIZA- TION (ρ k ) and THROUGHPUT k ) using equation 1-6 has been developed. The node-by-node estimation is decomposed based upon the above calculation formulae. Algorithm used for this iterative computation is listed in Fig. 41. Results from approximation method by altering number of nodes (mesh) are then compared vis-a-vis simulation results. It can be seen clearly that approximation results are outperforming in the line of simulation as shown in Fig. 42. that if the percentage of error between approximation and simulation can fall in the range of 10 percent then the approximation results will be very similar. The approximation method will be applied for the distributed IP lookup technique introduced in the previous section, and will be compared to results from the simulation program. From our simulation model, we will work out the computational cost for both techniques, and calculate the percentage of error. 6. COMPARISONS BETWEEN APPROXI- MATION VERSUS SIMULATION In this section, we will investigate the approximation and simulation results applying to the extended Routing with a Clue (ERC) network. Here the packet holding time is taken into account. The experiments are based on one- mesh to three-mesh network, and varying the data rates from 500 kbps to 2 Mbps. The performance measures from both techniques indicate throughput, mean queue length and utilization factor. A. One Mesh Fig.42: Throughputs for 1 mesh. From Fig. 42, we observe that approximation throughputs are very close to the simulation results. With the percentage of error shown in table 1, the approximation results error ranges from % which is very small compared to the simulation results. Fig.41: Algorithm of approximation analysis. The advantages of employing the approximation method are not only time consuming, but also involve computational cost. The approximation technique needs least computational cost because the output parameters can be iteratively computed by mathematic functions. In some cases, the approximation method may give an enormously different result due to a bottleneck situation ( ρ k is approaching 1). Unfortunately the approximation method will not be a useful tool for the case as such. It is also clearly seen Fig.43: MQL for 1 mesh. From figure 43, the MQL coming from approximation is also very close to the MQL results from simu-

10 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network 73 lation. However, in table 2, the error percentages for the data rate 0.5 and 1 Mbps are both 100%. The reason behind this calculation of error percentages is that the approximation results for both data rates are always zero as λ is always lower than µ. Thus, whatever the value of simulation is, the percentage of error becomes 100%. If the approximation result is not zero, we can see that the error for one-mesh condition will be not more than 5.6% as listed in table 2. Fig.46: MQL for 2 meshes. of error cannot be observed from the graph. If the value of MQL approximation is not equal to zero, the error ranges from only 0.4 to 2.8%. Fig.44: Network Utilization for 1mesh. According to Fig. 44 and table 5, the approximation of utilization factor seems to be very practical. The error percentage hits 0% in simulating two data rates, and is less than 4.2% even though in the worst case. B. Two Meshes Fig.47: Network Utilization for 2 meshes. From table 6, every node in both meshes has utilization factor percentage of error between 0 to 3%. However, there is only slight difference in the graph as shown in Fig. 47. C. Three Meshes Fig.45: Throughputs for 2 meshes. We can obviously see from figure 45 that throughputs from both approximation and simulation techniques are still very close with the error between 0.17 to 1.4% according to table 1. From Fig. 46, MQL graph from both simulation and approximation looks very close, but the approximation results of zero still mostly present on the graph especially the queue in the mesh 2 nodes. As most traffic is packed up in the first mesh nodes, the traffic left the first mesh can move through the second mesh very fast causing the approximation of MQL for the second mesh node close to zero. The zero value in approximation results in the percentage of error to be 100% in most value in table 3. However, the 100% Fig.48: Throughputs for 3 Meshes. The throughputs of three meshes coming from both techniques still confirm the utility of approximation technique with small percentage of error less than 2%. The results from Fig. 49 look very similar to Fig. 47 in two meshes case. The queue occurs only at the first mesh nodes at high data rates. In second and third meshes, no queue occurs according to the approximation technique results. However, in the sim-

