3 Analysis of LSR Model

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1 Performance Analysis for QoS Provisioning in MPLS Networks Shogo Nakazawa, Hitomi Tamura, Kenji Kawahara, Yuji Oie Department of Computer Science and Electronics Kyushu Institute of Technology Iizuka, Fukuoka , Japan Abstract LSR(Label Switching Router)s in MPLS (Multiprotocol Label Switching) networks map arriving IP flows into some labels on Layer 2 switching fabric and establish LSP(Label Switching Path)s. By using LSPs, LSRs can not only transmit IP packets fast with cut-through mechanism, but also solve traffic engineering issue to maximize resource utilization in the whole MPLS networks. So far, we have analyzed delay performance of LSR by focusing only on the real time traffic transmission. In this paper, we will consider the case where non-real time traffic arrives at LSR as well as real time traffic and analyze those packet loss rate under the assumption that the cut-through transmission is applied only to real time traffic. Furthermore, we discuss the bandwidth allocation policy and the buffer dimensioning to meet the requirement with respect to both delay for real time traffic and loss probability for non-real time one, and show the guide for QoS provisioning in MPLS networks. Introduction As the Internet continues to grow rapidly, the number of users is increasing explosively. There is also increasing demand for the multimedia applications such as IP-telephony, video-on-demand, which require quite stringent quality of service (QoS) delivery on packet delay, loss rate and minimum bandwidth. MPLS (Multiprotocol Label Switching) technology would meet this demand and thus LSR (Label Switched Router) in MPLS network is employed to combine Layer 3 routing with Layer 2 high-speed switching efficiently and transfer IP packets fast by cut-through transmission via LSP (Label Switched Path)s on Layer 2 [9]. Moreover, it can treat the traffic engineering issue by setting up various types of LSPs [] and provide Virtual Private Network (VPN) [8]. In order to establish cut-through LSPs, LSR has to map arriving long-lived IP flows into some labels on Layer 2 such as VCI (Virtual Channel Identifier) in ATM switch. This label mapping method is mainly divided into two schemes. One is the data-driven scheme and the other is the control-driven one [2]. For example, the former scheme is implemented in IP switch [6] and Toshiba s CSR (Cell Switch Router) [3] and the latter one is adopted in Cisco s Tag Switching [7] and IBM s ARIS (Aggregated Route-Based IP Switching) []. So far, we have analyzed the performance of LSR by focusing on the processing delay of IP packets in Layer 3 routing kernel in case of the data-driven scheme [5], in which we treated real time traffic and assumed the routing kernel with buffer of infinite length. However, in actual networks, LSR should accommodate non-real time traffic as well as real time one and further the latter assumption would not be realistic. Thus, in this paper, we will consider the case that both real time and non-real time traffic come into LSR and the buffer size is finite, and analyze packet delay and loss performance of both traffic. From now on, we will regard real/non-real time traffic as UDP(User Datagram Protocol) / TCP(Transmission Control Protocol) one, respectively. Since UDP traffic has stringent delay constraints, LSR transmits UDP traffic fast by using a limited number of cut-through LSPs on Layer 2 while TCP traffic is transfered via Layer 3 routing kernel and the default LSP on Layer 2 as in the traditional Internet. Therefore, it becomes important to allocate transmission bandwidth among some cut-through LSPs and the default LSP in a way to make transmission delay of UDP traffic less than that of TCP. On the other hand, packet loss rate should be kept relatively low for TCP traffic, so that the buffer dimensioning in Layer 3 routing kernel is essential. Therefore, by investigating the impact of both the bandwidth allocation and the buffer dimensioning to meet the requirement with respect to processing delay and packet loss rate of UDP/TCP traffic, we will show the guide for QoS provisioning in MPLS networks. This paper is organized as follows. Section 2 describes the mechanism and the analytical model of LSR. Section 3 analyzes the steady state probability of LSR and derives some performance measures. Section 4 provides numerical results and examines the impacts of some parameters on performance. Finally, Section 5 gives a brief conclusion.

