Scalability analysis of a multihomed network mobility protocol

Scalability Analysis of a Multihomed Network Mobility Protocol Md. Shohrab Hossain Mohammed Atiquzzaman William Ivancic School of Computer Science, University of Oklahoma Norman, OK 73019. Email: {shohrab, atiq}@ou.edu Abstract—Previous studies have analyzed cost and performance of multihomed network mobility management protocols, such as, Seamless IP diversity-based Network Mobility management scheme (SINEMO). However, increase in the number of mobile nodes raises scalability issues which can result in its performance degradation. In this paper, we have developed analytical models for scalability analysis of SINEMO in terms of network size, mobility rate, and traffic rate. We have used numerical results to validate the analytical model and compared scalability with basic Network Mobility (NEMO) protocol. Results show that the network-mobility protocols exhibit asymptotically identical scalability for the network though the mobility agent of SINEMO scales better than NEMO. This scalability model can help in quantitative scalability analysis of other mobility protocols, thereby visualizing the effects of future network expansion on the performance of the mobility protocols. Index Terms—Mobility Protocols, Scalability analysis, Network Mobility, Mathematical Modeling, Multihoming. I. I NTRODUCTION To facilitate continuous Internet connectivity to hosts moving together, Internet Engineering Task Force (IETF) proposed NEtwork MObility (NEMO) basic support protocol [1]. NEMO has a number of limitations including high handover latency, packet loss, and inefficient routing path. To address these drawbacks, we earlier proposed SINEMO [2], a multihoming-based network-mobility management scheme. SINEMO uses multihoming features (i.e., having multiple IP addresses) to reduce packet loss and handover delay. In a mobile computing environment, a number of network parameters (such as, network size, mobility rate, traffic rate) influence the signaling cost required for mobility management. With the proliferation of mobile computing, increasingly larger number of nodes will require support from the mobility management entities (e.g., home agent, location manager, mobile router, etc). Thus the expansion of network size incurs additional signaling load on these mobility management entities, resulting in the performance degradation of mobility protocols. Hence, scalability of mobility protocols has become a major issue [3]–[5] for the research community. A number of researches on scalability analysis of networking protocols can be found in the literature. Santivanez et The research work reported in this paper was supported by NASA Grant NNX06AE44G. NASA Glenn Research Center Cleveland, OH 44135. Email: [email protected] al. [3] present a novel framework to study the scalability of routing algorithms in ad hoc networks. Similar framework has been used in [4] and [6] for scalability analysis of mobile ad hoc network and wireless sensor network, respectively. A few simulation and testbed-based scalability analysis have also been performed on IP-mobility protocols [5], [7]. However, simulation results represent only a particular scenario being simulated for a given set of system parameters. In contrast, analytical models represent general scenarios which provide better insights into the behavior of the system being analyzed. The authors are not aware of any research work that quantitatively analyzes the scalability of the mobility protocols, which is required to visualize the effects of future network expansion on the performance of the protocols. The objective of this work is to perform quantitative scalability analysis of SINEMO based on signaling overhead. We have performed entity-based scalability analysis for SINEMO since these key mobility entities are subject to resource limitations in a mobility environment. The contributions of this work are: (i) developing a mathematical model to derive the asymptotic cost expressions for mobility management entities of SINEMO, (ii) performing scalability analysis of SINEMO in terms of network size, mobility rate, and traffic rate by comparing it with NEMO, and (iii) validating the results of the developed model through numerical analysis. Our results show that the network-mobility protocols (NEMO and SINEMO) have asymptotically identical mobility signaling overhead on the network. The numerical validation also