Dynamic Multithreshold Rate Control Mechanisms
for Supporting ABR Traffic in ATM Networks
Pau C. Ting and Maria C. Yuang,
Member, IEEEAbstract— Existing feedback-based rate control schemes
sup-porting the available bit rate (ABR) service in ATM networks mostly employ a single static buffer threshold at each switching node as the forewarning of congestion. In this paper, we first propose a continuous-based adaptive rate control mechanism, which employs, logically, an infinite number of thresholds. Each node periodically determines the precise permitted rate of im-mediate upstream nodes based on a simple fluid model aimed at satisfying both loss-free and starvation-free criteria. The scheme, as will be shown, achieves high utilization and low (zero) cell-loss probability under highly bursty (deterministic) traffic, but at the expense of a drastic increase in signalling overhead due to frequent adjustment of permitted rates. To reduce overhead, we further propose a so-called stepwise-based rate control mecha-nism adopting a limited number of movable thresholds, referred to as the threshold set. The threshold set shifts up (down) reflecting the increase (decrease) in departure rates. Compared to continuous-based control via simulation, stepwise-based control is shown to be efficient and accurate using a reasonably low number of thresholds. Moreover, we also display simulation results, which demonstrate that the stepwise-based mechanism outperforms existing single-static-threshold-based schemes in terms of cell-loss probability and link utilization.
Index Terms— Available bit rate, binary rate control, cell-loss
probability, feedback-based rate control, fluid model, quality of service.
I. INTRODUCTION
T
HE available bit rate (ABR) [1]–[5] service in ATM networks [6], [7] has been deployed to allow efficient use of available bandwidth without degrading the quality of service (QOS) [6], [7] of admitted traffic. While the QOS of admitted traffic is guaranteed through admission control [8]–[10] and bandwidth allocation [11], [12], the ABR has been realized via the feedback-based rate control [2]–[4], [6], [13]–[28]. Feedback-based rate control deals with the dynamic adjustment of the granted rates of ABR sources as network loads fluctuate in an attempt to minimize the performance degradation of QOS-guaranteed services. Existing rate control mechanisms operate either on an end-to-end [2], [15]–[18], [20], [28]–[30] or hop-by-hop [2], [5], [19], [21]–[27] basis. While both classes of control mechanisms possess individual performance merit, hop-by-hop-based control has been con-sidered to be more promising, due to its speedy reaction to the fluctuation of network loads [22], [23].Manuscript received October 13, 1996; revised February 4, 1997. The authors are with the Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, 30050 Taiwan, R.O.C.
Publisher Item Identifier S 0278-0046(98)00409-2.
Most hop-by-hop-based schemes adopt a static buffer threshold [2], [19], [22], [24]–[27] at each switching node as the forewarning of congestion. In these schemes, a switching node sends feedback messages to its immediate upstream nodes should the buffer occupancy exceed the predetermined threshold. The upstream nodes, in turn, adjust the cell departure rates on either a simple binary rate (i.e., start and stop) [2], [19], [26] or a specified rate [2], [22], [24], [25], [27] basis. Mishra et al. [22], [25] proposed a predictive rate control scheme for determining the permitted rate and illustrated that the buffer occupancy and throughput of a controlled connection converge to a desired operating point. Kawahara et al. [19] developed an analytical model based on binary rate control and showed significant performance improvement in terms of cell-loss probability (CLP) and resource utilization of the congested node, but at the expense of signalling overhead. Ko et al. [24] demonstrated the effectiveness of the proposed predictive control scheme in controlling congestion. Ideda and Suzuki [27] showed the effectiveness of a combination of the adaptive rate control with fast reservation protocol (FRP) in achieving high link utilization, while maintaining low head-of-line blocking probability, particularly on ATM local area networks. Exhibiting various performance credits, these schemes, however, result in improper rate determination due to the employment of one static threshold.
In this paper, we first propose a continuous-based adaptive rate control mechanism which employs, logically, an infinite number of thresholds. Each node periodically determines the precise permitted rate of immediate upstream nodes based on a simple fluid model aiming at satisfying both loss-free and starvation-free criteria. The scheme, as will be shown, achieves high utilization and zero CLP under deterministic traffic and low CLP under highly bursty traffic. The price paid is, however, a drastic increase in signalling overhead due to frequent adjustment of permitted rates. We further propose a so-called stepwise-based rate control mechanism adopting a limited number of movable thresholds, referred to as the threshold set. The threshold set shifts up (down) reflecting the increase (decrease) in departure rates. Compared to continuous-based control via simulation, stepwise-based control is shown to be efficient and accurate using only a reasonably low number of thresholds. Moreover, we also display simulation results which demonstrate that the stepwise-based mechanism outperforms existing single-static-threshold-based schemes in terms of CLP and link utilization.
