# Improving the Scalability of an Application-Level Group Communication Protocol

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3 <metricupdate>2 records=5 <record>2, 1 <metric>1.1,.12</metric> <record>2, 3 <metric>1.6,.1</metric> <record>2, 4 <metric>3.1,.195</metric> <record>2, 5 <metric>2.5,.1</metric> <record>2, 6 <metric>3.1,.12</metric> </metricupdate> # Message start for node id=2 # Number of metrics # metric between 2 and 1 # RTT=1.1ms, loss=.12% # Message end <topologyupdate>2 # Message start for node id =2 records=3 # Number of links =3 <record>2, 5 # link between 2 and 5 type=1 # type of link = 1: tree link groups=1 # Number of groups in this link =1 <group> , 1111</group> # group ip= , port = 1111 <record>2, 3 type=1 groups=2 <group> , 1111</group> # group ip= , port = 1111 <group> , 2222</group> # group ip= , port = 2222 <record>2, 6 type=1 groups=1 <group> , 2222</group> # group ip= , port = 2222 </topologyupdate> # Message end (a) Metric Update (MU) message (b) Topology Update (TU) message Figure 1: An example of MU and TU control messages. The outgoing rate, from the RP point of view, for all topology update messages, R tu (N), is given by: R tu(n) = s all tu(n) T tu(n) Total Rate of Control Messages It follows that the total rate, R ctrl (N), for all HBM control messages is the sum of R mu (N) and R tu (N): R ctrl (N) = R mu(n) + R tu(n) R ctrl (N) = N s mu header + N n rmu(n) s rmu T mu(n) N s tu header + 2 (N 1) s rtu T tu(n) 3.2 Strategies to Reduce the Control Overhead General ideas In order to limit the control traffic overhead, R ctrl (N) must not be greater than a given threshold. This threshold can be either a fixed predefined value, or be expressed as a given percentage, α, of the sum of both the average data traffic rate, R data and the control traffic rate, R ctrl (N). Let s consider this second case (RTP/RTCP do the same). Therefore: R ctrl (N) α (R ctrl (N) + R data ) R ctrl (N) + (2) (3) α 1 α R data = R ctrl max (4) For a given T mu (N) and T tu (N), let N n rmu max be the maximum N such that having n rmu = N 1 records, i.e. the maximum, in each metric update message satisfy this constraint. N n rmu max is the solution of a second order equation: R ctrl (N) = R ctrl max (see equation 3). This value of N is a major threshold, since for groups having less than N n rmu max members, an optimal solution is feasible, each member generating messages containing the new communication cost to all other members, while the total control message rate remains below a maximum threshold. On the contrary, for groups having more than N n rmu max members, specific measures must be taken in order to satisfy equation 4. Several strategies are possible, depending on the protocol parameters we play upon: (none) is the reference, and does not include any optimization. Therefore, as N grows, the constraint of equation 4 is not necessarily fulfilled. limits the number of records, n rmu (N), in a metric update message. When N > N n rmu max, this number of records is progressively reduced until a lower predefined bound is reached, n rmu min, at N = N n rmu min. Then, for N > N n rmu min the number of records remains constant and equal to n rmu min. strategy 3 limits the number of records too in a metric update message. The difference with is that when N > N n rmu max, the number of records remains constant, n rmu max, rather than being reduced. In order to keep the total control message rate below the upper bound, the T mu (N) period is progressively increased when N > N n rmu max.

4 also limits the number of records in each metric update message, but less aggressively than the previous two strategies. To compensate, the T mu (N) period is aggressively increased when N > N n rmu max. Therefore these strategies try to find a balance between the various protocol parameters (figure 2) by playing with the frequency and the size of the control messages. In some cases the messages are more frequent but contain less information, and vice-versa. Each of these strategies is now introduced with more details : Non optimized The first strategy, not optimized, is controlled by the following equation set: n rmu(n) = N 1 T mu(n) = max(t mu, T m eval (N 1)) T tu(n) = T tu where T m eval is the time (assumed constant) required to evaluate the communication cost between two members (section 3.3). Since the evaluation of (N 1) metrics grows linearly with N, the T mu (N) period is only constant (T mu ) when T m eval (N 1) T mu, and then equal to T m eval (N 1). Note that the same constraint applies to the three other strategies The second strategy is controlled by the following equation set: explained in section The T tu (N) period also needs an adaptation. Indeed, as N grows, more topology update messages are required (one per member), and this is not caught with a n rmu (N) adaptation. Therefore the topology update period is slightly increased for groups larger than N n rmu max members. An important question is: what is an appropriate minimum number of records in a metric update message, n rmu min?. This parameter obviously depends on the maximum topology fanout (i.e. the maximum number of neighbors, which in turns depends on the topology creation algorithm). n rmu min must be at least equal to this maximum fanout to discover potential congestion problems on the topology. Some extra records with a random subset of the remaining members are then added to enable the RP to improve the topology The third strategy is controlled by the following equation set: n rmu(n) = { N 1 if N Nn rmu max n rmu max T mu(n) = max(t mu, T m eval (N 1)) if N N n rmu max N T m eval n rmu max N n rmu max T tu(n) = { Ttu if N N n rmu max T tu s tu (N) s tu (N n rmu max ) n rmu(n) = { N 1 if N Nn rmu max n rmu min if N > N n rmu min n rmu max Nn rmu max N otherwise T mu(n) = max(t mu, T m eval (N 1)) if N N n rmu max N T m eval n rmu max N n rrm min if N > N n rmu min T m eval n rmu max otherwise T tu(n) = { Ttu if N N n rmu max The main difference with concerns the n rmu (N) adaptation. This parameter remains constant above N n rmu max members, while the T mu (N) is immediately increased. It means that this strategy progressively reduces the number of metric update messages but each of them refreshes a higher number of communication costs with other members Finally the fourth strategy is controlled by the following equation set: T tu s tu (N) s tu (N n rmu max ) n rmu(n) = { N 1 if N Nn rmu max This strategy essentially consists in a n rmu (N) adaptation. The T mu (N) period is adapted for the reasons T mu(n) = n rmu max + N (nrmu max+1) β

