TCP-Load Balancing: The Aequitas Equilibrium

Transcription

1 1 TCP-Load Balancing: The Aequitas Equilibrium Mahmoud Elhaddad University of Pittsburgh Pittsburgh, Pennsylvania Injong Rhee and Munindar Singh North Carolina State University Raleigh, North Carolina {rhee, Abstract We consider the problem of traffic allocation in multipath IP networks. We postulate that the desired equilibrium distribution of network bandwidth is one where every flow acquires a TCP-fair share along each of the routes connecting its ingress and egress. This characterization calls for connection striping at the ingress to balance the load among the available routes. Still, the desired equilibrium is not reachable when flows are allowed to compete freely for bandwidth, in which case, striping is known to reduce the throughput of TCP below the fair share on the least-congested path. Using the fairness properties of TCP congestion control, we prove that under connectionload balancing and ingress egress traffic isolation, multipath networks tend to reach the desired equilibrium at steady-state despite the interaction among flows within traffic aggregates. The practical value of this result stems from the accuracy with which ingress egress bandwidth allocations can be approximated using token buckets as rate limiters at the ingress routers and the availability of an efficient method for the accurate estimation of the TCP-fair shares. Index Terms TCP, multipath, traffic engineering, striping, load balancing, fairness, equilibrium, axiomatic solution. I. INTRODUCTION Packet-switched networks are invariably designed with multiple paths connecting router pairs to ensure survivability in the face of node and link failures. The availability of unused capacity on the alternate paths and the ever increasing demand for higher flow throughput and lower latency led researchers away from traditional shortestpath routing to consider sharing the traffic load among the multiple ingress egress paths. Multipath traffic engineering presents two challenging problems routing, and ingress egress traffic allocation. Whereas multipath routing involves constructing multiple QoS-constrained loopfree paths between the ingress and egress nodes, traffic allocation is concerned with computing the proportion of ingress egress traffic to forward along each of the candidate paths. Traffic allocation may be performed at different levels of granularity for example, flow (connection) allocation, where packets belonging to the same connection are forwarded along the same path, and connection striping, where the load of individual connections is shared among the ingress egress routes. We postulate that the desirable equilibrium-bandwidth distribution in multipath IP networks is the one in which every flow acquires a TCP-fair share of bandwidth along each of its ingress egress paths. We refer to this equilibrium as the Aequitas (perfect fairness) equilibrium. By definition, Aequitas requires connection striping at the ingress to balance the load w.r.t. the fair shares along the candidate paths. An accurate and efficient method for the estimation of the fair shares was recently introduced in [1]; however, load balancing is not sufficient for a multipath network to reach the Aequitas equilibrium at steady state. Connection striping causes packet reordering and risks increasing the loss-event rate, both of which may lead to significant reduction in throughput. Because packet reordering is common place in the Internet [2], TCP enhancements to ensure its robustness to persistent packet reordering have been introduced [3], [4]. Another solution to the reordering problem is the deployment of an ingress egress striping protocol [5] to ensure that packets leave the network in the same order they arrive. In this paper, we analyze the effects of striping on the throughput of NewReno TCP (simply, TCP) [6], assuming no throughput reduction due to packet reordering. Striping increases the loss-event rate beyond that on the least-congested path when flows are allowed to compete for bandwidth. This problem is akin to the loss-path multiplicity problem in multicast congestion control [7]: the probability that an in-flight transmission window faces congestion increases when it is spread across multiple paths. Our analysis indicates that under coarse-grain traffic isolation at the level of ingress egress traffic aggregates, connections tend to achieve the maximal throughput afforded by their respective allocations; that is, despite the competition among flows within the same ingress egress traffic aggregate. In case load balancing is applied to all connections, this result implies that given ingress