The remainder of this paper is organized as follows. Sec-tion II presents the architecture of the feedback-based rate 0278–0046/98$10.00 1998 IEEE
Fig. 1. System architecture.
controller and proposes the continuous-based rate control mechanism. Section III then introduces the stepwise-based rate control mechanism. Performance justification and comparisons through simulation results are provided in Section IV. Finally, concluding remarks are given in Section V.
II. SYSTEM ARCHITECTURE
Each switching node on which feedback-based rate control operates consists of a finite buffer and a rate-based controller (RBC), as shown in Fig. 1. In principle, in accordance with the buffer occupancy, the RBC of a switching node at each time unit (described later) determines the updated permitted transfer rate (UPR) for all immediate upstream nodes by sending feedback messages incorporating such rate. This rate then becomes the outbound permitted rate (OPR) of those immediate upstream nodes or the inbound permitted rate (IPR) of this current node throughout the next time unit.
The RBC is composed of a flow estimator, a rate determina-tor, and a rate regulator. At each time unit, the flow estimator predicts the aggregate flow of future incoming traffic based on the previous UPR and the current buffer occupancy. The rate determinator, in turn, determines the new UPR achieving two performance criteria (described later) based on a rate control law. Finally, the rate regulator ensures that the transfer rate never exceeds the granted OPR. In Sections II-A and B, we first introduce the two performance criteria, followed by the description of the design of the rate determinator and the flow estimator.
A. Performance Criteria
Basically, our rate-based control mechanism has been de-signed to achieve two performance criteria, i.e., loss free and starvation free. The loss-free requirement ensures that the buffer of each switching node never overflows. The starvation-free requirement then assures the achievement of a maximum of link utilization at all times. In the following, assumptions and notations used throughout the entire paper are first introduced, followed by the formulation of the two performance criteria.
In the system, the basic time unit for the determination of the UPR is the round-trip delay (assumed to be a constant) between any two adjacent nodes. This time unit is referred to as a superslot. The maximum normalized transfer rate of
node is denoted as The state of each node is
observed and modified upon receiving a feedback message at the beginning of each superslot. Consider a generic scenario [Fig. 2(a)] with sources having an infinite backlog of ABR traffic and a series of switching nodes, each of which (for example, node has a finite buffer of fixed size and serves a set of incoming sources. The data and control flows and variables used are depicted in Fig. 2(b). In the figure, the solid line and dotted line represent the data and feedback control flows, respectively. Let denote the buffer occupancy
of node and the UPR for node computed by node
at the beginning of superslot As shown in the figure,
upon receiving the UPR sent from node at the
beginning of superslot node , in turn, determines the UPR for node according to the current buffer occupancy Now, we are at the stage of formally defining the two performance criteria.
1) Criterion 1—Loss Free: Significantly, the loss-free cri-terion comprises the upper bound of the UPR. Clearly, this criterion for node throughout superslot is satisfied if
and only if the buffer occupancy where
Based on the deterministic fluid model [29], [30], can be expressed as a function of
the IPR and the OPR That is,
(1) Rearranging (1), we get
for (2)
Let denote the upper bound of occurring at
Thus,
(3) 2) Criterion 2—Starvation Free: Essentially, the starva-tion-free criterion forms the lower bound of the UPR. In principle, the starvation-free criterion for a node is satisfied if the buffer of the immediate upstream node remains nonempty at all times. Thus, the criterion directly applies that, considering node at superslot the buffer occupancy
(a)
(b) Fig. 2. A generic scenario. (a) Topology. (b) Data and control flows.
given in (1) should be greater than zero. That is,
for (4)
Rearranging (4), we get
for (5)
Let denote the lower bound of which occurs at
Obviously,
(6) Based on (3) and (6), we obtain the following inequality:
(7) The set of UPR’s satisfying (7) is depicted by the shaded area, referred to as the safe region, in Fig. 3.1 Notice that UPR’s violating the loss-free and starvation-free criteria fall into two other regions, namely, regions I and II, respectively. In Section II-B, we propose a continuous-based rate control mechanism for the determination of the UPR’s within the safe region.