support this claim, though some deviations are found between the observed and calculated results. The rest of the paper is organized as follows. In Section II, a brief description of SINEMO is given, followed by the scalability analysis in Section III. Section IV presents the numerical results. Finally, Section V has the concluding remarks. II. SINEMO The architecture of SINEMO [2] is shown in Fig. 1. SINEMO utilizes IP-diversity to achieve a seamless handover of mobile network. It consists of a multi-homed Mobile Router (MR) which can be connected to two wireless networks. MR acts as a gateway between a Mobile Network Node (MNN) Protocol X is said to be more scalable than protocol Y with Y respect to parameter λi if ρX λi ≤ ρλi . B. Assumptions Following are the assumptions of the model: • Session arrival rate for each MNN is equal. • Each session length is equal. • Each CN has one ongoing session with a MNN. • Binary search is used to search location database. C. Notations Fig. 1. SINEMO architecture [2]. and the Access Router (AR) for Internet access. There are two types MNNs: Local Fixed Node (LFN) and Mobile Host (MH). Correspondent Node (CN) sends traffic to a MNN. A Central Location Manager (CLM) maintains the IP address of the MR. The MR acts as the local location manager and keeps the IP addresses of the MNNs. When a mobile network moves into one subnet, MR obtains its own public IP address and one or more address prefixes. Thus, MR provides and reserves an IP address for each MNN. The MNNs are not aware of their public IP addresses; they use only the private IP addresses for connectivity. MR thus hides mobility from the hosts. III. S CALABILITY A NALYSIS In this section, we perform an entity-wise scalability analysis of SINEMO. We have chosen the CLM and the MR for the entity-wise evaluation since CLM is involved in every session between a CN and a MNN, and all communications with the mobile network are carried out through the MR. A. Definition Santivanez et al. [3] present a novel framework to study the scalability of routing algorithms in ad hoc networks. We use this notion of scalability (from [3]) since it is an excellent framework for asymptotic scalability analysis which is also used in [4] and [6]. Mobility protocol’s scalability can thus be defined as the ability to support continuous increase of network parameter values without degrading the performance of various network entities that are responsible for mobility management. Examples of such limiting parameters are network size, mobility rate, traffic rate, etc. Let ΓX (λ1 , λ2 , ...) be the total overhead induced by mobility protocol X, dependent on parameters λ1 , λ2 , and so on. Therefore, the protocol X’s mobility scalability factor with respect to a parameter λi is defined as follows: log ΓX (λ1 , λ2 , ...) λi →∞ log λi ρX λi = lim (1) The notations used in this paper are listed below. Nf Number of LFNs, Nm Number of mobile hosts, Nc Number of CNs communicating with all MNNs, δL Per hop transmission cost for Location Update (LU), δAL Per hop transmission cost for aggregated location update message, δB Per hop transmission cost for Binding Update (BU), δQ Per hop transmission cost for query message, δR Per hop transmission cost for registration message, δDT Per hop transmission cost for each data packet, δDA Per hop transmission cost for each (data) Ack packet, δRR Per hop transmission cost for Return Routability (RR) message, δDH Per hop transmission cost for DHCPv6 message, σ Proportionality constant (for transmission cost) of wireless link over wired link, ψ Linear coefficient for lookup cost, γl Unit processing cost at CLM, Tr Subnet residence time, hp Average number of hops between Internet to arbitrary CN or CLM or AR, hin Average number of hops in the Internet, λs Average session arrival rate, κ Maximum transmission unit, α Average session length (data file size). λp Average packet arrival rate, i.e., λp = λs × ⌈ ακ ⌉ D. Scalability parameters For the scalability analysis of SINEMO, we focus on the following network parameters: • Network size: This will be represented by the number of mobile hosts (Nm ) and number of LFNs (Nf ). • Speed of the mobile network (V ). • Traffic rate: This will be represented by the average number of CNs (Nc ) and packet arrival rate (λp ). Let us first consider the effect of mobility rate on subnet residence time, Tr . The reciprocal of subnet residence time gives the handoff