2 egress traffic isolation, multipath networks tend to reach the Aequitas equilibrium at steady-state. The practical value of this result stems from the accuracy with which the aggregate bandwidth allocations under ingress egress traffic isolation can be approximated using token buckets as rate limiters at the ingress nodes without requiring any special capabilities at the internal routers. The multipath traffic allocation problem has been studied in the context of minimum-delay routing [8], [9], [10], [11], and traffic dispersion [12], [13]. The resulting techniques are based on methods of incremental optimization that trade off convergence speed to stability, and require the frequent exchange of load information. We attribute this deficiency to the lack of a constructive characterization of the desired equilibrium. The paper is organized as follows: In section II, we present the merits of Aequitas as the desirable equilibrium, and briefly describe the concepts of TCP fairness and TCP throughput convergence. In section III, we prove that traffic isolation and load balancing are sufficient for achieving the Aequitas equilibrium. In Section IV, we provide a simulation-based illustrative example of convergence to the Aequitas equilibrium. And finally, in section V, we present our concluding remarks and outline the direction for future research. II. THE AEQUITAS EQUILIBRIUM Most of the traffic on the Internet is throughput sensitive. Delay and jitter requirements are handled through routing, bandwidth reservation, and packet-scheduling schemes. Therefore, the objective of multipath forwarding should be to maximize the throughput of the network through the efficient utilization of its links, while maintaining fairness among flows. A network is said to be in Aequitas equilibrium when, at steady-state, every flow acquires a TCP-fair share on each of the routes between its ingress and egress. Aequitas is defined in terms of the TCP-fair share along network paths because of the greedy nature of TCP which ensures good utilization of the links, and because the TCP-fair share also called the Bulk Transfer Capacity (BTC) [14], [15] has become the standard fairness metric for the Internet. Beside the dominance of TCP traffic, the latter is evident in the emergence of UDP-based congestion-control algorithms and protocols that emulate TCP fairness in a manner suitable for multimedia applications [16], [17], and in the availability of mechanisms for enforcing TCPfriendliness on congestion-insensitive flows [18]. The TCP-fair share along a path is the mean steadystate throughput of TCP connection forwarded entirely over that path. A TCP sender in the congestion avoidance phase estimates its fair share of network capacity using an additive rate increase and multiplicative decrease (AIMD) strategy. Every round-trip time the sender transmits an amount of data equal to the transmission window size w. For every acknowledgment packet it receives, the sender increments the window size by 1/w. Upon detecting a loss-event one or more packet loss within a transmission window the sender reduces the window size to w/2. In a moderately-loaded network, the throughput of individual TCP connections sharing the same path converges in probability to some limiting probability distribution [19]. The mean of the limiting distribution is thus the TCP-fair share along the path. Accurate estimation of the TCP-fair shares is critical to achieving the Aequitas equilibrium. The TCP-fair shares along network paths change relatively slowly. This can be deduced from the observation reported in [20] that the number of flows concurrently crossing an Internet link typically remains within 15% of the mean over 5-min intervals. Even though the majority of flows may be shortlived, their number and hence the fair shares exhibit little variability. Direct use of the measured BTC as estimates of the fair shares in computing the traffic allocations may lead to oscillations as flows would simultaneously shift the load toward the less congested paths. In [1], we show that TCP-fairness in sharing bottleneck capacity can be approximated as weighted max-min, when the weights correspond to the measured BTC along the paths of the competing flows. The estimates for the fair shares can thus be computed by periodically feeding the BTC measurements and the number of flows in each ingress egress traffic aggregate to a central server running the (weighted) max-min allocation algorithm [8]. Observe that our definition of the equilibrium assumes that flows originate and terminate at the network boundaries (i.e., flows sharing the same ingress egress pair have identical round-trip times), and that the throughput of a connection is not constrained by the maximum window size at the receiver. Flows with with limited throughput demands can be handled by having the ingress nodes report the effective number of ingress egress flows to the central server. The effective number is the total ingress egress throughput demand as a multiple of the sum of the fair shares along the paths during a given interval [1]. To achieve the desired equilibrium, ingress nodes must balance the load of individual connections among the candidate paths transparently from the connections endpoints (Figure 1). Load balancing is performed w.r.t. the TCP-fair shares along the candidate paths. Traffic allocation at the ingress is implemented by means of a weighted round robin mechanism (Deficit or Surplus Round Robin 2

