Providing End-to-End Delay Requirements in ... - CiteSeerX

Providing End-to-End Delay Requirements in Heterogeneous Networks using Zone Delay Assignment Chih-Chieh Hsu and Rudra Dutta Electrical and Computer Engineering and Computer Science departements North Carolina State University Raleigh, NC 27695, USA [email protected], [email protected]

Abstract Providing end-to-end delay has been an important issue in Quality of Service enabled networks. If we can assign a call’s end-to-end delay requirement optimally to each node along the route of that call, the whole network can be better utilized. In practice, routers in a network are likely to use different packet scheduling policies. Due to the differences in the scheduling policies, delay bounds one router can provide may be different from another, even if they have the same load. Therefore, using traditional per-node delay assignment methods may result in lower capacity. In this paper, we propose a hierarchical delay distribution method, called Zone Delay Assignment, to distribute the delay requirement first to the “homogeneous zones” that use different scheduling policies, then assign the distributed delay to each node within each zone. We verify using simulation that by applying Zone Delay Assignment, we can achieve better network capacity.

1. Introduction In the emerging broadband packet-switched networks, provision of Quality of Service (QoS) to realtime communication streams has become a key requirement. Applications such as web phones and video conferences typically require QoS guarantees in terms of end-to-end delays. Providing such QoS guarantees usually requires representing and distinguishing between different traffic flows inside the network as well as at the edges, and some form of resource reservation. One of the practical challenges that are likely to engage network engineers for some time into the future is the issue of integrating the control planes required to exercise such control over the network across various jurisdictional networks and autonomous systems. It is now generally acknowledged that while a completely transparent single control plane for the planetary network may be neither practical nor desirable, some measure of control plane cooperation and resource reservation across heterogeneous networks with multiple jurisdictional zones must occur in tomorrow’s global backbone. To support QoS requirements in the form of delay constraints for applications with real-time characteristics, network routers require more sophisticated packet scheduling schemes than simple Fist-In-First Out (FIFO). Many scheduling methods, such as Weighted Round Robin (WRR) [11], Generalized Packet Scheduling (GPS) [13], Packetized GPS or PGPS, also known as Weighted Fair Queueing, (WFQ) [6], and Earliest Deadline First (EDF) [7], are known to be able to provide delay bounds to traffic flows according to their fair shares. In the resource reservation phase of a new arrival of a traffic flow (called a call hereafter), an admission control mechanism is used to check if the sum of minimum delays the P56/1

Destination

Source

AS1 WRR

AS2 EDF

AS3 PGPS

Figure 1. A heterogeneous network.

routers along a possible route can provide is less or equal to the end-to-end delay requirement of the call. If there exists such a route, the new call will be accepted; otherwise it will be blocked, since its end-to-end delay requirement can not be guaranteed. Many publications have focused on providing end-to-end delay bounds by different scheduling mechanisms [12, 9, 10, 1, 14]. However, when a call passes call admission control and is admitted to the network, how to assign a real delay bound to this call along the routing path is comparatively less addressed in literature. If the network assigns the lowest possible delay bound it can possibly provide along the path of the call, the routers along this route will not be able to provide any more incoming calls, since all its remaining scheduling shares will be used up by this new call. While this may provide good QoS to the incoming call, subsequent calls cannot be admitted with any QoS. Moreover, this is also likely to be a waste of resources since the delay bound offered by the network to this call may well be less than the delay required by the application. Therefore, for efficient use of resources, the network has to assign the excess delay to the routers along the route. An intuitive way of assigning the excess delay along the route is to divide the end-to-end delay requirement by number of routers along the determined route. However, since each router along this route may have different outgoing link bandwidths, buffer capacities, as well as different traffic loads at the time of arrival of the new call, assigning equal delay to each router may not be the best policy for the network to support most calls for the future. For example, Figure 2 shows a four-hop route of a new call, where router 2 is relatively heavily loaded with a larger buffer capacity. On the other hand, router 3 is very lightly loaded, but its buffer capacity is small. In this case, if we assign end-to-end delay for the new call equally among the four routers, router 2 may have to spare a large part of its small remaining scheduling weight to guarantee the delay bound, while router 3 has to keep the packets in its buffer long enough so that the packets will not leave too early. This may prevent future calls from being accepted. On the other hand, if we can assign more delay to router 2 and less to router 3, both of them will benefit from the (re-)assignment and will possibly be able to accept more calls in the future if each call’s end-to-end bound can be carefully assigned to each node. From the example above, we can see that if optimal per-node delay assignment is used, the network will be able to support more calls, and thus improve the capacity of the whole network. Several publications have focused on solving this problem. For example, Znati and Melhem [16] construct an optimization problem to solve the optimal solutions for per-node assignment, and Field et al. [8], Chiang et al. [2], and Chu et al. [4, 3, 5] provide different heuristics to get the solution. In these papers, the authors assume same packet scheduling mechanism throughout the network, and find the solution accordingly.