1Notice that functionk
i01(ki01) can be expressed as a function of k01i ,
k
i, andxki, as shown in (3), namely, by a three-dimensional irregular-surface
diagram. By fixingk01i ,ki, andxki as constants, we illustrateki01(ki01 orki01) as a function ofk01i01 by a two-dimensional diagram, as shown in Fig. 3.
Fig. 3. The safe region of the UPRki01:
B. Continuous-Based Rate Control
Fundamentally, the UPR is dependent on the remaining buffer space and the OPR. Thus, at the beginning of superslot
at node the UPR is given as
(8)
where is the total number of multiplexed sources and parameter is the weight factor [22] with respect to the remaining buffer space. In particular, represents a fully linear relationship between the remaining buffer space and the UPR, whereas corresponds to an independent relation-ship instead. Basically, controls the rate of convergence to the buffer size in an attempt to achieve high link utilization. Notice that one can easily prove that the UPR at the beginning of any superslot would fall into the safe region if
Now, to compute in (8), we have to first obtain and Unfortunately, node has no knowledge of and at the beginning of superslot Therefore, the approximation
of denoted as is reexpressed from (8) as
(9)
where and are the predicted and
respec-tively.
Based on the deterministic fluid model, is simply evaluated as
(10) As for we first make the following observation. Suppose node located at hops upstream from the first node experiencing congestion, called the bottleneck. The bottleneck is supposed to send the throttle message at the beginning of superslot It is worth noting that node has transferred data by its maximum allowed transfer rate until receiving this throttle message at superslot Node , in turn, reduces its transfer rate in accordance with the transfer rate
of the bottleneck equally shared by upstream
nodes. Thus, can be estimated from its current OPR and the transfer rate of the bottleneck, excluding the consideration of factor With taken into account, is computed as
if
otherwise.
(11)
Replacing and by (10) and (11), respectively, in (9) becomes
(12) where
In Theorem 1, we state and prove that the rate control mechanism governed by (12) truly guarantees the loss-free criterion. Throughout the proof, we assume that there exists one bottleneck in the network. This bottleneck (for example, node possesses a transfer rate of and starts transmitting the throttle message at the beginning of superslot We now
observe node namely, hops upstream
from the bottleneck. It is worth noting that node is loss free prior to superslot i.e., before having received the throttle message.
Theorem 1: The buffer occupancy and UPR predicted based on (10) and (12) are conservative by nature. That is, considering node at the beginning of superslot
and (13)
Fig. 4. Sets of movable thresholds and UPR’s at nodei:
That is to say, the rate control mechanism governed by (12) satisfies the loss-free criterion.
Proof: See the Appendix.
III. STEPWISE-BASED RATE CONTROL
The continuous-based rate control mechanism proposed above performs rapid readjustment of UPR’s on a superslot basis. Consequently, frequent computation and adjustment of UPR’s results in a drastic increase in signaling overhead. To reduce the overhead, we introduce the notion of multiple movable thresholds and propose a stepwise-based rate control mechanism.
A. Basic Concept
In stepwise-based rate control, each node, for example,
node assigns a set of evenly distributed UPR’s,
namely, to respective
partitions of the buffer space, delimited by a set of movable thresholds. Basically, the threshold set is altered should the granted OPR or IPR be modified. Upon receiving the signalling of the reduction (increase) of the OPR, the threshold set shifts down (up) reflecting more (less) stringent constraint on the departure rate. On the other hand, as the granted IPR is reduced (increased), the threshold set shifts up (down) reflecting more (less) stringent constraints on the arrival rate. Fig. 4 depicts the threshold sets and legitimate UPR’s with respect to the alteration of the granted OPR and/or IPR at node
As shown at the right side of Fig. 4, the legitimate UPR set shifts up as the OPR declines and/or the IPR rises due to the reduction of prositive thresholds. On the other hand, the legitimate UPR set shifts down as the OPR increases and/or the IPR declines, as shown at the left side of Fig. 4. Accordingly, at the beginning of each superslot, a new UPR is reassigned and notified to immediate upstream nodes only when the current buffer occupancy is altered to a different partition (this may occur when either the buffer occupancy or the threshold set is changed). Thus, if the buffer occupancy settles in the same partition, the granted UPR remains the same, resulting in the elimination of transferring feedback messages and, thus, the reduction in signalling overhead.
Two problems have been considered in the design of the stepwise-based rate control. The first problem is the deter-mination of the most advantageous number of partitions subject to the round-trip delay and traffic characteristics. Apparently, the step-wise based mechanism using an infinitely large is logically identical to the continuous-based mecha-nism, whereas the mechanism using becomes a simple start–stop rate control mechanism. The impact of various ’s on the system performance will be evaluated in Section IV. The second problem is the computation of dynamic threshold sets, which is discussed next in great detail.