frequency which is typically proportional to the speed (V ) of a mobile network. Thus, Tr ∝ (1/V ). E. Central Location Manager In SINEMO, the CLM has the tasks of a) processing query messages from CNs and searching the location database, b) processing RR messages, c) processing LU messages from MR, and d) processing refreshing BU messages. • Every CN needs the IP address of the MNN before establishing a session. Hence, CN sends query message to CLM requiring transmission cost. This query request triggers a lookup at CLM which is proportional to the logarithm of the number of MNNs. • To prevent session hijacking, RR messages are exchanged among the MH, CLM and CN before each BU message. Therefore, transmission cost is incurred at the CLM for sending and forwarding RR messages. • In every subnet crossing, MR acquires new IP address from the foreign network and notifies CLM using LU message requiring transmission and processing cost. • Moreover, to prevent the binding entry from expiring, MR sends refreshing BU to the CLM and all the CNs during Tr and the frequency is ηr (= ⌊ TTer ⌋/Tr ), where Te is the lifetime of each binding entry. Therefore, the total cost of CLM can be obtained as follows. For details description of these cost expressions, readers are referred to the technical report [8]. RR LU RBU ΓCLM = ΓQR CLM + ΓCLM + ΓCLM + ΓCLM = 2Nc δQ λs + Nc ψλs log2 (Nm + Nf ) + 4Nc δRR /Tr (δAL + δL ) + γl + + ηr (δAL + δL ) Tr = Θ(V Nc + Nc log(Nm + Nf )) In each handoff, MR sends LUs to CLM informing newly acquired IP address and prefixes. • After acquiring the IP address and prefixes in every handoff, the MR uses the newly assigned public addresses (to the MNNs in the NAT table) to modify the session table of size proportional to number of sessions. In addition, MR sends BUs to CNs incurring more transmission cost. • MR sends refreshing BU to CLM and the CNs with a frequency of ηr . α • In every CN-MNN session, ⌈ κ ⌉ data packets are sent along with corresponding ACK. Each data packet arriving from CN is intercepted by MR which modifies the destination address by private IP address searching the NAT table. Therefore, the total cost on the MR can be obtained as follows: • RR BU LU RBU DD ΓM R = ΓAcq M R + ΓM R + ΓM R + ΓM R + ΓM R + ΓM R  1 = 2σδDH + ψ(Nm + Nf ) log2 (Nm + Nf ) Tr + 4σ(Nm + Nf )δRR + Nc log2 Nc + 2σδB Nc  + σ(δAL + δL ) + σηr (δAL + δL )(1 + Nc )   + λp Nc ψ log2 (Nm + Nf ) + σ(δDT + δDA ) (8) = Θ(V (Nm + Nf ) + λp log2 (Nm + Nf ) + V Nc log2 Nc )) (2) Hence, SINEMO’s mobility scalability factors for the MR S(MR) = 1, with respect to Nm , Nf , λp , V , and Nc are ρNm S(MR) S(MR) S(MR) S(MR) = 1, ρV = 1 and ρNc ρN f = 1, ρλp = 1. We have expressed the total cost on CLM using the Θ notation1. Therefore, SINEMO’s mobility scalability factors for the CLM with respect to Nm , Nf , λp , V , and Nc can be computed as follows: G. Complete Network In order to compute the total cost of the network as a whole, we consider all the resources (such as, bandwidth, processing power, etc.) consumed in all network entities. This includes cost incurred for query messages exchanged between CLM and CN, local registration of MHs, RR messages, LU messages, BUs to CNs, and data delivery cost. • The query-reply messages between CN and CLM are transmitted through hw (= hp + hin + hp ) wired hops and the lookup at CLM incurs processing cost. • In every handoff, the MR acquires IP address for the MNNs and reserves public IP addresses for the MNNs and modifies the NAT table whose size is proportional to (Nm + Nf ). • RR messages are exchanged among MH, CN and CLM before sending BU. • In each handoff, MR sends LUs to the CLM (hw wired hops and one wireless hop away) to inform the newly acquired IP address and prefixes. Moreover, to ensure session continuity, BUs are sent by the MR to the CNs in each handoff. • Each MR sends ηr refreshing BUs to CLM and all CNs in every Tr , • The data and ack packets travel directly through hw wired and one wireless hops to reach the MR which updates destination address and forward it to MNN Therefore, total cost on complete network due to SINEMO protocol can be obtained as: log(V Nc + Nc log(Nm + Nf )) =0 log Nm log(V N + N log(N + N )) c c m f S(CLM ) = lim ρNf =0 Nf →∞ log Nf log(V Nc + Nc log(Nm + Nf )) S(CLM ) =0 = lim ρ λp λp →∞ log λp log(V Nc + Nc log(Nm + Nf )) S(CLM ) ρV = lim =1 V →∞ log V log(V Nc + Nc log(Nm + Nf )) S(CLM ) = lim =1 ρNc Nc →∞ log Nc S(CLM ) ρNm = lim Nm →∞ (3) (4) (5) (6) (7) F. Mobile Router In SINEMO, the main tasks of the MR are: a) IP address and prefix acquisition, b) processing RR messages, c) sending LUs to the CLM, d) sending refreshing BU messages, e) processing data (ACK) packets to and from MNNs, and f) sending updates to the CNs. Here, we explain these costs in brief. • In every handoff, MR acquires IP addresses and prefixes from the AR in the foreign network by exchanging DHCPv6 request-reply messages. MR then reserves public IP addresses for the MNNs and modifies NAT table. • To prevent session hijacking RR messages are exchanged through MR, thereby incurring transmission cost. 1 Standard asymptotic notation has been used. A function f (n) = Θ(g(n)) if there exists some positive constants c1 , c2 , and n0 such that c1 g(n) ≤ f (n) ≤ c2 g(n) for all n ≥ no . 600 400 200 0 50 100 150 Number of MNNs Fig. 2. Impact of Number of MNNs on total cost of SINEMO’s CLM and NEMO’s HA. CLM: λ = 0.01 SINEMO: Nf = 10 s 2500 CLM: λs = 0.03 4000 Total Cost of MR 800 5000 CLM: Tr = 50s CLM: Tr = 250s HA: Tr = 50s HA: Tr = 250s Total Cost on CLM / HA Total Cost of CLM / HA 1000 HA: λ = 0.01 s HA: λs = 0.03 3000 2000 1000 SINEMO: Nf = 30 NEMO: N = 10 2000 f NEMO: N = 30 f 1500 1000 500 0 2 4 6 Packet arrival rate 8 10 4 x 10 Fig. 3. Impact of packet arrival rate on total cost of SINEMO’s CLM and NEMO’s HA. TABLE I A SYMPTOTIC C OST E XPRESSIONS FOR SINEMO ENTITIES . Entity Asymptotic Cost Expressions CLM Θ(V Nc + Nc log(Nm + Nf )) MR Θ(V (Nm + Nf ) + λp log2 (Nm + Nf ) + V Nc log2 Nc )) Network Θ((λp Nc + Nm + Nf ) log2 (Nm + Nf ) + V Nc log2 Nc ) 50 100 150 Number of Mobile Hosts Fig. 4. Total cost of MR vs. number of MHs for different number of LFNs. IV. VALIDATION In this section, we use numerical analysis to obtain the observed scalability factors for SINEMO and NEMO. The values for the system parameters are consistent with previous works [9], [10]: δL = 0.6, δAL = 1.4, δB = 0.6, δQ = 0.6, δDH = 1.4, δRR = 0.6, δDT = 5.72, δDA = 0.60, σ = 10, λs = 0.01, TABLE II γ t = 10, Nc = 30, hin = 5, hp = 1, Tr = 70s, Te = 60s, ψ = M OBILITY S CALABILITY FACTORS OF SINEMO AND NEMO. 0.3, α = 10Kb, and κ = 576b, Nf = 20, Nm =40. X X X X X ρNc ρV ρλp ρN Protocols ρNm Entity f Fig. 2 shows the impact of number of MNNs on the total SINEMO 0 0 0 1 1 CLM cost of CLM and HA for different subnet residence times. 1 1 1 1 1 MR 1 1 1 1 1 Complete Network The total cost of CLM is much less than that of HA. The cost NEMO 1 0 1 1 1 HA on HA increases with the increase of MNNs since increased 1 1 1 1 1 MR MNNs causes more data traffic to be routed through the HA 1 1 1 1 1 Complete Network (in NEMO) which is not the case for CLM (SINEMO). This NAT RR LU BU DD ΓNet = ΓQR is also evident from the scalability factors in Table II where Net + ΓNet + ΓNet + ΓNet + ΓNet + ΓNet = 2λs Nc hw δQ + ψλs Nc log2 (Nm + Nf ) SINEMO’s scalability factor is 0 with respect to Nm whereas 1  that of NEMO is 1. + ψ(Nm + Nf ) log2 (Nm + Nf ) + 2Nc δRR (3hw + 2σ) Tr In Fig. 3, the total costs of CLM and HA are shown as a + (δAL + δL )(hw + σ) + γl + 2δB Nc (hw + σ) + Nc log2 Nc (9) function of packet arrival rate (λp ) for different session arrival  rates. Again, we can see that λp has no impact on the total + ηr (σ + hw )(δAL + δL + 2Nc δB )   cost of CLM whereas the cost of HA increases for higher + λp ψ log2 (Nm + Nf ) + (hw + σ)(δDT + δDA ) values of λp . This verifies the scalability factors of SINEMO and NEMO with respect to λp which are 0 and 1, respectively = Θ((λp Nc + Nm + Nf ) log2 (Nm + Nf ) + V Nc log2 Nc ) (see Table II). Hence, SINEMO’s mobility scalability factors for the comFig. 4 shows the total cost of the MR as a function of plete network with respect to Nm , Nf , λp , V , and Nc are number of mobile hosts for different number of LFNs in the S S S S S ρNm = 1, ρNf = 1, ρλp = 1, ρV = 1 and ρNc = 1. mobile network. The cost of MR for both protocols increases H. Summary of Scalability Analysis with the increase of number of mobile hosts and are linear in Table I summarizes the asymptotic cost expressions of the nature. This validates the scalability factors for NEMO and mobility management entities of SINEMO. A similar analysis SINEMO with respect to Nm which are 1 (see Table III). Fig. 5 shows the cost of MR as a function of number of has been done for NEMO in [9]. In Table II, SINEMO and NEMO’s computed scalability factors (derived from analytical CNs for different