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Heavily loaded Lightly loaded Large Buffer Small Buffer 1

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Figure 3. Typical node model of a network router. Figure 2. An example of delay assignment.

1.1. Our Contribution The assumption of same scheduling policy throughout the network may not always be realistic. In real networks, routers along the route of a call may use different traffic shaping and/or scheduling methods. As an example, Figure 1 shows a network with 3 Autonomous Systems (AS), and each AS has its own scheduling (and possible buffer management and traffic shaping) policy. In general, a route for a new call may be covered by more than one homogeneous zones. In a homogeneous zone, all routers use the same scheduling and traffic shaping policy. Due to the different characteristics of scheduling policies in a heterogeneous network, using those methods designed for homogeneous networks may result in nonoptimal solutions, and thus decrease the capacity of the whole network. Thus, how to design a delay assignment mechanism to take the differences of scheduling policies into account becomes an important issue. In this paper, we propose a hierarchical approach to this problem that we call Zone Delay Assignment. By first distributing the delay to the homogeneous zones, we can consider the different characteristics in routing policies. Then for each zone, the distributed delay for this zone is again assigned to each node by methods that are already known. By considering the nature of different scheduling policies, we will be able to increase the capacity of the whole network. The rest of this paper is organized as follows. In Section 2, a basic node model for delay assignment problems, and relevant prior results on homogeneous networks are introduced. In Section 3, we propose the algorithm of Zone Delay Assignment. In Section 4, model and results of computer simulation are presented. Section 5 concludes the paper.

2. Node model and existing approaches A per-node delay assignment problem can be defined as finding an optimal way to assign a delay to each node along a predefined routing path of a new call, so that in addition to support the end-to-end delay requirement of that new call, the network will be able to support the maximum number of future calls. In this section, we introduce first the basic node model used in per-node delay assignment, then relevant prior work to solve this per-node assignment problem for homogeneous networks.

2.1. Node Model Figure 3 shows a typical node model commonly used in this context in the literature [16, 2, 4, 3, 5, 8]. From the figure, we can see that when a packet of a call arrives at the router, it will first pass and be regulated by a traffic shaper. Such a traffic shaper can be a leaky bucket or token bucket with parameters (σ, ρ), where σ is the size of the bucket, and ρ is the average packet rate. That is, if the number of departure packets from the traffic shaper in time [0, t] is denoted as D(t), we have D(t) ≤ σ + ρt.

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(1)

In a token bucket typed shaper, if the time period for averaging the packet number is n, instead of 1, the shaper is called a Linear Bounded Process (LBP). This can be seen as a generalization of token bucket. The output number of packets up to time t for an LBP with parameters (b, r, n) is at most   t Nj (t) = bj + · nj . (2) rj Other types of traffic shapers, such as moving window, peak rate, and jumping window may also be applied (see [8] and reference therein for details), but are not considered as frequently as (σ, ρ) type scheduler in literature in this area. By using traffic shapers, the number of arriving packets in a time interval will be upper-bounded, and thus the provision of delay bounds becomes possible for scheduling policies. After leaving the traffic shaper, a packet will arrive at the scheduler. Here the packet enters the input queue of the scheduler, and may be assigned a deadline, a priority, or other tags, according to the scheduling mechanisms used in the scheduler. As mentioned in the first section, the scheduler can be WRR, PGPS, EDF, etc, as long as the scheduling method selected can provide delay bound according to the fair share of a call. In general, publications in this area assume that a scheduler more sophisticated than simple FIFO is used. For the traffic shaper, however, a cut-through (no traffic shaper at the node) is possible if the traffic is already shaped or regulated at the source.

