On-Demand Provisioning of Data-Aggregation ... - Semantic Scholar

On-Demand Provisioning of Data-Aggregation Requests over WDM Mesh Networks Dragos Andrei, Massimo Tornatore, Dipak Ghosal, Charles U. Martel, and Biswanath Mukherjee University of California, Davis, CA 95616 Email: {andrei, tornator, ghosal, martel, mukherje}@cs.ucdavis.edu Abstract—Many large-scale scientific applications need to aggregate large amounts of data from multiple distributed sites to a centralized facility. We call such a request as a Data-Aggregation Request (DAR). In this study, we investigate the novel problem of on-demand DAR provisioning over a wavelength-division multiplexing (WDM) backbone network. We provide a mathematical formulation for our problem as a Mixed Integer Linear Program (MILP). To solve large versions of our problem, we propose a DAR provisioning heuristic (called DARP). We use the MILP with various objectives as a benchmark for studying the performance of DARP. Index Terms—Data aggregation, large-scale data transfer, scientific computing application, WDM mesh network, bandwidthon-demand, grooming.

I. I NTRODUCTION WDM optical networks have large transmission and switching capacity, and can support bandwidth-hungry applications. Large-scale scientific computing applications such as OptIPuter [1], or Large Hadron Collider (LHC) experiments at CERN [2] commonly require the transfer of huge amounts of data from remote experimental sites to a central location, which needs to use/process/visualize this data (which may be needed on-demand). These requirements can be addressed by WDM networks with agile control plane. Practical examples are lambda grids, which are deployed to support large-scale distributed applications, such as National LambdaRail [3], DOE’s UltraScience Net [4], etc. One instance of these data-aggregation applications is called Data-Aggregation Request (DAR). A DAR is a whole session of multiple file transfers with a single destination (e.g., a supercomputer), which needs to aggregate data from multiple distributed data sources. A DAR has a reverse treelike structure, with the nodes that initially possess the files being the “leaves” and the aggregating supercomputer being the “root”. We consider dynamically provisioning DARs. Multiple DARs generate trees that may share the same physical links. Even inside the same wavelength, sub-wavelength granularity requests have to be aggregated (also known as traffic grooming). Moreover, all the file transfers in a DAR can be scheduled at any time between the DAR arrival instant and a maximal waiting time, set by the supercomputer. Some work has been done to study the static version of the problem. The work in [5] considers a single DAR (in a static traffic model), under the limiting assumption of a 

This work is supported in part by NSF Grant No. CNS-06-27081.

single wavelength per link and with connections requesting the same bandwidth. In the literature, there are several works which allow requests to have flexible starting times; but, to the best of our knowledge, they do not address the DAR provisioning problem. An example is the sliding scheduled traffic model proposed in [6]. The work in [7] devises a mathematical solution for scheduling lightpaths under a sliding traffic; however, it does not consider traffic grooming and is designed for a static environment. The work in [8] studies a bandwidth scheduling approach that computes all the available time intervals between a source and destination. An approach for provisioning a dynamic sliding scheduled request is studied in [9]. The works in [8], [9] do not consider multi-channel (wavelength) networks. In [10], it is shown that considering requests’ holding times can improve the performance of dynamic traffic grooming. In this work, we study the problem of DAR provisioning in a dynamic traffic environment. We consider a realistic setting with grid sites interconnected by a high-speed WDM network (we also term such a network as a lambda grid). We formulate our problem as a MILP and design a heuristic approach (DARP ) to solve it. We also compare DARP ’s solutions with those obtained by the MILP using different objectives. The rest of the paper is organized as follows. Section II presents our problem, Section III states it as a MILP, and Section IV presents heuristic approaches. Section V discusses illustrative examples, and Section VI concludes the study. II. P ROBLEM D ESCRIPTION We are given a WDM network (lambda grid), represented by graph G(V, E), with V = set of nodes, E = set of links. Each link has W wavelengths of capacity C (e.g., C=10 Gbps). A grid node is connected to the network through an opaque Optical Cross-Connect (OXC). The grid node consists of a Multi-Service Provisioning Platform (MSPP), which connects end-hosts to the network. End-hosts may be computers (part of computer clusters) or storage devices (e.g., Storage Area Networks (SANs)); they contain files that may be needed by a supercomputer located at a remote grid node. The rates of the network interface cards (NICs) for these end-hosts may be heterogeneous (e.g., 1/10 Gbps Ethernet (GbE) interfaces, 1/2/4/8 Gbps Fibre Channel (FC) interfaces, etc.) We consider a dynamic environment, in which we need to provision DARs on-demand. Let d be the destination, which aggregates data from multiple sources. Let M be the

