Traffic Engineering of Tunnel-based Networks in the Presence of Heterogeneous Streams Shekhar Srivastava, Appie van de Liefvoort, Deep Medhi Computer Science & Electrical Engineering Department University of Missouri-Kansas City, Kansas City, MO
Abstract— Different multi-media traffic streams can have different traffic characteristics which raises the issue of whether to multiplex (some of) these streams. This issue becomes even more important in traffic engineering of a backbone network when a decision needs to be made on which streams to multiplex when there are constraints on tunneling and capacity along with routing requirements for tunnels. In this paper, we first present a method for determining distortion between two different traffic streams and propose an approximate distortion metric that closely follows distortion. The advantage of the approximate distortion metric is that it can be readily use in traffic engineering of backbone networks in the presence of tunneling and capacity constraints by presenting a distortion-aware optimization formulation. We then present a two phase heuristic approach to solve this problem where in the first phase the problem is decoupled into two subproblems and in the second phase we show how the non-linear problem (for one of the subproblems) can be simplified. We then present numerical results for both small and large networks to show where and how our approach helps in determining when and which streams to multiplex depending on whether the tunneling and/or capacity constraint is dominant; furthermore, by comparing our distortion-aware traffic engineering model with a distortion-ignorant traffic engineering model, we show the effectiveness of our approach. Index Terms— Traffic Engineering, Tunneling constraint, Correlated Traffic, Traffic Distortion, Quadratic/linear integer programming.
I. I NTRODUCTION Traffic at packet level for different applications tends to have different characteristics. This fact has been observed for emerging applications such as video conferencing, peer-to-peer, multimedia applications [2], [6], [9], [25]. Moreover, heterogeneous traffic streams are multiplexed together to share the same server This work is supported in part by NSF grant # CNS-0106640. Corresponding Author: Tel: +1 816 235 2006, e-mail:
[email protected]
or link. When traffic of different characteristics are multiplexed together, traffic distortion occurs which can be significant depending on the characteristics of the streams [15], [27]. Specifically, such impacts can be fairly strong when one or more of them are correlated in nature. Consider now a tunnel-based network such as an MPLS (multi-protocol label switching) network. In order to minimize distortion, a possible approach would be to classify and multiplex appropriate streams into tunnels so that distortion is minimized within a tunnel. That is, “like-minded” streams can avoid (or minimize) distortion if the network has the capability to do so. For this purpose, one can consider an MPLS (multi-protocol label switching) network where multiple label switched path (LSP) tunnels can be set up between source and destination nodes; such tunnels can be used to ensure logical separation between streams in order to avoid distortions. There are multiple different ways to think about how to take advantage of the tunneling idea. On one extreme, a separate tunnel for each possible traffic stream can be set up to avoid any distortion. The difficulty with this approach is that the number tunnels can be prohibitively large; this then impacts packet processing and forwarding at an MPLS router; furthermore, administratively, too many tunnels lead to higher network management cost and difficulty in managing them. On the other extreme, all streams for the same source-destination node pairs can be multiplexed in the same tunnel. Such an allocation will result in streams having considerably high amount of distortion, while administrative overhead on managing tunnels is minimized. In this work, we address the trade-off between distortion and manageability of tunnels in a networked environment. Specifically, we address the following question: given information on the characteristics of individual streams and the number of tunnels that can be supported on each link, can we engineer a network such that
the distortion level and the required number of tunnels are both acceptable? Undoubtedly, given capacity of a network is another constraint to consider. Our approach is motivated by the traffic engineering issue of the tradeoff between distortion and limiting the number of tunnels (and capacity), especially in a backbone network setting. In order to minimize distortion, our approach can be considered as multiplexing each group of “like-minded” streams (details discussed later) into different tunnels. The “like-minded” streams that share the same tunnel are chosen in such a way that the combined distortion in streams is minimal.
B. Related work The literature is rich in regard to queueing analysis of heterogeneous streams to understand traffic distortion; for example, see [11], [22], [29]. However, the second-order per-stream effects of multiplexing using FIFO (first-in-first-out) scheduling are not generally well known. Similarly, network traffic engineering literature is rich; for example, see the recent book [24] and the references therein. At the same time, there is little work that accounts for distortions due to queueing effects in a traffic engineering framework. The work that is closest to our work in concept is by Su and Veciana [28]. They study the problem of routing streams to a given set of allocated VPs between a node pair based on the packet arrival distribution of the streams (considering Gaussian and On-Off models). They concluded that maintaining certain degree of homogeneity in the streams that are sharing a VP is useful. Thus work tries to address the question of whether to mix traffic streams or not. The target of the study was the QoS requirements of the streams. We, however, take a different view point. We consider a network wide approach where we do not have QoS restrictions and we determine the routing/bandwidth allocation of tunnels while honoring the capacity and tunneling restrictions. We have also considered general source models (semi-Markov processes). Moreover, we have developed a combined queueing and optimization technique to ensure a holistic approach. An important question is the determination of first and second order statistics of traffic streams from collected data. Recently, Duffield et. al. [3], [4] have presented mechanisms towards capturing and estimating flow distributions/statistics in a network. For our part, we focus on the fact that given different traffic streams with different characteristics, how do we balance between minimizing distortion, and the limitation on number of tunnels and capacity. Thus, determination of such statistics from measured data is outside the scope of this work. The formulated traffic engineering problem is a discrete quadratic programming problem. While there are solution approaches available for solving such problems [13], [23], we take advantage of the special structure of the objective function and the constraints to arrive at a simplified solution approach. We draw upon on a decoupling heuristic proposed in [21] to decouple the main problem; however, our decoupled subproblems are not related to [21] and are solved exploiting the special structure.