2.2. Homogeneous Zones Here we briefly describe, for ease of reference, two prior works of homogeneous per-node delay assignment methods that we will use in the second stage of the Zone Delay Assignment mechanism. 2.2.1

Delay assignment for GPS: an optimization approach

Znati and Melhem [16] proposed an optimization approach to solve the per-node assignment problem. In this approach, GPS scheduling method is assumed for every node. For the traffic shaper, the authors assumed that the traffic of a call is regulated at the source, and the arriving packets of call j to the network arrive in accordance with a LBP with parameter (bj , rj , nj ). From these assumptions, if there are already N such calls in a router i, one can calculate the worst case upper bound and lower bound this router can guarantee to a new call, call N + 1, from the GPS assumption and the buffer size of that router. The lower bound is as follows:  bN+1 +nn+1 +µ  ,t ≤ ∆  P x − nN+1 i rN+1 (3) lN +1,i = bN+1 +nn+1 +µ   x 1 nN+1 , otherwise Pi − ∆ − r

N+1

where t is the delay of the new call, Pix is the current remaining percentage of service capacity of node i, ∆ is the current minimum delay bound the node is providing (among current N calls), and µ = maxj µj,i is the maximum amount of service time required to process a packet from different calls at node i. The upper delay bound is rN +1 x uN +1,i = (B − bN +1 − nN +1 ), (4) nN +1 i where Bix means the excess buffer capacity at node i that can be allocated for call N + 1. Now for each node along the routing path, we have two delay constraints for the new call. Moreover, the end-to-end delay requirement for the new call has to be satisfied. Hence if we have K nodes along P56/4

the routing path, there will be 2K + 1 constraints. The author suggests that the optimal solution will be obtained if we can find δi , i = 1 . . . K such that the relative occupancy along the routing path is balanced. That is, heavily loaded nodes P will be assigned larger per-node delays than lightly loaded nodes. The objective function is then K i=1 (µi /σi ) , and the optimization problem is: PK Find δ1 , . . . , δk such that i=1 (µi /δi ) is minimum, subject to K X

δi ≤ ∆, and

(5)

li ≤ δi ≤ ui .

(6)

i=1

2.2.2

V-net: A heuristic approach for EDF

This method is introduced by Field et al. in [8]. A simpler prior version can also be found at [15]. In this paper, Non-preemptive EDF (NP-EDF) is used as scheduling method in every node in the network, and packets are classified into 4 classes, BT, ET, XT and DT. BT packets are delay-sensitive and have to satisfy delay end-to-end delay bounds. For each node, possible upper and lower delay bounds are calculated. The bounds, in addition to the end-to-end requirement, are still used as constraints to test the feasibility in the problem. However, instead of solving an optimization problem, a heuristic method is provided to approach a balanced resource allocation: l m l m δ δi,k−1 +δi,k mi + ri,k m + n α ni αi i i i ri i (7) = δi,k Bkt where mi , ni , ri are parameters of a LBP typed traffic shaper of call i, α is the ratio of BT packets over (BT+ET) packets, δi,k is the delay of traffic i assigned at node k, and Bkt is the total buffer capacity at node k. Since the upper and lower bounds come from available buffer and available fair share of node k, the idea behind this equation is to balance the fair share and the buffer after the new call arrives. The heuristic is as follows. Calculate ∆max I δi,k = di,k PP k=1 di,k Di,k − di,k−1 − di,k II ), δi,k = di,k + ( 2

(8) (9)

and return I II δi,k = min(δi,k , δi,k )

(10)

where ∆max is end-to-end constraint of the new call, Di,k and di,k are the upper and lower bounds node k can provide to call i, and P is the number of nodes along the route. After the node delay are calculated, they are again mapped back to the node as routing parameters.

