Performance Evaluation of Overlay-based Range Queries for Mobile Systems

In a previously proposed architecture, the mobile user is able to look up and connect to the wireless technology that best matches his context. In order to support such an architecture, the mobile user needs to access information about wireless cells across different management domains and about different access technologies.The P2P overlay aggregates meta-data of heterogeneous cellular networks according to their geographic coverage. The mobile user can then start a location-based range query to find other accessible cells within his movement range for instance. Dependent on the movement pattern and geographic context of a mobile user (e.g., direction of movement and speed) the overhead of such a range query could increase significantly. This paper aims at quantifying the expected overhead. Both an analytic and simulative performance evaluation will be given within the extended version of the paper. Keywords—Context-aware, Location-based services, range queries, overlays. I. LOCATION-AWARE P2P ARCHITECTURE FOR 4-G NETWORK ORGANIZATION In [1] a P2P architecture has been designed as a middleware managing heterogeneous wireless cells in 4th generation network scenarios. The overlay organizes wireless networks across traditional network operator, or technology boarders. Each peer gathers information about cells independent of their wireless link technology. The peer stores a description and pointer to each resource indexed according to its geographic position and the range it covers. The overlay offers a middleware abstracting from the management domains while bridging different signaling techniques and languages [1]. The designed middleware allows a context-aware mobile node to lookup supported technologies by connecting to a P2P network. The mobile node can then stay Always Best Connected (ABC) (i.e. triggers a vertical handover based on its navigation system, or network-assisted context information). The user of the overlays locates wireless resources by starting location-based range queries. Instead of waiting for a beacon from access points and base stations, an active scan is done via the overlay. The meta-data describing heterogeneous wireless cells is searched for across the operator and technology domains. The Chord P2P protocol was modified by replacing the hash function with a space-filling curve based function. This replaces the randomly partitioned Chord space using a hash function such as SHA-1. Fig. 1. A 2-dimentional Hilbert space-filling curve, with degree 1, 2, 3, and 4 (from left to right, top-down). II. FRACTAL-BASED HILBERT ADDRESSING FUNCTION The selected function maps a 2-dimensional geographic location (latitude and longitude) or a 4-dimensional geographic range into a single binary coded ID. The ID corresponds to the square cell in which a given point or range is positioned in a grid-partitioned 2-dimensional space (corresponding to the flattened surface of the earth). This space is then filled with a Hilbert curve. The degree of a Hilbert curve indicates the granularity in which to address a larger range or a smaller range (Fig. 1 shows the multiple degree Hilbert curves). The Hilbert curve is said to be self-similar (i.e. it exhibits a fractal nature). The self-similarity of a Hilbert space filling curve is exploited in the addressing of objects by selecting different degrees. A wireless cell is approximated as a geographic cell fitting within a grid-cell of the space filled by a Hilbert curve (see Fig. 2). The length of the ID of a cell depends on its geographic size. The smaller the addressed geographic range, the higher is the Hilbert curve’s. Therefore, the higher the address resolution needed to describe the range (Fig. 1). Fig. 2 shows the query path taken logically to Fig. 2. Range query along a Hilbert curve. search a given range. The objects found are addressed with different resolutions revealing their covered geographic range. Knoll et al. [2] show that out of the Peano space filling curves, the Hilbert curve maps geographic neighborhood at best. In other words, given two neighboring binary addresses obtained following a Hilbert curve, these two points are geographically closest compared to other space filling curves. Knoll et al. [2] however, use a single degree space filling curve where the same address resolution is chosen to describe all types of objects as well as peers in an overlay key space. III. RANGE QUERY OVERHEAD FOR P2P LOCATION BASED SERVICES (LBS) Key to the location-aware range queries is the possibility to extend the Chord get(key) function to look up geographic ranges. In our architecture, peers are assigned a lower resolution address following a lower degree Hilbert curve. An address mask assigns peers a larger geographic range which covers all the higher resolution smaller ranges, managed as objects. It is shown in [3] that the clustering effects in the Hilbert curve guarantees that a given range can be well described with a rectangular area in a 2-dimensional space. This selforganizing aspect allows any geographically close objects to be clustered together. The function, although distributed at each bootstrapping peer, clusters objects effectively. This early work focuses on the object addressing function for the modified Chord protocol. The same function will be used in defining ranges based on geographic areas (e.g. along a predefined navigation path). This distributed function is investigated for both inserting objects in the LBS Chord ring, and for defining a range query. The query is started as a sequence of get(key) requests for the rectangles that cover a given range. The clustered objects emerge from the insert object function. These selforganized clusters should reduce the search overhead.