A mixed-integer approach to Core-Edge design of storage area networks

Abstract

In this paper we address the problem of optimal network design for a storage area network. We consider the Core-Edge reference topology and present two formulations for the Core-Edge storage area network design problem. One formulation excludes explicit host/device connections to the edge (as is common in currently available heuristics), the other includes these connections to allow the modeling of multiple disjoint paths between hosts and devices. These formulations include generic component types to reduce the number of constraints and variables, with the properties of these components being determined as part of the solution process. The size of the formulation is further reduced by a preprocessing method that removes suboptimal switches and links from consideration.

We test our formulations on a randomly generated set of problems, all of which are of a size consistent with those encountered in industry. We generate solutions using our two formulations for all test problems in good time.

Finally we apply a relaxation of one of our formulations to re-configure the Cecil back-end network, which is currently used across the University of Auckland. We present two designs for the re-configured network to significantly increase reliability and scalability.

Introduction

The centralization of data storage is now standard practice in most large organizations. Apart from the economies of scale inherent in managing all one's data in a central location, the separation of the data storage devices from the local area network has the advantage of reducing this network's congestion and facilitates data security. The mechanism for connecting the data storage devices to the local area network is the storage area network (SAN). The design of the SAN determines the network's ability to be reprovisioned for future growth, as well as impacting directly on the speed and reliability of data retrieval in the system. Thus it is of major importance.

The SAN design problem (SANDP) involves the selection and configuration of links, hubs and switches (the standard components in computer networks) to allow data to flow between hosts (servers) and storage devices. The objective for the designer is to construct the minimum cost SAN that meets the performance criteria of the user (these usually being adequate speed and reliability). Ideally a solution to this problem would include not only a network configuration, but also the flow paths along which the data would travel. Finding such a solution requires the origin, destination and bandwidth information for all network traffic a priori. In general these flow requirements are not known, so a common design goal is a network with full host–device connectivity that can be easily scaled to support increases in flow bandwidth. To avoid network failure due to the failure of a single component, it is also desirable to include at least two disjoint paths between every host–device pair in the design. This feature has the secondary advantage of allowing for more even load balancing.

A typical SAN in industry could connect 50 hosts to 100 devices. The complexity in a design for such a SAN makes it extremely difficult for technicians to determine which is the better of two solutions. For this reason technicians are extremely resistant to deviations from a set of reference topologies. One of the most popular reference topologies is the Core-Edge topology, because of its inherent reliability and scalability. The Core-Edge topology consists of two disjoint cores (each comprising of one or more high-bandwidth core switches) connected to one or two layers of lower-bandwidth edge switches. The edge switches connect to the hosts and devices in a Single-edge or Double-edge design, as shown in Fig. 1 (note that the Core-Edge topology includes no hubs). Data are routed from a host through an edge switch to one of the core switches and onto the appropriate device via a second edge switch, unless the host and device are connected to a common edge switch, in which case the data need not pass through the core. This means that no host–device pair is separated by more than three intermediate connections. Determining a design with two disjoint paths between every host–device pair is simplified by the disjoint nature of the cores in the Core-Edge topology. Furthermore, with the addition of switches to the edges or the core, an existing design can be scaled to accommodate additional hosts or devices (often without taking the existing network off-line).

The SANDP fits into the broader area of network design. If we restrict our discussion to computer networks, the network design problem (NDP) typically reduces to two subproblems. The first of these is a facility location problem (referred to as the node location problem¹—see for example the survey papers by ReVelle and Eiselt [1] and Drenzer and Hamacher [2]). This subproblem involves the design of an access network to connect a set of access nodes to a subset of transit node locations. In the second subproblem the transit nodes lying adjacent to access nodes in the access network are themselves connected via a backbone network. It is assumed that a set of flow demands between access nodes is known a priori, and a path for each commodity needs to be assigned through the connected network [3]. A number of papers [4], [5], [6], [7] present surveys of network design across the areas of telecommunication, facility location, network design, computer systems and transportation.

Klincewicz [6] classifies types of network design problem by topology, surveying the literature in each category. Networks of star/star² [8], [9], [10], [11] and fully interconnected/star [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] topologies appear to be the best understood (and most commonly used). Networks with star/star topology require that an access node be connected to a central site through a set number of transit nodes in a tree structure, as shown in Fig. 2. The inclusion of this central site means that the star/star network design problem can be modeled as two node location problems: one problem is to create the access network; the second is to connect the appropriate transit nodes to the central site [23], [24].

Networks with fully interconnected/star topology require the access nodes to be connected via a fully interconnected core network of transit nodes, as shown in Fig. 3. A star topology is again created between the access nodes and transit nodes. Limited examples with a non-fixed partial mesh topology can also be found, such as Gavish [25].

The SANDP is known to be NP-hard: if we ban flow-splitting (so that each flow demand must follow one path) it generalizes the non-bifurcated network loading problem [25], [26], otherwise it is equivalent to multicommodity network design [27]. It combines elements of degree-constrained network design with node costs and node capacities. Literature referring directly to the SANDP is extremely limited. Ward et al. [28] present two algorithms for designing SANs and refer to a model (without formulation) that includes all possible components in the network and uses mixed-integer programming (MIP) to select the optimal design. O’Sullivan et al. [29] present the formulation referred to by Ward et al., and outline a preprocessing method for significantly reducing the size of this formulation. O’Sullivan and Walker [30] present a MIP formulation for SAN design that uses generic network components and assigns capabilities to them as part of the decision process. This formulation, together with a modified version of the preprocessing method outlined by O’Sullivan et al., results in a further significant reduction in the number of variables and constraints. All these models assume a priori knowledge of the network traffic.

By removing the requirement of assigning flow paths a priori, the Core-Edge SAN design problem (CESANDP) is a simplification of the SANDP, but remains NP-hard. This problem involves the design of a SAN with full host–device connectivity, conforming to the Core-Edge topology. The only direct reference to the CESANDP in the literature known to the authors is Strand [31]. Strand outlines an extension of the storage area network toolkit (SANTK), a software application created by the Fibre Channel Group at the University of Minnesota. Strand's extension generates Core-Edge designs to meet the user's design criteria, but does not do so optimally.

We present MIP formulations for four types of CESANDPs. Our formulations incorporate generic component types and a preprocessing method to significantly reduce the number of variables and constraints. We test our formulations on a set of randomly generated problems, all of which are of a size consistent with those standard in industry. We then adapt one of our formulations to re-configure the design for a network that is currently in use across the University of Auckland.

We introduce our notation and give the problem description in Section 2. We present our formulations for the Double-edge CESANDP in Sections 3 and 4, respectively (omitting the Single-edge instances of these problems as their formulations are so similar). In Section 5 we describe our test problems and present solutions and performance results. We describe the Cecil back-end network and give our designs for the re-configured network in Section 6. Finally in Section 7 we make our concluding remarks.