3. Zone delay assignment method for heterogeneous networks Consider a generalized heterogeneous network as in Figure 1, with n homogeneous zones. Zone i has ni nodes and uses the same scheduling method for all its routers, but in general the scheduling method is different for different zones. Due to the different nature of scheduling policies, to provide the same delay bound, nodes in different zones may have to allocate a new call different fair shares, even if they have P56/5

When a new call arrives with a route containing routers N1~Nm and end-to-end delay requirement D For (every Ni ) Calculate upper and lower delay bounds end Define homogeneous zone Z1~Zn Calculate the weights wi for zone Zi Do weighted assignment using Zj as nodes D as total delay requirement Get delay Dj for each Zj end If (one or more zone has discrete bounds) Do Discrete reassignment end end For (every Zj ) Do per-node assignment using Nk (Nk belongs to Zj )as nodes Dj as delay requirement Get delay DNk for node Nk Modify parameters in Nk according to DNk end end

Figure 4. Zone delay assignment method.

the same load before the call arrives. For example, if a WFQ node and a WRR node allocate the same fair share to a new call with an shaped traffic with (σ, ρ) constraints, the WRR node will have a worse delay bound, due to the worst case delay of the WRR scheduling method. Hence, to provide the same delay bound, a WRR server must allocate more fair share to the new call than a WFQ server does. Therefore, if we apply per-node assignment methods that assume the same scheduling policy throughout the network to such a heterogeneous network, network servers with “worse” scheduling policy (WRR in this case) are more likely to become bottlenecks, and thus decrease the capacity of the whole network. Hence we have to take the effect of scheduling policies into our consideration when doing per-node assignments. From the viewpoint of optimization problems, we can change the objective function to optimize, so that it reflects different scheduling policies. However, we will not be able to simplify the expression due to different nonlinearity relationships in different scheduling policies; the objective function will become very complicated, and solving it will not consist a practical algorithm. On the other hand, if we see each homogeneous zone as a single node, we can pose a (possibly much) smaller optimization problem to distribute the end-to-end requirement to these n nodes with n different routing policies. After a delay requirement is assigned to a zone, per-node assignment methods in homogeneous networks that are known to perform well can be used to assign the delay to each node in this zone. We call this hierarchical approach “Zone Delay Assignment”, and the algorithm is shown in Figure 4. In the first phase of Zone Delay Assignment, to take the different scheduling methods into P 1 , where δj is the consideration, we use the objective function in homogeneous networks (which is δj delay to be to node j), and assign different weights to each term (so that the objective function P assigned wj becomes ). We can see that if we assign larger weights to worse scheduling methods, they will be δj assigned larger delays, and thus keep the relative occupancy equal after the assignment.

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Now our optimization problem Pn becomes Find δ1 , . . . , δn such that i=1 (wi /δi ) is minimum, subject to n X

δi ≤ ∆, and

(11)

li ≤ δi ≤ ui ,

(12)

i=1

where li and ui are lower and upper delay bound zone i can provide, that is, the sum of bounds of all nodes in zone i.