2 UDP TCP ½ µ Label Switching Router 2.2 Source Model Description Upstream Node ) default LSP Layer 3 routing kernel Downstream Node In this paper, we assume that data flows into LSR are two kinds of transmission protocols, UDP(User Datagram Protocol) for real time traffic and TCP(Transmission Control Protocol) for non-real time one, and that those packet length is fixed. Thus, we consider a discrete-time queueing system with time slot being equal to a packet transmission time. Since we define the rate of UDP traffic as, the total amount of UDP and TCP traffic on average, UDP and TCP, are given by 2) cut-through LSP Layer 2 switching fabric Label Switched Path Figure : Concept of LSR. 2 Analytical Model and Traffic Model 2. Label Switching Router: Cut-through Mechanism Fig. illustrates the concept of the LSR, which consists of the Layer 3 routing kernel and the Layer 2 switching fabric. The LSR is connected with both upstream and downstream nodes by physical circuit whose bandwidth is (Mbit/s). In the data-driven scheme, if the first packet in some IP flow, which is classified by source-destination IP addresses and/or port numbers, arrives at LSR, it is mapped into the specific label and one cut-through LSP is established between the corresponding upstream and downstream nodes. When the bandwidth for cut-through transmission is set to cut (Mbit/s) and the Ò number (½ Ò Ô Æ Ô Ô ) of LSPs are used, the bandwidth of each cutthrough LSP becomes cut Ô (Mbit/s), where Æ Ô is the maximum number Ò of LSPs which can be set on the Layer 2 switching fabric. If the Æ number Ô of LSPs have been established already and new IP flow arrives, packets in the flow cannot be cut-through, so that they are raised to the routing kernel of Layer 3 and transmitted hop-by-hop. In order to transfer them, the default LSP has to be pre-established via the routing kernel and its bandwidth is set to def (= cut ) (Mbit/s). where is the total amount of incoming traffic at LSR Traffic Model of UDP sources We adopt the Bernoulli process as traffic model of each UDP source in which a packet arrives with probability UDP per slot. When the maximum number of UDP sources multiplexed in LSR is Æ UDP, probability È UDP µ that packets arrive LSR simultaneously in a slot is expressed as follows. UDP µ ½ È µ Æ ÆUDP UDP ÆUDP UDP (2) Therefore, UDP is given by UDP UDP UDP (3) Traffic Model of TCP sources The IP flow model from TCP sources is shown in Fig. 2. Each TCP source generates packets according to an interrupted Bernoulli process (IBP), which is characterized by a parameter set of (,«, ). IBP has two states: on-state and off-state. In each slot, the process changes its state from on to off with probability «, and from off to on with probability. In on-state, one packet arrives in each slot with probability, while no packet arrives during offstate. We suppose that the period of one on-state corresponds to one IP flow. Then, the steady state probability of each state is easily obtained by: () on off (4)

3 λ λd slot off on off on β on : IP flow is established E [on] = / α (packets) Figure 2: TCP source model: 2 state IBP α t off : IP flow is not established E [off] = / β (packets) TCP packet is transmitted with Prob. λd packet transfer time = slot loss R Λ TCP (-w)b IP Processing: Bdef when rejected Label Switched Path: Bcut Λ wb UDP Np Figure 3: Analytical model of LSR. The probability È TCP µ that TCP packets arrive at LSR simultaneously from TCP sources in on-state is given by È TCP µ Thus, we have TCP as ½ µ (5) TCP onæ TCP (6) where Æ TCP is the maximum number of multiplexed TCP sources. In actual networks packet transmission in TCP flows is highly correlated and aggregated IP packet traffic at LAN backbone exhibits so-called selfsimilar characteristics (e.g., [4]). Although IBP does not capture self-similar nature well, it can express the burstiness of packet transmission and we can easily analyze the basic performance of LSRs with some types of traffic by assuming that TCP traffic follows IBP. 2.3 Analytical Queueing Model In this analysis, the physical bandwidth of LSR is shared by both the default LSP and the Æ number Ô of cut-through LSPs at most. Here, we let the Û ratio of the bandwidth for cut-through transmission to, namely, in some slot, one packet assigned on some cut-through LSPs is transmitted with Û prob. while one stored in the routing kernel is with ½ prob. Û. In actual LSR, although some datagrams in default LSP and cut-through ones does not be served in a probabilistic manner, we assume that the LSR serves them in both LSPs probabilistically in order to make evaluation possible for any Û, and that a data arrival at the LSR is on a IP packet basis. The analytical model of LSR is shown in Fig. 3. We will deal with the ideal condition that the LSP is just assigned during one datagram transmission, and that the Layer 2 switching fabric can assign up to the Æ number Ô of LSP for cut-through transmission. Thus, we assume the processing part of Layer 2 as the virtual queue in which the buffer size Æ is Ô and the service rate is Û(Mbit/s) in a slot. Therefore, it is modeled by the geom/d//k(=æ batch Ô ) queue with the arrival rate UDP and the batch Æ size UDP. Here, we do not suppose the buffering of whole IP packet on Layer 2 switching fabric. When the LSR uses all cut through LSPs, newly arriving UDP and TCP packets are raised to the Layer 3 routing kernel. Therefore, if its buffer size is Ê(packets), the Layer 3 can be expressed by the batch geom+ibp/d//k(=ê) queue with the service rate ½ Ûµ(Mbit/s). 3 Analysis of LSR Model 3. Random Variable of System Since UDP packets not assigned on any cut-through LSPs are processed on Layer 3, we cannot analyze each queue of Layer 2 and Layer 3 separately.