5 Metric refresh time period (sec) N n_rmu_max 5 1 N n_rmu_min 15 strategies 1, 3 2 Topology refresh time period (sec) strategies 2, 3, 4 N n_rmu_max (a) Metric update period, T mu(n), at a member. (b) Topology update period, T tu(n), at the RP. n rmu (N) n rmu_max n rmu_min 5 strategy 3 N n_rmu_max N n_rmu_min 1 15 Representativity Ratio N n_rmu_max 1 15 strategy 3 2 (c) Number of records, n rmu(n), in a metric update message. (d) nrrm(n) (N 1) ratio, i.e. representativity of a MU message. Avg. nb of metric update msg per topology update N n_rmu_max Nn_rmu_min strategy 3 2 Metric evaluation data rate (packet/sec) N n_rmu_max 1 strategies 3, 4 N n_rmu_min 15 2 (e) Average number of metric update message per topology update. (f) Metric evaluation overhead (with the ping command). Figure 2: Theoretical results for the various strategies.

7 Transmission and Reception data rates (bps) R mu(n) R tu (N) R ctrl (N) Transmission and Reception data rates (bps) R mu(n) R tu (N) R ctrl (N) (a) (b) Transmission and Reception data rates (bps) R mu(n) R tu (N) R ctrl (N) Transmission and Reception data rates (bps) R mu(n) R tu (N) R ctrl (N) (c) (d) Figure 3: Experimental total control overhead for the various strategies. In our opinion offers a better compromise. The metric evaluation overhead is reduced compared to and many members are probed during the metric update processes (figure 2-(c)), thereby offering a better opportunity to improve the overlay topology. The price to pay is a lower metric update frequency. Finally goes to far in this direction, and the T mu (N) period for very large values of N is by far too high, leading to a bad adaptability. Note that results are largely impacted by the various protocol parameters (parameter max(t mu, T m eval (N 1)) in the T mu (N) equations). For instance this is the reason why the T mu period is only constant for N << 1 and keeps increasing afterward (at least up to N n rmu max, and sometimes after this value depending on the strategy chosen). Having fast (i.e. not in O(N)) yet reliable metric evaluation techniques between the various members would largely modify our results. 6 Conclusions This work discusses the scalability of a control protocol, called HBM, that provides an application level group communication service. HBM is a centralized solution, where everything, including group membership management and overlay topology creation, is under the control of a single Rendez-vous Point (RP). This feature naturally leads to scalability problems. After a detailed modeling of the protocol behavior, this paper explains how the scalability can be largely improved, with a few simple protocol parameter adjustments: the number of records in a metric update message, the metric update generation period, and the topology update period. Finally an appropriate solution, strategy 3, that in our opinion offers a good compromise between the various aspects, is identified. This paper also highlights the practical limitations raised by the metric evaluation process which largely impacts our results. References [1] M. Castro, P. Druschel, A-M. Kermarrec, and A. Rowstron. Scribe: a large-scale and decentralised application-level multicast infrastructure. IEEE Journal on Selected Areas in Communication (JSAC), 22.

8 Tmu period (s) Influences of Rctrl_max and strategy on periods strategies 1, Rctrl_max (kbps) [7] Beichuan Zhang, Sugih Jamin, and Lixia Zhang. Host multicast: A framework for delivering multicast to end users. In Proceedings of IEEE INFOCOM 2, June 22. (a) T mu period Influences of Rctrl_max and strategy on periods Ttu period (s) strategies 2, 3, Rctrl_max (kbps) (b) T tu period Figure 4: Influences of R ctrl max on the various periods for N = 2 members. [2] C. Diot, B. Levine, B. Lyles, H. Kassem, and D. Balensiefen. Deployment issues for the ip multicast service and architecture. IEEE Network, January 2. [3] A. Elsayed, V. Roca, and L. Mathy. A survey of proposals for an alternative group communication service. IEEE Network, special issue on Multicasting: an enabling technology, January 23. [4] Yang hua Chu, S. Rao, and H. Zhang. A case for end system multicast. In ACM SIGMETRICS, June 2. [5] Laurent Mathy, Roberto Canonico, and David Hutchison. An overlay tree building control protocol. In In proceeding of the third International COST264 Workshop, Networked Group Communication (NGC 21), London, UK, November 21. [6] Vincent Roca and Ayman El-sayed. A host-based multicast (hbm) solution for group communications. In First IEEE International Conference on Networking (ICN 1), Colmar, France, July 21.

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