3.1. Calculation of weights Obviously, the calculation of meaningful weights is the key factor in ensuring good performance for the Zone Delay Assignment method. Since the relationship between the assigned load and the delay bound is nonlinear, we should consider the current state when calculating the weights. In this section, we propose a method for calculating the weights of the objective function for homogeneous zones that use different scheduling mechanisms. The procedure of assigning the weights follows naturally from our previous discussion, and is explained with the help of Figure 5. In the figure we can see a plot of delay bounds versus assigned fair shares for each scheduling policy. The figure illustrates the relative natures of the delay bounds provided by the scheduling disciplines, this is why the delay bounds are not assigned units. For real numerical instances, actual delay bounds can be calculated using formulas derived in [16] for PGPS, and [8] for EDF. For WRR, the worst delay bound is obtained in a straightforward manner as dP GP S + µ1 ( fk − 1), where dP GP S is the discretized version of the bound of PGPS, µ is the maximum service time in the router, f is the total number of packets in a WRR frame, k is the number available for assignment (hence the share is k f ). Note that as expected the delay bound is worse (higher) for lower shares assigned, for any discipline. A router whose outgoing link in the path of the incoming call is already loaded to x fraction of its capacity can at most take on 1 − x more load. Thus both share and resulting increment of load can be plotted along the horizontal axis. To obtain the relative weights for each zone, we simply locate the point on the curve corresponding to the discipline used in that zone that corresponds to 1 − x. The weight to be assigned to this zone is the ratio of the share value given by this point on this curve to the share value on the GPS curve that corresponds to the same delay bound. That is, we first map the load to the delay bound it provides for this discipline, and then check the factor by which this share is large than that necessary to provide the same delay bound for the GPS scheduler. The GPS thus serves as the baseline for comparing share values. Doing this for every zone yields the required set of weights. Figure 5 shows an illustrative example. Assume that the current load for the EDF zone and the WRR zone are both 0.8, so each is capable of only assigning a 0.2 share more. We want to find the weight for each. We can see for a share of 0.2, the EDF scheduler needs about 1.1 times of share to provide the same bound as GPS, while the WRR scheduler needs about 1.66 times. Therefore, the weight for the EDF and WRR zones is 1.1 and 1.66, respectively. In the above, we tacitly assumed that we have a single current load value for each zone. However, the definition of load and share apply directly only to single routers, and a homogeneous zone contains (in general) more than one node. We can treat each router as a homogeneous zone, but this defeats the intent of reducing the problem sizes in the hierarchical approach. As a good approximation, we can also get the current load of a zone by taking the average of the loads of each node in the zone. This makes sense since our goal is to balance the load after each arrival of a new call; thus there should be no node that has an extremely large or small load under the assignment method. This is the approach we take in generating our numerical results in the next section. P56/7

In practice, a further drastic simplification is possible, by assigning a characteristic weight or “figure of merit” to each discipline, regardless of c urrent load or number of nodes. We may have many different zones, each with different number of nodes and loads. To calculate the weight for each node may become a large overhead. This approach will be more efficient in such a case, especially when the calls can be categorized into predetermined classes by path (so that the weights can be calculated in advance). In such an approach, we would simply assign a weight to each discipline by following the above procedure of taking ratios, but integrating it over the entire curve (that is, averaging over delay). We investigate the performance of this approach as well in our numerical simulations.

3.2. Discrete Reassignment After the weight for every homogeneous zone has been calculated, one can solve the optimization problem and get the delay assignment for each zone. Then the second stage of Zone Delay Assignment, that is, assign the delay for each zone to nodes inside the zone using already-known per-node assignment methods, can be done. However, due to the discrete nature of the WRR scheduler, the optimal solution for the problem is likely to lie in between two possible values WRR can provide. Modeling this problem to a mixed integer nonlinear programming is possible, but will be very hard, if not impossible, to solve. Therefore, we propose rounding down the assigned delay to WRR to the nearest possible value, then redistribute the excess delay to other zones that can support continuous delay bounds. That is, if we have a excess delay ∆e , and the assignment to WRR is originally δW RR , we pose another optimization problem. Assume the WRR zone is the nth zone in the P network, the problem is now: Find δ1 , . . . , δn−1 such that i6=n (wi /δi ) is minimum, subject to X

δi ≤ ∆ − δW RR + ∆e , and

(13)

li

(14)

i6=n

≤ δi ≤ ui .

After the reassignment, we can go to the second phase of the Zone Delay Assignment method and assign delay to each node in the zone.