4 ½µ Õ Õ Ëon Ø off Ø ½µ Õ Æ Ë TCP Õ Æ TCP Å µå ÑÒµ ܵ ¾µ Õ ¼ È UDP Æ Ô µè TCP Ü µè Ò if ¼ÑÆ Ô ¼ È UDP Æ Ô ½ µè TCP Ü µè Ò if ¼ÑÆ Ô Table : Transition of the number of TCP sources in each state shown in Table. From this table, we È thus have as Ëon ص Ë off ص ÑÒ Æ TCP µ È Õ ½ «µ Õ ÆTCP «Õ ½ µ ÆTCP Õ (8) ÕÑÜ ¼ µ Õ Æ TCP Æ TCP Therefore, we need to evaluate simultaneously both queue lengths of the routing kernel and cut-through LSPs in use as in the analytical model, and we define following random variables in the Ø-th slot. ص: the queue length of the buffer of the routing kernel; Ë Ô Øµ: the number of cut-through LSPs under packet transmission in Layer 2 switching fabric; Ëon ص: the number of TCP sources being in on-state. We can completely describe the state of our system by the above variables and the system ØµË state Ø ¼ ½ ¾ Ô ØµËon ص can form a discrete time Markov chain. Here, we Ë define as the state space Ë for Ô ØµËon صµ, Ë i.e., µ¼ Æ Ô ¼ Æ TCP. A state µ is labeled using the following one-to-one mapping function Å µ: Å µ Æ TCP ½µ. Therefore, Ë can be equivalently represented by the state space Ë ¼ Å µ Å Ë ½, where Å Ë Æ Ô ½µ Æ TCP ½µ. 3.3 Packet arrival probability at routing kernel In this analysis, we assume that the buffer size of Layer 3 routing kernel is finite, i.e., Ê(packets). Here, we denote the random variable ص that represents the number of packets arriving at the routing kernel in the Ø-th slot. There are two cases representing the situation that the state (Ë Ô Øµ,Ëon ص) changes from Å µ to Å Ñ Òµ and Ü packets arrive at the routing kernel in some slot.. The case when the UDP packet in some cut-through LSPs is served. 2. The case when the UDP/TCP packet in the routing kernel is served. In the former case, since LSR processes one packet of cut-through LSPs, LSR can accommodate up Æ to ½ Ô packets on cut-through LSPs and more packets are raised to the routing kernel. If ¼, i.e., no cut-through LSP is Æ used, Ô packets can be held on Layer 2 at most. So, we define packet arrival probability in the former case as Å µå ÑÒµ ܵ and obtain it as follows. ¾µ 3.2 Transition probability of the number of TCP sources being in on-state We first define the transition probability of the number of TCP sources in on-state. ÈÖËon ص Ëon Ø ½µ (7) È ÈÖ ØµÜ Ë Ô ØµÑ Ëon صÒË Ô Ø ½µ Ëon Ø ½µ when the UDP packet in some LSPs is served at Ø-th slot È UDP ÑµÈ TCP ÜµÈ Ò Ü if ¼ÑÆ Ô if TCP ÜµÈ Ò ¼ ½ Ñ Æ Ô È ½µÈ UDP Ñ Ü (9) By assuming that Õ sources change their states from on to off, we can completely give the transition of the number of TCP sources being in on-state as ¼ otherwise

5 Å µå ÑÒµ ܵ µ ¼ È UDP Æ Ô µè TCP Ü µè Ò if Ñ Æ Ô Ùµ ܵ Ùµ ¼Å ÑÒµ ܵ Ùµ ¼¼ Ùµ Å µå ÑÒµ ܵ Ùµ Å µ¼ ܵ Ùµ Ë Å Ùµ Å Ë ½¼ ܵ Ùµ Å Ë ½Å Ë ½ ܵ ½Å ÑÒµ ܵ Similarly, we can obtain packet arrival probability Å µå ÑÒµ ܵ in the latter case as follows. µ and the steady state probability and its vector representation as follows. Å µµ ÐÑ Ü È Ø Å µµ (4) ؽ ÈÖ ØµÜ Ë Ô ØµÑ Ëon صÒË Ô Ø ½µ Ëon Ø ½µ when the packet in the routing kernel is served at slot Ø-th if µè Ò ÑÆ Ô È TCP ÜµÈ UDP Ñ Ü (0) Ü Ü ¼µ Ü Å µµ Ü Å Ë ½µµ (5) Ü Ü ¼ Ü Ü Ê µ (6) Since the system state forms Markov chain of M/G/ type queueing system, we can show the transition probability matrix Ì for Markov chain Å µ using ¾ ܵ, ܵ, ¾ ܵ, ܵ, and (6) as following. As mentioned above, we can show the transition probability matrix ¾ ܵ, ܵ representing that the packet on Layer 2 and Layer 3 is transmitted, respectively, and Ü packets arrive at routing kernel with changing state of established cut-through LSPs on Layer 2 as follows. Ì ¼ ¼µ ½µ ¾µ Ê ¾µ Ê ½µ ʵ ¼µ ½µ ¾µ Ê ¾µ Ê ½µ ¼ ¼ ¼µ ½µ Ê µ Ê ¾µ ¼ ¼ Ê µ Ê µ ¼ ¼ ¼µ ½ (7) otherwise ¼ ٠ܵ ¼ Ùµ.... Furthermore, we define ٠ܵ Ù ¾ µ as follows... Å µå Ë ½ ܵ ½ for Ù ¾ () where ¼ represents a zero matrix of dimension Å Å and µ µ µ µ are given as following, respectively. µ µ ¼ ¼ ¼ ¼ ¼µ ¼ ½ Ûµ ¼µ if ¼ Û ¾ ½µ ½ Ûµ µ otherwise, ¾ ¼µ ½ Ûµ ¼µ Û ¼ if ¾ ½µ ½ Ûµ µ otherwise, Û ¼ ¼ ¼ ¼µ ½µ ¼ ¼Å Ë ½ ܵ ٠ܵ 3.4 Steady state probability ½ We define the system state probability at the Ø-th slot as Ü Ù µ (2) È Ø Å µµ ÈÖ Øµ Ë Ô Øµ Ëon ص (3) µ Û ¾ µ ½ Ûµ µ Û ¾ µ ½ Ûµ µ µ Ü Thus, Ü ÜÌ satisfies, or equivalently, Ü Ü ¼ µ ½ Ü Ê ½ Ü ¼ Ê ½µ ½ Ü ½ µ ¼ Ê ¾ (8) Ê ½ Ü Ê µ (9)

6 Ê Ê Ê ¼µµ Å Ü ÑÒ Æ Ô Û ÑÜ Ê ½µ Ê µè TCP µè UDP Æ Ô µ ¼ È UDP µ Û ½ Ü Å µµ ¼ È UDP µ ÑÜ Ê µ Ê ½µÈ TCP µè UDP Æ Ô ½ µ ½ Ü Å µµ Ê ½ Ê µè TCP µ ÑÜ Ê ½µ Ê µè TCP µè UDP Æ Ô µ Å ¼µµ Ü È TCP µè UDP Æ Ô µ Ê ½ Ü Å µµ È TCP µè UDP Æ Ô ½ µ Ê ½ ½ Ü Å µµ È TCP µè UDP Æ Ô µ Ê Ô ½ Æ Ô Æ Ü Ê Ü ¼ ʵ (20) Ê Ü ½ (2) ¼ where is a column vector of ones. Furthermore, (8) (2) can be stably solved by using the algorithm proposed in [0]. Û Æ UDP Ô ½ Æ ½ Ê ½µÈ TCP µ Ê Ô Æ 3.5 Derivation of performance measures By using the steady state probability obtained in the previous subsection, we can get following performance measures. ½ Ûµ Æ UDP Ô Æ Ô Æ È UDP µ ¼ (23) 3.5. Cut-through rate, Ê We will first derive the cut-through rate Ê. Ê is the ratio of the average number of UDP packets transmitted by cut-through to that of packets generated from whole UDP sources when the maximum number of cut-through LSP is set to Æ Ô. This is given by the following. Next, we can derive the amount of lost UDP packets TCP of TCP,, is obtained from UDP besides. UDP ½ Æ TCP Ê Æ UDP Ô Æ UDP, in (24), and that Ê µ ÑÒ ¼ ¼ ½ ÑÜ ¼ Ê µ ÑÜ Ê ½µ Æ TCP Æ UDP Ê ½ Ü Å ¼µµ ÑÒ Æ Ô µè UDP µ ¼ UDP ¼ ½ Ô Æ Æ UDP Ô ½ Æ Ô Æ Ê ½µ ÑÒ Æ UDP Ü Å µµ ½µ ÑÜ Ê µ ½ ½ ÑÜ ¼ Ê ½µ ½ ÑÒ Æ Ô µ È UDP µ (22) Ûµ ½ Ê ½ Packet loss rate, È We can show the amount of total packet loss,, that the packets arriving at Layer 3 cannot enter the buffer by (23). Æ TCP ½ Ûµ Ô Æ Ê ½ ½µ ÑÜ ¼ Ê µ ÑÜ Ê Ê µ ÑÒ (24) Æ UDP Ô Æ Ô Æ Ê µè TCP µ Therefore, we will obtain the UDP/TCP packet loss rate as follows. ¼ Æ UDP Ô Æ UDP È UDP TCP È UDP TCP (25) TCP ¼ Ê ½ ½

7 ½ Average packet processing delay, Ï There are two cases of packet transmission in LSR. One is hop-by-hop transmission via Layer 3 routing kernel and the other is cut-through one by cutthrough LSPs. First, we can derive the average packet waiting time in case where packets are stored in the routing kernel as follows. N sources Np TCP & rejected UDP default LSP IP Processing Ï def ½ Ê UDP Ê Ô Æ Æ TCP ¼ Ü Å µµ (26)... LSP allocation... 