3 [21], [5]), and requires support for path selection at the ingress. An MPLS-based implementation of this traffic allocation strategy is presented in [1]. network, flow isolation is achieved by allocating a channel along each of the flow s ingress egress paths. 1 window size W ingress/ striping point egress W/2 time Fig. 2. Congestion window behavior over a fixed-bandwidth channel. W corresponds to the channel capacity. Fig. 1. TCP striping at the ingress to achieve the Aequitas equilibrium. Striping is transparent to the connections endpoints. A weighted round-robin mechanism is used to balance the load among the candidate paths. Flows sharing the same ingress and egress have equal fair shares on the candidate paths. Simulation indicates that connection-load balancing can be approximated by balancing the load of the ingress egress traffic aggregates, thus eliminating the need for per-flow state at the ingress routers. III. TCP-LOAD BALANCING The mean steady-state throughput S of a TCP connection can be approximated using the throughput-loss formula [22] S = B 3 (1) RT T 2bl where B is the connection packet size, RT T is the roundtrip time, l is the loss-event rate observed by the sender, and b is the number of packets acknowledged by each ACK packet. Note that in the absence of large variation in RT T due to changing queuing delays, the mean throughput is dominated by the loss-event rate. It follows that connection striping is justified if it results in reducing the loss-event rate below that over the least-congested path. If flows forwarded along common links are allowed to compete for bandwidth, then, at any window size, there is a nonzero probability that a connection incurs packet loss on each link it traverses. Load sharing increases the number of such links hence resulting in lower mean throughput than that achievable by transmitting the entire flow load over the least-congested path. Competition among flows introduces noise-corrupted observations in the AIMD estimation of the fair capacity share. These observations are in the form of loss events incurred below the fair transmission rate. This is in contrast with the ideal model of TCP congestion window behavior where packet loss occurs on a given path only when the connection throughput reaches a certain rate. The ideal model is valid only if the network supports flow isolation using bandwidth reservations (Figure2). In a multipath A. Load Balancing under Flow Isolation Consider a TCP connection split among a set of ingress egress paths P, we define the flow s unit share along a path p i P as the ratio c i /φ i, where 0 < φ i 1 is the fraction of the flow assigned to p i, and c i is the capacity of the flow s channel along p i. The TCP-fair share along channel p i is σ i = ρc i where ρ = 3 4 is the utilization of any channel due to the saw-tooth behavior of TCP congestion window under flow isolation. 2 Observe that in the absence of false-congestion indication due to reordering or transmission errors, the flow incurs a loss-event only whenever the flow load reaches the capacity limit on the channels with minimum unit capacity share. We refer to such channels as bottlenecked. Since in reaction to every loss event, the TCP sender cuts the transmission rate by half, the rate limit on nonbottlenecked channels is never reached. Let R be the peak transmission rate of the connection, then R = min p i P c i φ i (2) The capacity limit is reached on all bottlenecked channels in the same transmission window, hence the resulting losses are perceived by the TCP sender as a single loss event. This means that load sharing has the potential to decrease the loss-event rate below than that on the highestcapacity channel. The mean transmission rate is r = ρr. The multiple channels are thus perceived by the sender as a single channel with capacity C = R. Equation (2) states that the quality of flow allocations determines the amount of wasted capacity on nonbottlnecked channels. Under load balancing all channels are bottlenecked: The flow allocations are computed as φ i = c i p j P c j 1 We assume that bandwidth reservation is implemented using perflow FIFO queuing at the core routers, and TDM link sharing. 2 The ideal model as described makes the stolen-lag assumption [19], actual channel utilization may be less than 3/4. (3) 3