B. Determination of Threshold Sets
Let denote the UPR computed by node at the
beginning of superslot Assume that falls into the range
of That is,
where (14)
Replacing by the right-hand side of (12) and then rearranging the inequality, we obtain
(15)
(16) The expression at the right-hand side of inequality (15) is designated as defined as the th threshold of node during superslot Similarly, the expression at the right-hand side of inequality (16) is denoted as That is,
(17)
where is the fixed increment
be-tween two adjacent thresholds, referred to as the interthreshold width. Equation (17) is hereinafter referred to as the threshold-setting function. Notice that node initially sets as Clearly, since each threshold value is a function of the previous UPR and the current OPR the number of possible threshold sets generated by the threshold-setting function is bounded by
In addition, the threshold-setting function is monotonically nondecreasing with respect to the OPR and monotonically nonincreasing with respect to the IPR.
Fig. 5. Stepwise-based rate control algorithm.
Upon determining the threshold set, the UPR can af-terward be assigned according to the current buffer occupancy. As a result, if if where if (18)
as shown by the initial case in Fig. 4. As
the OPR increases and/or IPR decreases until is
satisfied
if if
and
(19) as shown at the left part of Fig. 4. On the other hand, as
the OPR decreases and/or IPR increases until is
satisfied
if and if
(20) as shown at the right side of Fig. 4. The stepwise-based rate control algorithm based on the above dynamic thresholds is formally presented in Fig. 5. Finally, in the following theorem, we prove that the stepwise-based rate control mechanism satisfies the loss-free criterion.
Theorem 2: Given the threshold-setting function, the UPR determined from (19) and (20) is more conservative than the UPR computed from (12). That is, considering node at the beginning of superslot
Fig. 6. Configuration for simulation.
(a)
(b)
Fig. 7. Performance of continuous-based rate control. (a) CLP. (b) System throughput.
That is to say, the stepwise-based rate control mechanism satisfies the loss-free criterion.
Proof: Notice that rate determined based on continuous-based rate control must fall between the two bounds in the inequality in (14). Moreover, from (18), is taken as a low bound of legitimate UPR’s. Thus,
holds for Hence, the more conservative stepwise-based rate control indeed satisfies the loss-free criterion.
IV. EXPERIMENTAL RESULTS
We first examine the effectiveness of our continuous and stepwise-based rate control under both deterministic fluid flow and realistic bursty traffic via simulation. Next, for the stepwise-based mechanism, we further investigate the
(a)
(b)
Fig. 8. Performance of stepwise-based rate control. (a) CLP. (b) System throughput.
impact of the number of partitions, weight factor, and traffic burstiness, on three performance metrics, namely, CLP, system throughput, and signalling overhead. System throughput is defined as the ratio of the total number of successfully trans-mitted cells to the total number of generated cells. Signalling overhead is quantized as the ratio of the total number of feed-back messages generated using stepwise-based control to those using continuous-based control. Finally, we draw performance comparisons with respect to the three aforementioned metrics between the stepwise-based mechanism using one movable dynamic threshold and the existing binary rate control scheme [19], referred to as BRC, using one static threshold.
In simulation, any bursty traffic was modeled by an inter-rupted Bernoulli process (IBP) [31]. Such arrival process can be characterized in terms of mean burst length mean silence length peak arrival rate and the burstiness Accordingly, for an IBP arrival, the mean arrival rate
and burstiness are given by and
respectively. The network configuration used in simulation is depicted in Fig. 6. In the experimented network, each switching node was assumed to possess a finite buffer of 200 cells and a maximum transfer rate of 1 cell/slot. Traffic from different sources was assumed to be homogeneous, and each has an infinite backlog of traffic. In addition, the total offered load, defined as the sum of the mean arrival rate from each source, is set as unity, designating the heavy traffic condition of the network.
(a) (b)
(c)
Fig. 9. Performance comparisons between continuous-based and stepwise-based control. (a) CLP. (b) Utilization. (c) Signalling overhead.
Fig. 7 illustrates CLP and system throughput under various burst lengths, based on continuous-based rate control adopt-ing a weight factor of 0.35. The figure shows that, under deterministic traffic, loss-free transmissions and a system throughput of unity can be achieved, as was justified by the analysis. Under bursty traffic, on the other hand, the mechanism yields nonzero CLP and system throughput of less than one. In particular, the higher the burstiness, the greater the CLP and the smaller the system throughput. This is because an increase in traffic burstiness results in a decrease in statistical multiplexing gain [7]. Moreover, smaller ’s yield better CLP and system throughput due to faster adjustment of UPR’s.