2 Round-Robin np-... Next, we can derive the average packet transmission delay if packets are transmitted by cut-through LSPs as follows. ½ Ï cut Ê UDP Ê ¼ Æ Ô Æ TCP ¼ ¼ Ü Å µµ (27) Therefore, we will obtain the average UDP and TCP packet processing delay in LSR, Ï UDP and Ï TCP as follows. Ï UDP ½ Ê µï def Ê Ï cut (28) Ï TCP Ï def (29) 4 Numerical Results and Discussions In this section, we first show some performances as a function of Æ Ô, and discuss the impact of bandwidth ratio Û for cut-through transmission and the buffer size Ê on the performance. Throughout this section, we set the both number Æ UDP and Æ TCP of UDP and TCP sources to 20, the physical bandwidth of LSR,, to 50(Mbit/s), and the packet length to 400(bytes). We assume that the total amounts of UDP and TCP traffic are even, that is, equals 0.5. Rc(cut-through rate) Figure 4: Simulation model of LSR np Ana(random) Sim(cycle= 2) Sim(cycle=20) Sim(cycle=40) cut-through LSP # of sources=40,total traffic=0.9,c=0.5,w=0.5 buffer size=00,packet length=400[bytes] Np(# of cut-through LSP) Figure 5: Performance Comparison: Cut-through rate, Ê ½ 4. Comparison with Simulation Results and Impact of Æ Ô As mentioned in Sec.2., the bandwidth of each cut-through LSP becomes cut Ò Ô, where Ò Ô ½ Ò Ô Æ Ô µ is the number of cut-through LSP in use. However, we approximately modeled the processing part of Layer 2 as the virtual queue whose buffer size is Æ Ô and the transmission bandwidth is set to Û, namely cut. Therefore, we simulate the above exact model to verify the accuracy of our analytical model. In the analysis, datagrams assigned to some cut-through LSP are stored in one virtual queue and transmitted with

8 Wudp(UDP transmission delay)[msec] Ana(random) Sim(cycle=40) Sim(cycle=20) Sim(cycle= 2) # of sources=40,total traffic=0.9,c=0.5,w=0.5 buffer size=00,packet length=400[bytes] Np(# of cut-through LSP) PlossU(UDP packet loss prob.) Ana(random) Sim(cycle=40) Sim(cycle=20) Sim(cycle= 2) e-05 # of sources=40,total traffic=0.9,c=0.5,w=0.5 buffer size=00,packet length=400[bytes] e Np(# of cut-through LSP) (a) UDP packet transmission delay: Ï UDP (a) UDP packet loss rate: È UDP Wtcp(TCP transmission delay)[msec] Ana(random) Sim(cycle=40) Sim(cycle=20) Sim(cycle= 2) # of sources=40,total traffic=0.9,c=0.5,w=0.5 buffer size=00,packet length=400[bytes] Np(# of cut-through LSP) PlossT(TCP packet loss prob.) Ana(random) Sim(cycle=40) Sim(cycle=20) Sim(cycle= 2) e-05 # of sources=40,total traffic=0.9,c=0.5,w=0.5 buffer size=00,packet length=400[bytes] e Np(# of cut-through LSP) (b) TCP packet transmission delay: Ï TCP (b) TCP packet loss rate: È TCP Figure 6: Performance Comparison: Average transmission delay Figure 7: Performance Comparison: Packet loss rate probability Û, and the datagrams stored in the routing kernel are transmitted via the default LSP with ½ Û prob. at each slot. This probabilistic transmission is not realistic. Thus in the simulation, as shown Fig. 4, we apply the weighted round-robin fashion to the datagram transmission; the weight of datagrams allocated to each of Ò Ô LSPs is set to ÛÒ Ô and that of a datagram in the routing kernel is ½ Û. We compare the analytical result with that obtained by the simulation in Figs We set the bandwidth rate Û for cut-through transmission to 0.5,