4 that is, c i φ i = c j p i P (4) p j P or, all channels are bottlenecked. From (2), R = c j (5) p j P The mean transmission rate over the channel along any path p i P is rφ i = ρc i, which is equal to σ i the TCPfair share along the channel. Thus, under load balancing and per-flow bandwidth reservations, network flows achieve the Aequitas equilibrium at steady-state if the TCP-fair share along a channel is the same as the TCPfair share along the underlying path. Under flow isolation only a fraction ρ of the bottleneck link capacities are utilized, whereas TCP flows competing for bandwidth at a bottleneck may fully utilize its capacity. Thus, the equilibrium rate along a path is at most a factor ρ below that under Aequitas. In addition to the limited utilization under flow isolation, per-flow treatment at the internal routers introduces a scalability problem. From a practical point of view, it is desirable for a traffic allocation strategy not to require special capabilities at the network s core. In networks with single FIFO queues at the output router links, the capacity reservations for different traffic trunks can be approximated using token buckets as rate limiters at the ingress. For instance, in [23], such a scheme was proposed in the context of differentiated services to approximate guaranteed bandwidth allocations to flows in the expedited-forwarding class. Each token bucket is supplemented with a packet buffer, and, to prevent bursts, the bucket depth must be equivalent to only one packet. The packet-loss probability facing a set of regulated streams, multiplexed at the output link of a core router, depends on their number. Losses occur due to synchronized arrivals from the multiplexed streams that cause the link buffer to overflow. Therefore, rate limiters can be used effectively to approximate bandwidth reservations at the aggregate ingress egress traffic level, but not at the connection level. Compared to flow isolation, bandwidth reservations at the aggregate level results in better utilization of the bottleneck links due to allowing competition among flows within the same aggregate, but also at the cost of introducing noise in the AIMD estimation of the fair rate. In the next section, we show that despite the random loss events, load balancing together with ingress-egress traffic isolation are sufficient conditions for weak convergence to the Aequitas equilibrium. B. Load Balancing under Ingress-Egress Traffic Isolation For convenience we henceforth use the MPLS terminology [24] to describe traffic aggregates. Since flows with common ingress-egress pair share the same set of candidate paths and have identical traffic allocation parameters, we refer to the ingress egress traffic as a Forwarding Equivalence Class (FEC). We also refer to a FEC s stream along a particular path as a traffic trunk. Consider a FEC represented by a set of flows F and forwarded over a set of paths P F. Along each path p i P F, F is allocated a channel of capacity C i. By balancing the load of component flows, together, the individual channels form a single virtual channel of aggregate capacity C = p i P F C i. This result follows from TCP fairness: Individual FEC flows have equal fair shares along each of the channels and hence identical load balancing parameters; since the instantaneous FEC throughput r = f F r f, we have rφ i = C i rφ j = C j p i, p j P F (6) Equation (6) states that all the FEC channels are bottlenecked the FEC reaches the rate limit on all channels simultaneously; at which point, a subset of the FEC flows incurs packet loss. Thus, from the viewpoint of FEC traffic, the multiple channels appear as a single bottlenecked channel of capacity C. A packet loss incurred by a particular connection results in the creation of slack capacity proportional to the load balancing allocations on each of the channels. The FEC flows increase their transmission rate and eventually fill the slack. The utilization of a channel is determined by the slack size and the number of round-trips required to fill it. The smaller the number of flows incurring losses the smaller is the slack, therefore, to reduce loss synchronization among flows in case FEC isolation is approximated using ingress rate limiters, the associated packet buffers should use the RED packet dropping policy rather than drop-tail [25]. The number of round-trips required to recover the slack is determined by the number of flows in the FEC, thus creating a tradeoff between the channel utilization and the capacity shares of individual flows. Note that by the definition of load balancing, all channels have equal utilization, which is also the utilization of the aggregate channel ρ. Let r be the mean FEC throughput, we have 3 r = ρ C (7) TCP fairness in sharing the aggregate FEC channel implies that the mean rate of the individual FEC flows con- 3 Generally, for any traffic allocation of F, we have r = ρ min pi P F C i φ i 4