Fig. 8 demonstrates the impact of round-trip delay on the performance of stepwise-based control under various mean burst lengths. In simulation, was altered in correspondence with the round-trip delay yielding the ratio of to , a constant. The rationale behind this is that the conservativeness or aggressiveness of the control mechanism is dependent on the dual consideration of and namely, in this case. The figure exhibits that simulation results for the deterministic traffic justify the correctness of the above analysis. Moreover, traffic with greater mean burst length yields deteriorate per-formance. More significantly, compared to the performance of continuous-based control, stepwise-based rate control, having been proved to be more conservative, results in better CLP, but poorer system throughput.
Fig. 9 draws performance comparisons between continuous-based and stepwise-continuous-based control for a variety of partitions under various weight factors. The results show that the increase of the weight factor results in profound improvement in link utilization, however, at the expense of degradation in CLP and signalling overhead. This result can be justified as follows. Notice that the weight factor designates the significance of the buffer occupancy to the determination of the UPR. Consequently, higher yields more aggressive UPR and, in turn, results in higher link utilization and poorer CLP due to frequent fluctuation of the buffer occupancy. It is worth noticing that stepwise-based control performs compatibly to continuous-based control as increases, resulting in better link utilization, but poorer CLP and signalling overhead.
Finally, we draw performance comparisons, via simulation, between our stepwise-based control mechanism using single dynamic threshold and the existing static-threshold BRC. In simulation, we employed a simpler network, with sources and removed from the network shown in Fig. 6. In the simulation of BRC, the static threshold at each buffer
was set as (the number of multiplexed
sources In the simulation of our mechanism, we set the
interthreshold width as 40, namely, Simulation
results are depicted in Fig. 10. As shown in Fig. 10(a) and (b), BRC imposes higher CLP due to its deficiency in the adaptabil-ity to the throttled departure rate. As a result, the node which is located upstream from the congested node suffers from high
(a) (b)
(c)
Fig. 10. Performance comparisons between static-based and dynamic-based control. (a) CLP. (B) System throughput. (c) Signalling overhead.
cell loss. By contrast, our dynamic-threshold-based control achieves much reduced CLP, however, with the price of greater signalling overhead being paid, as shown in Fig. 10(c). Moreover, Fig. 10(b) exhibits that our mechanism achieves higher system throughput than BRC.
V. CONCLUSIONS
In this paper, we first proposed a continuous-based adap-tive rate control mechanism logically employing an infinite number of thresholds. Each node periodically determines the precise UPR of immediate upstream nodes based on a simple fluid model aiming to satisfy both loss-free and starvation-free criteria. The scheme, as has been shown, achieves high utilization and low CLP under even highly bursty traffic. We further proposed the stepwise-based rate control mechanism, adopting a limited number of movable thresholds. Simulation results justified the performance compatability of stepwise-based control to continuous-stepwise-based control with signalling overhead much reduced. Moreover, simulation results also demonstrated the superiority of the stepwise-based mechanism over the existing single-static-threshold-based scheme in terms of cell loss probability and link utilization at the expense of tolerable signalling overhead.
APPENDIX PROOF OF THEOREM 1
It is worth reminding that node transfers data by until receiving the throttle message at the beginning of
the th superslot. Let the actual aggregate arriving rate
of node at time be denoted as Thus, for
and
(22) After the th superslot, the node employs a transfer rate
of That is, for and
(23) Equations (22) and (23) yield
(24) Consider the bottleneck first, i.e., By directly applying the result of (24) to (8) and expanding based on (10), we get
(25) Now, consider one node upstream from the bottleneck, i.e.,
(25), we obtain the following result:
(26) Therefore, we get
(27)
As for at node we have
as given in (11). Hence, (27) holds for Subsequently, we directly apply this result and (24) to (8) and replace by (10). That is,
(28) By the same token, we have
and
for (29)
Combining (25), (28), and (29), the permitted rate inequality in (13) is directly derived.
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Pau C. Ting was born in Tai-Tong, Taiwan, R.O.C.,
in 1967. He received the B.S. and M.S. degrees in computer science and information engineering in 1993 and 1994, respectively, from the National Chiao Tung University, Hsinchu, Taiwan, R.O.C., where he is currently working toward the Ph.D. degree.
His current research interests include congestion control and bandwidth management in high-speed networks and performance modeling and analysis.