4. Simulation methods and results 4.1. Simulation model In this section, we use computer simulation to evaluate the performance of Zone Delay Assignment. We used Matlab to implement the nonlinear programming core for the Zone Delay Assignment, and Arena for simulation scenario. In this paper, we have adopted a flow level rather than a packet level simulation. That is, once a flow arrives and provides its end-to-end requirement, delay assignment methods calculate the optimal per-node assignment, and update the load and buffer occupancy of each node. Then the next flow arrives, so on so forth. We thus do not verify directly the actual delay suffered by packets in the flows, but since we use upper bounds to calculate the delay, all packets will suffer a delay that is equal to or less than the requirement of its flow. The simulation setup is as the following. There are 20 nodes in tandem and 3 homogeneous zones in the network. The zones apply EDF, WRR, and PGPS, and have 7, 7, 6 nodes, respectively. New calls are individually generated by the simulation. We adopt the incremental traffic model, that is arriving calls do not depart during the period of simulation. Upon an arrival of a new call, the delay requirement is determined following [16], that is by picking a random number uniformly from one of the three intervals P56/8

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Figure 5. Weight Calculation. Figure 6. Simulation results.

[0, 100], [0, 350], or [0, 500] (the three intervals are used randomly with equal probabilities). The source and destination are randomly selected. For the first stage of Zone Delay Assignment, both original and simplified (average) version of weight calculation are used. Discrete reassignment is also considered. For the second stage, the optimal method “Opt” from [16], as described in Section 2, is used for PGPS and WRR zones, and V-net heuristic method from [8] is used for EDF zone. We also use the Opt method for the whole network as a representative for per-node assignment methods using homogeneous assumptions in heterogeneous networks. We stress that this is purely for representative reasons, since the Opt method itself cannot be expected to perform well for heterogeneous networks. 30 instances of random call arrival sequences are generated, each consisting of 5000 call arrivals, and for each sequence the four different assignment methods are independently applied.

4.2. Simulation results Figure 6 shows the average number of accepted calls versus the number of arrivals for different assignment settings. In the figure, Opt stands for the optimization method for homogeneous networks introduced in [16], ZA stands for Zone Delay Assignment, ZAA stands for Zone Delay Assignment using average weight calculation, and ZA-DRA stands for Zone Delay Assignment with discrete redistribution. From the figure, we can see that when the number of arrivals are low, calls are blocked only due to their over-stringent delay requirements. As number of arrivals increases, we can see that the Opt method starts to saturate due to the bottleneck happens at WRR zone. On the other hand, Zone Delay Assignment methods can accept more calls. ZA-DRA method has the largest capacity, but the algorithm is the most complex. ZAA is the simplest, but still performs pretty well. The 95% confidence intervals show that the advantage of using an assignment method that is aware of hetergeneity (such as ours) over a method that is unaware of heterogeneity is real and significant. One surprising observation is that the ZAA method performs almost as well as ZA; we conjecture that this is a consequence of the tandem topology we investigate and in a more general topology with more cross-traffic possibilities a larger difference will be obtained.

5. Conclusions and future works Providing end-to-end delay bounds has become essential in modern networks, as more and more applications require end-to-end real-time response. Assigning end-to-end delay to each node along the routing path can increase the total network capacity. Assignment methods for heterogeneous networks that consists of routers using different scheduling policies is a comparatively new field of research. In this P56/9

paper, we proposed such a method, Zone Delay Assignment, that assigns the delay requirement to the homogeneous zones first, then assigns the delay in each zone using methods that are already known. We took the different nature of scheduling policies into account by introducing a weighted object function in the first stage of Zone Delay Assignment method. Moreover, by discrete redistribution, we avoid wasting excess delay due to the discrete nature of some scheduling policies. From the simulation results, our method outperforms the homogeneous method and thus validates the effectiveness of Zone Delay Assignment method. Our method can be easily extended to other scheduling disciplines. There are several possible extensions to this work, some of which we are working on now. Our approach needs to be tested by simulation at the packet level, over a larger variety of network topologies and homogeneous zones. In real networks, the delay assignments are likely to be calculated distributively in a short time interval when a new call arrives. Our method requires one or more nonlinear programming procedures and thus may have too much overhead. Therefore, a good heuristic method that has nearly optimal solution may be a good goal for future research. Moreover, it is possible that not all of the packets has to follow a strict delay bound in real neteworks. Whether this method can be used in stochastic bounds or not is also an interesting problem.

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