5 verges in probability to the TCP fair share σ along the channel. It follows that at steady-state, r σ F (8) From (7) and (8) we gather that at steady-state, σ C ρ F Given load balancing, the network flows converge in probability to the Aequitas equilibrium iff for every FEC F σ = σ = σi (10) p i P F where σ i is the fair share along the path p i P F. In other words, when each FEC F is allocated a channel of capacity C i = σ i /ρ (11) along every path p i P F. Note that this condition is feasible (i.e., for every link, the sum of the capacities of FEC channels crossing the link does not exceed its capacity) if the utilization of the bottleneck link under FEC isolation is equal to that under unrestricted competition for bandwidth a valid approximation since individual FECs are typically composed of a large number of competing flows. IV. AN ILLUSTRATIVE EXAMPLE In this section, we present ns [26] simulation experiments to demonstrate the convergence of network flows to the Aequitas equilibrium under load balancing. The experiments also demonstrate that static traffic allocation may lead to an arbitrarily-inefficient equilibrium. Fig ms 7 trunk 1 trunk 2 2ms trunk Simulated topology. Figure 3 shows the topology used to conduct the experiments. All links are 20 Mb/s with 1ms propagation delay, except as noted in figure. FEC 1 is composed of 20 FTP flows that originate at node 0 and terminate at 5. Its packets are forwarded along trunks 1 and 2. FEC 2 flows are forwarded along trunk 3. Each FTP flow is controlled by TCP NewReno with a receiver window large enough to 5 (9) saturate the ingress egress paths. Connections transmit 1000 byte packets. Links are full-duplex and have RED output queues with default parameter values. To eliminate the effects of false congestion indication due to reordering, at the egress of each FEC, the FEC packets are sorted back into the same order in which they entered the network before being delivered to the receiving applications. In the first set of experiments we compare the Aequitas equilibrium to that achieved through load balancing (denoted with LB). The topology is designed so that the TCPfair share along each trunk is easily calculated and hence the bandwidth allocations under Aequitas. We assume that TCP flows sharing a bottleneck link utilize its bandwidth in full(i.e., the sum of the TCP-fair shares across a bottleneck is equal to its capacity). Measurements across the experiments set indicated that trunks 2 and 3 always saturate link 2 3, thus validating the assumption. Let n 1 = 20 and n 2 denote the number of flows in FEC 1 and FEC 2 respectively. We varied n 2 from 0 to 80 with an increment of 20 flows. For each value of n 2, we repeatedly ran the simulation for a duration of 120 seconds of simulated time until the 95th. percentileconfidence interval of the aggregate throughput of FEC 1 became no greater than 0.5 Mbps. Also for each value of n 2, the TCP-fair share along the traffic trunks and the load-balancing parameters were calculated. Trunks 2 and 3 share the same path, thus the fair capacity share 20 along each is n 1 +n 2 Mb/s. The fair share along trunk 1 is 20 n 1 Mb/s. In figure 4, the ensemble average of throughput of flows in FEC 1 is plotted against the volume of FEC 2 and compared to the theoretical curve (Aequitas) representing the throughput of a FEC 1 flow under the Aequitas equilibrium. The theoretical and experimental curve nearly coincide, indicating that (by TCP fairness among same-fec flows) the throughput of individual flows in FEC 1 converges to their fair shares under Aequitas. Because the bottleneck link (2 3) is always saturated, we can deduce from the above result that FEC 2 flows converge to their bandwidth allocations under Aequitas. Since all network flows converge to their desired bandwidth allocations, we have demonstrated convergence to the Aequitas equilibrium. In this particular example, link 2 3 emulates the effect of FEC isolation. Specifically, each FEC acquires a share of the slack on the only bottleneck (link 2 3) equal to its share under FEC isolation. This is due to two factors: First, the RED buffer at the bottleneck distributes losses between the two FECs in proportion to their throughput; second, since link 2 3 is the only bottleneck in the net- 5