9 Figure 8: Impact of bandwidth ratio on Cut-through rate:ê the total traffic to 0.9, and the buffer size of Layer 3 routing kernel to 00 packets. In the simulation, we set the cycle of the round-robin scheduling to 2, 20, and 40(slots). From these figures, regardless of the cycle, the simulation results are well in agreement with analytical ones. Therefore, from now on, we will only show performance measures obtained by the analysis and investigate the impact Æ of Ô on performance in the rest of this subsection. In Fig. 5, the cut-through Ê rate increases Æ as Ô monotonously. We can find that all UDP packets are not always transmitted by cut-through even if the Æ number Ô of cut-through LSPs is set Æ to UDP, which is the maximum number of multiplexed UDP sources. In other words, Æ if Ô gets large, the holding time of cut-through LSP for one packet becomes long because the allocated bandwidth of each LSP becomes small. Therefore, as shown in Fig. 6, both Ï UDP Ï and TCP do not decrease Æ when Ô exceeds 0. Moreover, we find that UDP packets are transmitted about eight times faster than TCP packets even if we allocate the bandwidth of default LSP and cut-through LSPs equally, namely, Û=0.5 Æ and Ô =0. From Fig. 7, it is found È that UDP decreases exponentially, È TCP while does not improve Æ if Ô is set to more than 0. In this case, about 5 percent of TCP packets is lost. Thus we will take following countermeasures to prevent the loss of TCP packets;. LSR should have a large buffer size of the routing kernel. Table 2: Logarithmic decrease rate of TCP packet loss rate Rc(cut-through rate) Û ½¾ ½¼ ¾ ¾ ½½½ ½¼ ¼ ½¼ ¾ ¾ ¼ ½¼ # of sources=40,total traffic=0.7,np=0,c=0.5 packet length=400[bytes] w(=bcut/b) R=00[packets] R=200[packets] R=300[packets] R=400[packets] R=500[packets] 2. Besides, we should allocate the bandwidth of default LSP larger. 4.2 Impact of bandwidth allocation and buffer size In this subsection, we investigate the optimal condition which makes UDP packet processing delay smaller than that of TCP while keeping TCP packet loss rate within some permissible value. In this model, we assume that amounts of UDP and TCP traffic are equal to ¾. However, in order to achieve the above condition, we should examine whether it is adequate or not to allocate each half of the total bandwidth to default LSP and cutthrough ones respectively. Therefore, we firstly investigate the impact of the bandwidth Û ratio for cut-through transmission on the performance when the buffer size of Layer 3 routing kernel, Ê, is set to 00,200,300,400 and 500(packets) in Figs We set the total traffic to 0.7 and the maximum Æ number Ô of cut-through LSPs to 0. Fig. 8 shows Ê cut-through rate Ê. is not sensitive to the buffer size, Ê, and it is in Û proportion to up to about Û 0.4. If takes more than 0.4, almost all UDP packets are transmitted by cut-through. Fig. 9 indicates the transmission delay of UDP/TCP packet. We Û should set to more than 0.36 to transfer UDP packets faster than TCP ones. Furthermore, since the bandwidth of ½ default LSP, Ûµ, becomes Û smaller if gets larger, more TCP packets would be discarded. As shown in Fig. 0(a), when the Ê buffer size is 00, TCP packet È loss rate, TCP, never become less ½¼ than. Hence we also show the impact of the buffer size, Ê, TCP in the same figure. As Ê onè increases, TCP decreases exponentially when Û is smaller than 0.7. Here, È we define the logarithmic decrease rate of TCP packet loss rate with the following formula and values of is shown in table 2.