A. Contributions of the Paper We first present a distortion measure that captures distortion suffered by a steam when multiplexed with another stream. This measure is derived using a linear algebraic queueing model [14]. Due to computational difficulty with this measure, we then develop an approximate distortion metric which adequately captures the negative impacts of multiplexing compared to ”exact” approach. It may be noted that this is not the only way to construct a distortion metric. More sophisticated methods can be used to define another metric which more accurately reflects the impact of high variance and long term correlations. However, our approximate distortion metric is readily computable and works well in a traffic engineering framework. Next, using the approximate distortion metric, we construct an optimization formulation which minimizes the distortion suffered by individual streams for different source-destination node pairs. The formulation also incorporates restriction in terms of the maximum number of allowed tunnels for manageability and the capacity on a link. The formulation is general in the sense that it is transparent to the method used to compute the value of distortion metric. The formulation is a nonlinear integer programming problem in nature and has a large number of binary variables and constraints; to solve this formulation, we first decouple the problem into two phases. The first Phase Is solved by relaxing the binary variables. The second phase (non-linear objective function) is first linearized and solved using Lagrangian relaxation and subradient optimization. Using numerical results, we demonstrate the utility of our formulation (”Distortion-Aware Model”) towards allocating streams to tunnels while minimizing the distortion suffered by the individual streams, compared to the case when distortion is not explicitly incorporated (”Distortion-Ignorant Model”). 2
node A to node D traversing through node B and node C where stream and stream are the only streams sharing the tunnel. Upon passing through the tunnel and exiting from the network, they are referred to as and , respectively. Note that streams and are seen by the receiving customer and thus, reflecting the actual behavior observed by the customer. In order to capture the user experience, we consider passing the streams through separate dedicated servers. We assume that the bandwidth/servers are not shared between different tunnels. Such an assumption avoids the coupling between the tunnels and makes the problem tractable; furthermore, this is implementable in a tunnel-based network such as MPLS. Here, we assume that each tunnel is served at a predetermined fixed rate at each node that the tunnel passes through. In addition, we assume that the tunnel is allocated sufficient rate (bandwidth) based on the average arrival rate of the streams allocated to it. We assume that one and only one node amongst the transit nodes is overloaded and distorts the streams at a particular point of time. In other words, the streams pass through undisturbed (in terms of distribution) through all the nodes except one, which causes distortions in the characteristics of the streams. The culprit node could be any one of the intermediary nodes. We assume that the culprit node is operating under heavy load (always has a packet to serve). Based on this assumption, we construct the model presented in Figure 4, where the shared server is operating under heavy load (culprit node). This assumption has practical appeal as tunnels are allocated bandwidth at regular intervals (medium to large time scales) based on the variability in traffic streams. Since traffic distortion has been observed to take place during times of high congestion [17], [18], we are particularly interested in behavior under heavy traffic (i.e., the server is always
busy). We determine distortion as = "!$# &%'( ,
) % + ( * . "!$#
The rest of the paper is organized as follows. In section II, we present the framework used to capture distortions suffered by the streams sharing a tunnel. In section III, we present the formulation as a quadratic integer programming problem. In section IV, we present our solution approach which decouples and decomposes the problem into smaller subproblems. In section V, we present and discuss numerical results, especially the benefit of distortion-aware models compared to distortionignorant models. We summarize in section VI. II. A F RAMEWORK
FOR
C APTURING D ISTORTION
We start with the issue of capturing distortions induced in a traffic stream by other streams when they are multiplexed. Consider two traffic streams ( and ). Here, a traffic stream refers to having a source and a destination where the source generates a packet stream with stationary inter-arrival distribution. All packets of a traffic stream are assumed to follow the same path in the network. The first- and second-order characteristics of a traffic stream are specified by the mean, and either the squared coefficient of variation, , for marginals, or the correlation decay, , or both as the second-order parameter in the construction of the arrival processes. We assume that service times are exponential and waiting packets are served in the order of their arrival. We introduce a measure of mismatch, referred to as distortion, between streams and using the notation
. Mismatch is defined loosely as the extent of distortion in the traffic streams and if they are multiplexed together. For example, when and are Poisson, we would expect , since they would not distort each other, whereas when and have high and correlation, we would expect to be high, since they would distort each other more. Such a Metric Can be used as follows: suppose that we are required to route three streams , and with the same source and destination nodes, and know the pair-wise relation we among streams as . Suppose that we only have two tunnels to route the packets from traffic streams , and . Since is highest ( and have the largest mismatch), we want to route and on different tunnels as shown in Figure 1. Next, we want to decide on which tunnel to route the stream . Since, , we route together with as shown in Figure 2 and is routed by itself on the other tunnel. Such a routing ensures minimal distortion in all the streams , and . Our aim is to quantify distortion experienced by stream and when sharing a tunnel in a networked environment. In Figure 3, we consider a tunnel from
A. Construction of Streams
In order to evaluate the distortions in the streams and after being multiplexed, we take the LAQT (linear algebraic queueing theory) based approach [14] to construct streams and . We first briefly review LAQT definitions and notations; for details, see [14]. A matrix exponential (ME) distribution is defined as a probability distribution whose density can be written as
, -/.10 32547698 -;:=.09