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set of source files: each source file m ∈ M has size Fm , and is located on an end-host of the grid node sm . The NIC speed of the end-host (i.e., Rm Gbps) determines the transfer rate for the file. Note that heterogeneous transfer rates generate connections with different sub-lambda granularities, hence traffic grooming is needed. File-transfer holding time Fm . The DAR arrives at time S and (Hm ) is given by Hm = R m all its file transfers must be served before a deadline D [11]. Our solution approaches have to provision DARs (compute routes, assign wavelengths, groom, and schedule each of the DAR’s files), while maximizing available bandwidth. An efficient solution for our problem has to jointly address two conflicting objectives. On one hand, we want to retain maximum resources unused to accommodate future traffic. On the other hand, the DAR service time (difference between the last finish time of DAR’s file transfers and DAR’s arrival time) has to also be minimized, since the aggregating supercomputer may need all files before continuing its computation. A good balance between service time and maximizing available bandwidth is what we look for. III. M ATHEMATICAL M ODEL To better understand our DAR provisioning problem, we present its mathematical formulation. Our problem works in a dynamic environment; hence the formulation considers current network state to optimize provisioning of an incoming DAR. The work in [5] proves a simplified version of our problem (provisioning of one DAR in a static environment, with single wavelength per link and no grooming) to be NP-complete; hence the offline instance of our problem is also NP-complete. We state our problem as a MILP optimization below. Given: 1) DAR R, defined by tuple R = (M, d, S, D). File m’s transfer rate Rm ∈ {1, ..., G}, where 1 represents smallest bandwidth granularity and G corresponds to line rate (e.g., if line rate is 10 Gbps and G = 10, smallest granularity is 1 Gbps). Note that wavelength capacity can be divided into G sublambdas, each of capacity LineRate/G. 2) Current network state (background traffic on each channel): a) The utilization of each wavelength w on link ij (during the period [S, D]) is divided into a set of Nij,w timeq q , Eij,w ] (Begin/End times), with q = intervals [Bij,w 1, ..., Nij,w , each having the remaining free capacity q q q ∈ {0, 1, ..., G}. Intervals [Bij,w , Eij,w ] have the Cij,w Nij,w q q properties that: (i) q=1 [Bij,w , Eij,w ] = ∅ and (ii) Nij,w q q q=1 [Bij,w , Eij,w ] = [S, D]. b) The background traffic utilization of wavelength-link (ij, w), captured during the time-window [S, D], is represented by binary input BUij,w . It is 1 if (ij, w) is used by background traffic; 0, otherwise. 3) For each file m ∈ M , we pre-compute the K-Shortest Paths [12], using a congestion-aware cost assignment (see Sec. IV). For each file m, the links of k-th alternate path (k = 1, ..., K) are described by the binary variables Pijm,k (=1, if the k-th path of file m uses link ij; 0, otherwise).