10 Table 3: Minimum buffer size making TCP loss rate less than some value packet transmission delay[msec] 00 0 TCP Û ½¼ È È TCP R=500[packets] R=400[packets] R=300[packets] R=200[packets] R=00[packets] 0. W_UDP # of sources=40,total traffic=0.7,np=0,c=0.5 packet length=400[bytes] w(=bcut/b) W_TCP Figure 9: Impact of bandwidth ratio on Average packet transmission delay ÐÓ È TCP µ (30) Ê We can see from table 2 that is larger, i.e., the improvement È of TCP due to the increase Ê of is larger Û when gets smaller while no improvement achieves Û when exceeds 0.7. Therefore, in order to satisfy the assumed Û condition, should be in range ¼ that Û¼. Here supposing some permissible packet loss rate for TCP packets, we can find the minimum buffer size that È makes TCP less than this value from (30) and show it in table 3. From this table, we can see that the minimum buffer size obtained Û ¼ for becomes about 60 percent of that Û for ¼. In Fig. 0(b), we display the TCP packet loss prob. UDP packet loss prob e-05 e-06 e-07 e-08 e-09 # of sources=40,total traffic=0.7,np=0,c=0.5 packet length=400[bytes] e e-05 e-06 e-07 e-08 w(=bcut/b) R=00[packets] R=200[packets] R=300[packets] R=400[packets] R=500[packets] (a) TCP packet loss rate:è TCP e-09 # of sources=40,total traffic=0.7,np=0,c=0.5 packet length=400[bytes] e w(=bcut/b) R=00[packets] R=200[packets] R=300[packets] R=400[packets] R=500[packets] (b) UDP packet loss rate:è UDP Figure 0: Impact of bandwidth ratio on packet loss rate UDP packet loss È rate UDP. It decreases when Ê increases and takes minimum value Û around ¼. Therefore, we can say Û ¼ that gives the optimum bandwidth allocation in terms of the packet loss characteristic of UDP under the condition that both UDP and TCP traffic are equal.