11 74 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.4, NO.1 FEBRUARY 2006 from the technique. Fig.49: MQL for 3 Meshes. ulation results, there are small numbers of queues in the last two meshes. We have already explained this phenomenon in the previous section. Fig.50: Network Utilization for 3 Meshes. The utilization factor in nodes of every mesh from both techniques is almost identical. From Fig. 50, we observe only slight difference in both columns. With the data in table 7, the error percentage for approximation techniques is less than 3%. From experiments on throughputs and utilization factor, the percentage of errors ranges from zero, exactly the same as the simulation results, to 4%. In MQL approximation, there are some cases that the result of the technique equal to zero which directly affect the calculation of percentage of error. The result from zero value in MQL approximation causes 100% of error. Except in the special case of zero MQL, the approximation technique results are less than 9% of error. With acceptable error percentage, approximation technique needs no computational cost or simulation time according to table 8. In simulation technique, up to 100 sec of simulation time is used to conduct the simulation output, but no time is needed for approximation technique. Moreover, to develop or to learn how to use the simulation program is a complicated task, and time-consuming process. We propose the application of the easier approximation method, which requires only mathematical knowledge to solve some formulae derived from techniques needed for performance comparison. The error of 4-9% from the technique can be overcome by quick results achieved 7. CONCLUSIONS When the data rates are increased, throughputs in both RC and IP networks also increased, but the throughputs of RC network are better than that of IP network. The network traffic fluctuated into the first mesh causing nodes in the first mesh to process more traffic than the following meshes, so performance parameters for nodes in the first mesh are not as good as those in the following meshes. We can obviously perceive that nodes in the last mesh will have very low traffic, so there are very few packets waiting in their queues. Moreover, in the meshed network, as we increase the number of nodes by cascading another two nodes to the existing mesh network, RC network can maintain its throughputs in all meshes. In ERC network, RC network with O notation for packet holding time, the performance relied only on the address length of the packets. In contrast, the performance of IP network relied on both address length and number of prefixes in the table. As number of nodes increases, the number of prefixes in the hash table also increases, so we can assume that number of nodes directly influences the performance of IP network. This results in the IP network s throughputs to be lower as the number of nodes in the backbone is increased. With simulation technique, excessive time has been used for developing the simulation programs, and for simulating events in the model before we could get the performance measures from the simulation program. An approximation method has been proposed. Three performance measures, throughputs, MQL, and utilization factors can be collected from the approximation method. It applies mathematics to carry out all performance measures in no time. The error from the approximation compared to simulation technique ranges from 4% to 9%. References [1] Y. Afec, A. Bremler-Barr, and S. Har-Peled, Routing with a Clue, in IEEE/ACM Transactions on Networking, 6, pp , [2] P. Viriyaphol and C. Jittawiriyanukoon, Evaluation of Routing Techniques over IP-based Network, in Proc. IASTED EuroIMSA, pp , Feb [3] G. Chandramenon and G. Varghese, Trading Packet Headers for Packet Processing, IEEE Trans. on Networking, 4, pp , [4] M. Waldvogel, G. Varghese, J. Turner, and B. Plattner, Scalable High Speed IP Routing Lookups, Proc. 27th ACM SIGCOMM, [5] W. Doeringer, G. Karjoth, and M. Nassehi, Routing on Longest-Matching Prefixes, in Proceedings, IEEE/ACM Trans. on Networking, 4, pp , 1996.

12 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network 75 [6] V. Srinivasan,and G. Varghese, Faster IP Lookups using Controlled Prefix Expansion, in Proc. ACM SIGCOMM, pp. 1-10, [7] M. Degermark, A. Brodnik, S. Carlsson, and S. Pink, Small Forwarding Tables for Fast Routing Lookups, in Proc. ACM SIGCOMM, pp. 1-14, [8] B. Khoshnevis, Discrete Systems Simulations, New York, McGraw-Hill, [9] S. Sahni and K.S. Kim, An O(log n) Dynamic Router-Table Design, in IEEE Trans. Computers, Vol. 53, pp , Mar [10] M. J. Akhbarizadeh and M. Nourani, An IP Packet Forwarding Technique Based on Partitioned Lookup Table, in Proc. IEEE Int. Conf. on Communications, May [11] Cheng-Chi You, Yuan-Sun Chu, Chi-Fang Li, Hui-Kai Su, Fast IP Routing Lookups and Updates in Hardware, in Proc. Int. Sym. on Communications, Nov [12] A. Buchsbaum, G. Fowler, B. Kirshnamurthy, Kiem-Phong Vo, and Jia Wang, Fast Prefix Matching of Bounded Strings, in Proc. ACM SIGACT ALENEX03, Jan [13] K. Kim and S. Sahni, IP lookup by binary search on length, Journal of Interconnection Networks, Vol. 3, pp , [14] D. Taylor, J. Turner, J. Lockwood, T. Sproull, and D. Parlour, Scalable IP Lookup for Internet Routers, IEEE Journal on Selected Areas in Communication, Vol. 21, No. 4, May [15] Rosen, MPLS Architecture, RFC [16] K. Gopalan, and T. with T. Chiueh, Improving Route Lookup Performance Using Network Processor Cache, in Proc. SC2002 High Performance Networking and Computing, Nov [17] I. Ioannidis, A. Garmar, and M. Atallah, Adaptive Data Structures for IP Lookups, in Proc. IEEE Infocom, Mar Chanintorn Jittawiriyanukoon received the B.Eng degree in electrical engineering from Kasetsart University, Bangkok, Thailand in 1984, the M.Eng. and D.Eng. in communications engineering from Osaka University, Osaka, Japan in 1987 and 1990 respectively. He is presently an assistant professor of faculty of science and technology, Assumption University of Thailand. He is also a leader in a data communication research group at the faculty. His research interests include satellite communications, performance evaluation of parallel processing, fast routing algorithm and high speed networks. Piboonlit Viriyaphol received the B. Eng. degree in Computer Engineering from Kasetsart University, Thailand, and the M.Sc. degree in Computer Information System from Assumption University, Thailand. He is currently a Ph.D. candidate in Telecommunications Science at Assumption University of Thailand. His research interests include IP network, network performance evaluation, routing algorithm and network of queue.

13 76 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.4, NO.1 FEBRUARY 2006 Table 1: Throughputs percentage of error. Table 2: MQL percentage of error for one mesh. Table 3: MQL percentage of error for two meshes. Table 4: MQL percentage of error for three meshes. Table 5: Utilization factor percentage of error for one mesh. Table 6: Utilization factor percentage of error for two meshes.

14 Approximation Analysis for Routing with Clue in Mesh TCP/IP Network 77 Table 7: Utilization factor percentage of error for three meshes. Table 8: Computational cost for simulation and approximation techniques.