Variables: 1) Route chosen by each file m is described by pm,k (=1, if m is routed on path k, with k = 1, ..., K; 0, otherwise). m ∀ m ∀ ij ∈ E, 2) Virtual connectivity binary variables Vij,w,g ∀ w ∈ W , ∀ g ∈ {1, ..., G}, are assigned 1 if m is routed through wavelength-link (ij, w), using granularity g. 3) Sm , ∀ m ∈ M shows the start time to transfer file m. 4) Integer variables Lw ij represent the number of sublambdas used (by all files) on wavelength-link (ij, w). Its values may range from 0 to G. w show the usage of wavelength-link 5) Binary variables LUij (ij, w) by the to-be-provisioned (DAR’s) traffic (=1, if the link is used by any of DAR’s files; 0, otherwise). w shows if wavelength-link (ij, w) is used by either: (i) 6) Uij the new (DAR’s) traffic, or (ii) by background traffic. Constraints: For simplicity, we utilize logical constraints (e.g., disjunctions, implications, maximizations, etc) in our mathematical model. They can be easily linearized by introducing auxiliary variables. Also, some commercial MILP solvers (e.g., CPLEX [13]) allow specification of logical constraints in their models. 1) Routing, wavelength and sublambda capacity assignment: K  pm,k = 1, ∀ m ∈ M (1)  G

k=1 m Vij,w,g



= Rm



 G

g=1

m Vij,w,g

 =0

g=1

∀ m ∈ M, ∀ ij ∈ E, ∀ w ∈ W |W | G  

m Vij,w,g = Rm

w=1 g=1

K 

Pijm,k · pm,k , ∀m, ∀ij

(2) (3)

k=1

Equation (1) states that only a single path must be chosen to route a file m. Equation (2) denotes that file m is either: (i) routed on wavelength-link (ij, w) with all its bandwidth (Rm ), or (ii) it is not routed on (ij, w). Equation (3) establishes the relation between variables V and p. Its left term is the number of sublambdas used by file m on link ij; its right term checks if link ij is used by m (depending on path variable p), and multiplies with the sublambdas required by file m (Rm ). 2) Time-interval assignment:  S m1

S ≤ S m ≤ D − Hm , ∀ m ∈ M   Sm2 ≥ Sm1 + Hm1 ≥ S m 2 + Hm 2   m1 m2 ≤ 1 , ∀ ij, ∀ w, ∀ g Vij,w,g + Vij,w,g

(4)

∀ m1 , m2 ∈ M, m1 = m2

(5)

Equation (4) constrains the start/end times to be in timewindow [S, D]. Equation (5) states that any two distinct files m1 , m2 either have non-intersecting time-schedules (first line of the equation), or they do not share any physical resources (same link, wavelength, and granularity). 3) Background traffic constraints:

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  q q Sm + Hm ≥ Bij,w Sm ≤ Bij,w     q q Sm > Bij,w Sm ≤ Eij,w =⇒

G 

m Vij,w,g =0

q g=Cij,w +1

∀ m ∈ M, ∀ ij ∈ E, ∀ w ∈ W, ∀ q = 1, ..., N Iij,w

(6)

In Eqn. (6), we consider the network’s existing traffic. For each file m and wavelength-link (ij, w), we check each of the q q Nij,w time-intervals [Bij,w , Eij,w ] . If the scheduling interval of file m ([Sm , Sm +Hm ]) intersects in time with a timeq q interval [Bij,w , Eij,w ] , then the already utilized sublambdas cannot be used to route file m. Figure 1 exemplifies all these possible cases of intersection with a background-traffic timeinterval. In Fig. 1, Scenario A, respectively Scenario B, are captured in the first, respectively second line of Eqn. (6).

we also jointly consider more criteria for our multidimensional problem, evaluating the two approaches: WAVE + ·WAIT and LOADB + ·WAVE (with  a small fractional parameter). The objective in the first term of the sums has priority, but the second objective is also jointly considered in the optimization. Because of the high computational complexity of MILP approaches, we next propose heuristic approaches.

Fig. 1. Possible scenarios for file-transfer time-intervals ([Sm , Sm + Hm ]), q q which overlap in time with a background-traffic time-interval [Bij,w , Eij,w ].