6 work, both FECs are able to acquire their share of the slack generated by either of them. An example where rate limiters are needed can be created by letting FEC 1 share the path along trunk 1 with another FEC. The random losses on trunk 1 would prevent the FEC from acquiring its share of the slack on trunk 2 and vice-versa, unless FEC isolation is enforced so as to allow each FEC to regain the slack it creates in full. The second set of experiments aims at comparing the Aequitas equilibrium to that achieved using static traffic allocation (denoted with STATIC) such as Equal-Cost MultiPath routing (ECMP) or load balancing based on the nominal capacity along ingress egress paths. This set of experiments is a repetition of the above except for splitting the load of FEC 1 equally between trunks 1 and 2 independently from n 2. In Figure 4, the ensemble-average throughput of FEC 1 flows under STATIC at different values of n 2 is compared to the theoretical curve for the corresponding equilibrium. The equilibrium under STATIC can be made arbitrarily inefficient by increasing the volume of FEC 2. The throughput of a FEC 1 flow is at most twice its share on trunk 2, leaving trunk 1 underutilized, and approaching zero as the congestion on link 2 3 increases. Note that under STATIC no traffic isolation is possible since we assume the traffic allocation strategy to be oblivious of the TCP fair-share along the network paths. It is worth noting that in the experiments above, load balancing was implemented using Deficit Round Robin (DRR) [21] at the FEC-level rather than at the TCPconnection level. We conjecture that due to the large number of flows in a FEC, balancing the load of the traffic aggregate approximates connection-load balancing. The convergence under LB in the above example, as well as the experiments in [1], are in support of this conjecture. FEC 1: Flow Throughput (Mb/s) FEC 2 Volume (#flows) Aequitas LB STATIC: Theoretical STATIC: Measured Fig. 4. Convergence to Aequitas. Average FEC 1 flow throughput obtained through simulation for LB and STATIC compared to that obtained analytically from the corresponding equilibria. V. CONCLUSIONS AND FUTURE WORK A multipath network is in the Aequitas equilibrium if every flow acquires a TCP fair share along each of its ingress egress paths. Using the convergence properties of TCP congestion control, we proved that connectionload balancing based on the TCP-fair shares along the candidate paths, together with ingress-egress traffic isolation are sufficient conditions for the network flows to converge to the Aequitas equilibrium. We also showed that TCP-striping based on static traffic allocation may lead significant reduction in throughput. In [1], we reduce the problem of estimating the fair shares to one of computing the weighted max-min allocations, and describe a scalable traffic allocation solution to approximate the Aequitas equilibrium while taking into consideration flows with limited throughput demands (e.g., due to congestion in other domains the flows traverse), and sudden traffic swings. Aequitas can be extended to the case where flows of service differentiation using prioritized packet dropping. This extension requires a model for the fairness among flows of different service classes sharing the same path. REFERENCES [1] Mahmoud Elhaddad, Adaptive traffic allocation in multipath IP/MPLS networks, M.S. thesis, North Carolina State University, [2] J. C. Bennett, C. Partridge, and N. Shectman, Packet reordering is not pathological network behavior, IEEE/ACM Transactions on Networking, vol. 7, no. 6, pp , [3] Ethan Blanton and Mark Allman, On making TCP robust to reordering, Computer Communication Review, vol. 32, no. 1, January [4] S. Floyd, A report on recent developments in TCP, IEEE Communications Magazine, vol. 39, no. 4, pp , [5] H. Adiseshu, G. Parulkar, and G. Varghese, A reliable and scalable striping protocol, in Proc. of the ACM SIGCOMM, 1996, pp [6] S. Floyd and T. Hendersen, The NewReno modification to TCP s Fast Recovery algorithm, Internet RFC 2582, IETF, April [7] Supratik Bhattacharyya, Donald F. Towsley, and James F. Kurose, The loss path multiplicity problem in multicast congestion control, in INFOCOM, 1999, pp [8] D. Bertsekas and R. Gallager, Data Networks, Prentice Hall Inc., 2nd edition, [9] S. Vutukury and J.J. Garcia-Luna-Aceves, A simple approximation to minimum-delay routing, in ACM SIGCOMM, Cambridge, Massachusetts, September 1999, pp [10] S. Vutukury and J.J Garcia-Luna-Aceves, A traffic engineering approach based on minimum-delay routing, in Proceedings of the Ninth International Conference on Computer Communications and Networks, Las Vegas, Nevada, October 2000, pp [11] A. Elwalid, C. Jin, and I. Widjaja, MATE: MPLS Adaptive Traffic Engineering, in Proceedings of IEEE INFOCOM, Anchorage, Alaska, April 6

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