session lengths. Again, both graphs are linear model) are listed with respect to Nm , Nf , λp , V and Nc in nature, thereby validating their computed scalability factors (Home Agent (HA) for NEMO corresponds to SINEMO’s (see Table III). However, cost of MR for NEMO is higher than CLM). It is found that the mobility scalability factors of the SINEMO as the latter sends aggregated binding updates to the overall network for these two protocols are identical. However, CLM unlike the former. SINEMO’s CLM is found to be scale better than NEMO’s In Fig. 6, the total cost of the network are shown for varying HA with respect to Nm and λP . This is because SINEMO number of LFNs with different values of Nc and number uses optimal route for data traffic between any MNN and CN, of hops in the Internet. It is found that cost of SINEMO whereas in NEMO, all data traffic are transmitted through the does not vary significantly with respect to Nf since Nf only HA. influences the query and NAT translation cost which are very 2500 Total Cost on the Network Total Cost of MR 6000 SINEMO: α = 10k SINEMO: α = 50k NEMO: α = 10k NEMO: α = 50k 3000 2000 1500 1000 500 0 10 20 30 40 50 Number of CNs Fig. 5. Total cost of MR vs. number of CNs for different session lengths. 5000 NEMO: hw = 10, Nc = 10 4000 NEMO: hw = 20, Nc = 30 3000 SINEMO: hw = 10, Nc = 10 SINEMO: hw = 20, Nc = 30 2000 1000 0 10 20 30 40 50 Number of LFNs Fig. 6. Total cost of MR vs. number of LFNs for different number of CNs and number of Internet hops. small compared to the data delivery cost. This is why we see the deviation between the computed and observed scalability factors of SINEMO with respect to Nf (see Table III). In Fig. 7, the total cost of the network are shown as a function of speed of mobile network for different session lengths. Here, we find that speed has very little impact on the total cost. Higher speed produces more signaling packets which are insignificant when compared to data packets. That is, data delivery cost dominates over mobility signaling costs. Due to the same reason the calculated scalability factors for NEMO and SINEMO does not match the observed ones (see the columns for ρX V in Table III). TABLE III C ALCULATED AND O BSERVED M OBILITY S CALABILITY FACTORS ρX ρX ρX ρX ρX Nm Nf λp V Nc Protocol Entity Cal Ob Cal Ob Cal Ob Cal Ob Cal Ob 0 0 0 0 0 0 1 0 1 1 CLM 1 1 1 1 1 1 1 0 1 1 MR SINEMO 1 1 1 0 1 1 1 0 1 1 Net. 1 1 0 0 1 1 1 0 1 1 HA NEMO 1 1 0 0 1 1 1 0 1 1 MR 1 1 1 1 1 1 1 0 1 1 Net. A. Comparison of scalability factors In Table III, we list all the calculated scalability factors (obtained from analytical model) and observed scalability factors (obtained from the analysis of graphs) of SINEMO and NEMO. However, we have not been able to present all the graphs due to the page limitation of the paper. Most of the observed mobility scalability factors match with the calculated values, thus validating the analytical model. However, some of them do not match with the computed ones. One of them is with respect to speed of mobile network (see the columns for ρX V in Table III). As explained earlier in this section, the deviation is due to the dominance of the data delivery cost over mobility signaling cost. The increase of signaling cost is insignificant when compared to the data delivery cost, thereby suppressing the impact of speed. This is an important lesson learnt from the numerical analysis. Moreover, from the graphs, it is also evident that costs of SINEMO are much less than that of NEMO. Total Cost on the Network 3500 8000 NEMO: α =10k NEMO: α =50k SINEMO: α =10k SINEMO: α =50k 6000 4000 2000 0 10 15 20 25 30 35 Speed of Mobile Network (m/s) Fig. 7. Total cost of the network vs. speed of mobile network for different session lengths. V. C ONCLUSION In this paper, we have developed a mathematical model for the quantitative scalability analysis of SINEMO, a multihoming-based seamless network-mobility protocol with respect to network size, mobility rate, and traffic rate. We have used numerical results to validate the scalability model. We have also compared the scalability features of SINEMO with its IETF counterpart NEMO. Our results show that the network-mobility protocols exhibit asymptotically identical scalability feature as far as the complete network is concerned though some of the mobility management entities exhibit differences in terms of scalability feature. 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