IV. H EURISTIC P ROVISIONING A PPROACHES 4) Other constraints: |M |

Lw ij =



G 

m Vij,w,g ∀ ij ∈ E, ∀ w ∈ W

(7)

m=1 g=1 w Lw ij ≥ 1 =⇒ LUij = 1, w Lw ij = 0 =⇒ LUij = 0, 

 w LUij (BUij,w = 0)    w LUij (BUij,w = 1)

∀ ij ∈ E, ∀ ∀ ij ∈ E, ∀ =0 =⇒ =1 =⇒

w∈W w∈W

(8)

w Uij =0 w Uij =1

∀ ij ∈ E, ∀ w ∈ W

(9)

Equation (7) computes the number of sublambdas used on wavelength-link (ij, w), during entire [S, D]. Equations (8) compute the link-utilization variables (LU ) from L. Variables U in Eqns. (9) state if (ij, w) is used by existing or new traffic. Objectives Investigated: 1) Minimize DAR’s service time (objective called WAIT): M inimize (M ax(Sm + Hm )) , ∀ m ∈ M

(10)

2) Minimize total number of wavelength-links needed to provision the current DAR (objective called WAVE): |W |   w LUij (11) M inimize ij∈E w=1

3) Minimize the largest number of wavelengths utilized (by both existing and new traffic) on all links, to promote loadbalancing and grooming (objective called LOADB): |W |  w Uij ), ∀ ij ∈ E (12) M inimize (M ax w=1

Each objective in Eqns. (10)-(12) separately optimizes only one dimension of our problem (which includes four dimensions: routing, wavelength, time and grooming assignment), so they may not necessarily find global optimum. Consequently,

In this section, we devise heuristic approaches for provisioning DARs in a WDM network equipped with opaque switches (i.e., each node has wavelength-conversion capabilities). We need to find routing, grooming, and wavelength assignment (WA), and also schedule the start time of a DAR. Our DAR provisioning algorithm uses the approach in [9] and [8] for finding the optimum path time-scheduling in onechannel networks, which we extend to accommodate WDM wavelength-convertible networks. Note that this integrated wavelength/time assignment problem is much easier in a onewavelength system as in [8], [9], [5], where, in order to find all possible scheduling intervals, it is sufficient to compute the intersections between all the intervals along the links of a path P . On the contrary, in a wavelength-convertible network with W wavelengths, for each h-hop path P , there are W h possible wavelength assignments (not considering grooming). Our purpose is to find a computational-effective DAR provisioning method in WDM wavelength-convertible networks. Since a Bellman-Ford approach used in [8], [9] would require retaining a huge number of intervals, we use the more lightweight approach of enumerating K shortest alternate paths [12]. Our provisioning algorithm is called DARP (for a detailed description of DARP please refer to [14]). Below we describe the main features of DARP . DARP Algorithm - Description. For an incoming DAR, we first compute average wavelength utilization during period [S, D], and use it in the metric for DARP ’s routing (described in the next subsection). We then sort DAR’s file transfers m ∈ M in the descending order of one of the metrics: rate (Rm ), holding time (Hm ) or distance (sm , d), so that the more demanding file transfers are provisioned first. Next, for each file m, we generate the K Shortest Paths (KSP ) (i.e., Pkm , k=1,...,K). For each path Pkm , we perform an integrated scheduling, WA and grooming by computing the intersections of the wavelength-link utilization time intervals from path Pkm ’s links (as described below). We will schedule

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V. P ERFORMANCE A NALYSIS We study the performance of our algorithms on the 24node topology in Fig. 2. Each link has 16 wavelengths, each of capacity 10 Gbps. DAR arrivals are independent, with destination d chosen uniformly between five grid nodes with supercomputers (e.g., Chicago, San Diego, Oak Ridge, Pittsburgh, Seattle). Number of files for each DAR are uniformly distributed between 1-23. File sizes are uniformly distributed between 5-25 GB. End-hosts are: (i) computers (with NIC distribution of: 60% - 1GbE, 20% - two 1GbE, and 20% 10GbE) and (ii) SANs (with FC interfaces distributed between

the rates used in practice of 1/2/4/8 Gbps). The maximum transfer time of the m files (M axm∈M (Hm )) is also the lower bound on the DAR’s waiting time (denoted as LB). DAR’s deadline D may be considered as α · M axm∈M (Hm ). Simulation results are averaged over five runs with different random seeds, each of 6,000 DARs (equivalent to 72,000 file transfers). Number of KSP s considered is K=3 (if not specified otherwise). Se 19

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Fig. 2. A 24-node US nationwide topology. Fig. 3.