11 5 Concluding Remarks In this paper, we have considered the situation that two different classes of traffic flow arrive at LSR; one is the real time traffic with cut-through transmission due to high priority in terms of delay and the other is non-real time one. Thus in the situation, we analyzed the finite buffer model to evaluate the packet transmission delay and the packet loss rate of the routing kernel to investigate the guide for QoS provisioning in MPLS networks. Through some numerical results, we have obtained the followings. When the amount of real and non-real time traffic are equal setting, the bandwidth ratio for cut-through Û transmission to 0.4 would be optimum to satisfy both QoS of the transmission delay of real time traffic and the packet loss rate of non-real time one. We can show the minimum buffer size that meets the requirement of packet loss rate. For example, Û when is 0.4, the minimum buffer size for satisfying that packet loss rate keeps less ½¼ than becomes about 60 percent of that when is 0.5. Û We represented the guideline of optimal bandwidth allocation and buffer dimensioning to meet the requirement on both the packet transmission delay and the packet loss rate. Hence, it can contribute to the QoS control in MPLS networks greatly. However, as mentioned in the part of Traffic Model, aggregated IP traffic in the current Internet exhibits self-similar characteristics, Thus, we will further investigate the impact of this nature on the performance of Traffic Engineering. Acknowledgments This work was supported in part by Research for the Future Program of Japan Society for the Promotion of Science under the Project Integrated Network Architecture for Advanced Multimedia Application Systems (JSPS- RFTF97R630), Telecommunication Advancement Organization of Japan under the Project Global Experimental Networks for Information Society Project, and a Grant-in Aid for Scientific Research (No and No ) of the Ministry of Education, Culture, Sports, Science and Technology, Japan. References [] Awduche, D. et al., Requirements for Traffic Engineering Over MPLS, RFC2702 (999). [2] Davie, B. and Y. Rekhter, MPLS: Technology and Application, Morgan Kaufmann (2000). [3] Katsube, Y., K. Nagami, and H. Esaki, Toshiba s Router Architecture Extensions for ATM: Overview, RFC2098 (997). [4] Leland, W. E., M. S. Taqqu, W. Willinger and D. V. Wilson, Katsube, Y., K. Nagami, and H. Esaki, On the Self-Similar Nature of Ethernet Traffic, IEEE/ACM Trans. Networking, vol.2, no., pp. 5 (2002). [5] Nakazawa, S., H. Tamura, K. Kawahara, and Y. Oie, Performance Analysis of IP Datagram Transmission Delay in MPLS: Impact of both Number and Bandwidth of LSP of Layer 2, IEICE Trans. Commun., vol.e85-b, no., pp (2002). [6] Newman, P., G. Minshall, and T. Lyon, IP Switching: ATM Under IP, IEEE/ACM Trans. Net., vol.6, no.2, 7 29 (998). [7] Rekhter, Y. et al., Cisco Systems Tag Switching Architecture Overview, RFC205 (997). [8] Rosen, E. and Y. Rekhter, BGP/MPLS VPNs, RFC2547 (999). [9] Rosen, E., A. Viswanathan, and R. Callon, Multiprotocol Label Switching Architecture, RFC303 (200). [0] Takine, T., T. Suda, and T. Hasegawa, Cell Loss and Output Process Analyses of a Finite-Buffer Discrete-Time ATM Queueing System with Correlated Arrivals, IEEE Trans. Commun., vol.43, no.2 4, (995). [] Viswanathan, A. et al., ARIS: Aggregate Route-Based IP Switching, Internet draft (997).

12 Shogo Nakazawa received the B.E. degree in communication engineering from National Defense Academy in 993, the M.E. degree in information science from Nara Institute of Science and Technology in 999, and the Ph.D. degree in computer sciences and electronics from Kyushu Institute of Technology, Japan in 2002, respectively, Since 993, He has joined Japan Air Self-Defense Force. His research interests include performance evaluation of computer networks. Hitomi Tamura received the B.E. and M.E. degree in computer sciences and electronics from Kyushu Institute of Technology, Japan in 2000 and 2002, respectively. Since 2002, She has been a Ph.D candidate at the Graduate School of Computer Science and Systems Engineering, Kyushu Institute of Technology. Her research interests include computer networks, Traffic Engineering and Multiprotocol Label Switching. Kenji Kawahara received the B.E. and M.E. degrees in computer sciences and electronics from Kyushu Institute of Technology, Japan in 99 and 993, respectively, and the Ph.D. degree in information and computer science from Osaka University, Japan in 996. From 995 to 997, he was an Assistant Professor in the Information Technology Center, Nara Institute of Science and Technology. From 997 to 999, he was an Assistant Professor in the Department of Computer Science and Electronics, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology. Since April 999, he has been an Associate Professor in the same department. His research interests include computer networks, error and congestion control in high speed networks. He is a member of the IEEE and IEICE. Yuji Oie received the B.E., M.E., and D.E. degrees from Kyoto University, Japan in 978, 980 and 987, respectively. From 980 to 983, he worked at Nippon Denso Company Ltd. From 983 to 990, he was with the Department of Electrical Engineering, Sasebo College of Technology, Japan. From 990 to 995, he was an Associate Professor in the Department of Computer Science and Electronics, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology. From 995 to 997, He was a Professor in the Information Technology Center, Nara Institute of Science and Technology. Since April 997, He has been a Professor in Kyushu Institute of Technology. His research interests include performance evaluation of computer communication networks, high speed networks, and queueing systems. He is a member of the IEEE, IPSJ, and IEICE.