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Figure 4 shows unprovisioned bandwidth for the different DAR provisioning methods. DARP , by using congestion awareness, can outperform U N IF and achieves even more significant performance improvement over F F (e.g., more than 3 times for an arrival rate of 75 DARs/min) and RAN D. 0.4 Fraction of Unprovisioned Bandwidth

file m during the earliest interval found for the K paths (if a scheduling interval is found). We consider two types of time intervals: (i) wavelength-link m ), for wavelength-link (ij, w), utilization time intervals (Tij,w which are maximal intervals that can accommodate file m (i.e., longer or equal than Hm and with enough capacity for file q q m are computed from [Bij,w , Eij,w ]) (see Sec. III) and m); Tij,w m (ii) intersection intervals Ik [i] computed at each node i of a given path. Consider a KSP Pkm : for each link ij ∈ Pkm , we compute all the Ikm [j] intersection intervals at node j by intersecting intervals at node i (Ikm [i]) with the utilization m ). Each interval intervals of all wavelengths w of link ij (Tij,w m Ik [j] has to keep track of the wavelengths assigned on the previous links of Pkm . In order to keep the number of intersection intervals from growing exponentially, on any link ij we prune the smaller intervals which are included in other (larger) intervals (found on different wavelengths). Only maximal time intervals on all wavelengths on ij are kept. Routing. We consider two approaches. First, U N IF assigns uniform unity cost to each link. DARP uses a congestion-aware policy, which considers network state. Use of a congested link (a link with many used wavelengths out of W ) should be avoided, as the network connectivity can be affected if, e.g., a link’s wavelengths are all fully utilized. For an incoming DAR, we compute λ, the average number of wavelengths used during period [S, D], for each link. The link metric is βW1−λ , where β is a parameter > 1.0, so that weights of highly-congested links are not too large compared to lesscongested links. Also, to save wavelengths on congested links (and pack requests densely on used wavelengths), we discourage utilization of wavelengths with higher indices, using them only when the DAR would be blocked otherwise. Other Wavelength-Assignment Policies. To study the performance of WA in DARP , we consider two benchmark approaches. The first one is named RAN D: for each link ij on path Pkm , we assign the wavelength randomly, and do the intersection with the intervals at node i (by considering all time-intervals on that wavelength). If a suitable time-interval (larger than Hm ) is found, we continue; else we break and try the next KSP . The second approach is F F (First Fit), which chooses (on each link ij) the first wavelength which allows us to find feasible intersection intervals. If no interval is found, we try the next KSP . These approaches require less computation, but are less likely to find a usable path.

RAND FF UNIF DARP

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 55

Fig. 4.

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Unprovisioned Bandwidth for DAR provisioning approaches.

Figure 5 shows average DAR waiting time (W T ). Lower bound (LB) is the best service time achievable by a DAR, while deadline D is the upper bound. Please note that D and LB are computed over accepted DARs, so they are slightly increasing as arrival rate increases: for higher loads, the network tends to accept DARs with more relaxed (larger) deadlines, as they are easier to schedule. When the network is lightly loaded (i.e., arrival rate of 55), W T equals average LB (LB), i.e., there are enough available resources so that (most of) the DAR’s file-transfers can be served immediately. DARP achieves better waiting times compared to U N IF . F F and RAN D have large waiting times, even for low loads. Figure 6 shows the impact of K on DARP . For K=2, the network can provision significantly more bandwidth compared to K=1. K=3 has a good tradeoff between performance and computation time. For K larger than 5, performance gain is small. W T (not shown because of space limitations) improves with increasing K, but also saturates for larger values of K.

978-1-4244-2324-8/08/$25.00 © 2008 IEEE. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.

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Fig. 7. Wavelength utilization for DARP and for mathematical approaches.

approaches: a heuristic (DARP ) is able to achieve better resource utilization, as there is little contention for bandwidth in time. For higher loads, there is more need for contention resolution and more refined traffic engineering; MILP approaches use their intelligence to achieve these goals and succeed to outperform DARP (except W AIT ). Still, DARP is able to achieve close results to the MILPs. Similarly, DARP achieves a small W T , almost similar with that of W AIT , which optimizes wait time (please see [14]).

DARPK=1 DARPK=2 DARPK=3 DARPK=5

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Our MILP is solved by using CPLEX [13], a linearprogramming commercial package. We (i) study the performance of the MILP approaches and (ii) benchmark the performance of DARP . We use the small topology in Fig. 3 (with links equipped with 4 wavelengths). The other problem settings have been slightly modified with respect to the previous settings, in order to make the problem more tractable. First, please note that, in a dynamic environment, it is not necessarily the best choice to use greedy mathematical methods that optimize a single dimension of the problem. Each MILP has a limited objective (wavelength utilization, waiting time, or load balancing), since a multi-objective optimization would be computationally infeasible. In turn, DARP is more flexible and considers all aspects of the problem (i.e., wavelengths, grooming, time). Hence, DARP can get the better features from both W AV E and W AIT MILPs. In this work, we use the MILPs as benchmarks that minimize one dimension of the problem, and compare them with DARP . Figure 7 shows wavelength utilization for MILPs and DARP, and exemplifies the above ideas. WAIT uses more resources compared to DARP (and to other MILPs), since WAIT only optimizes wait time. LOADB + ·WAVE (we chose  = 10−2 ) outperforms the other MILPs, while WAVE + ·WAIT has intermediate performance between WAVE and WAIT. For lower loads, we do not need exact (mathematical)

We investigated the problem of DAR provisioning over WDM networks. The problem combines routing, WA, grooming, and scheduling. We stated our problem as a MILP and devised heuristic approaches (DARP ) to solve it. DARP is aimed at jointly considering the different aspects of this multidimensional problem and outperforms other heuristics and MILP solutions that focus only on a single problem dimension. R EFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

Optiputer, http://www.optiputer.net/, 2008. European Organization for Nuclear Research (CERN): www.cern.ch/. National LambdaRail: http://www.nlr.net/, 2008. DOE’s UltraScience Net: http://www.csm.ornl.gov/ultranet/. A. Banerjee et al., “Algorithms for Integrated Routing and Scheduling for Aggregating Data from Distributed Resources on a Lambda Grid,” IEEE Trans. on Par. and Dist. Syst., vol. 19, no. 1, pp. 24-34, Jan. 2008. B. Wang et al., “On Service Provisioning under a Scheduled Traffic Model in Reconfigurable WDM Optical Networks,” Proc., IEEE Broadnets, vol. 1, pp. 13-22, Oct. 2005. A. Jaekel, “Lightpath Scheduling and Allocation Under a Flexible Scheduled Traffic Model,” Proc., IEEE Globecom 2006, Nov. 2006. N. Rao et al., “UltraScience Net: Network Testbed for Large-Scale Science Applications,” IEEE Comm. Mag., vol. 43, no. 11, Nov. 2005. B. Wang and A. Deshmukh, “An All Hops Optimal Algorithm for Dynamic Routing of Sliding Scheduled Traffic Demands,” IEEE Communications Letters, vol. 9, no. 10, pp. 936-939, Oct. 2005. M. Tornatore et al., “Dynamic Traffic Grooming with Holding-Time Knowledge,” IEEE J. on Sel. Areas in Comm., vol. 26, no. 3, Apr. 2008. D. Andrei et al., “Deadline-Driven Bandwidth Allocation with Flexible Transmission Rates in WDM Networks,” Proc., IEEE International Conference on Communications, May 2008. J. Yen, “Finding the K Shortest Loopless Paths in a Network,” Management Science, vol. 17, no. 11, pp. 712-716, July 1971. ILOG CPLEX 9.0: http://www.ilog.com/products/cplex/. D. Andrei et al., “Provisioning Data-Aggregation Sessions in Lambda Grids,” Technical Report, UC Davis, paper ID: CSE-2008-11.pdf, 2008.

978-1-4244-2324-8/08/$25.00 © 2008 IEEE. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.