Design of a Sliding Window over Asynchronous Event Streams

The proliferation of sensing and monitoring applications motivates adoption of the event stream model of computation. Though sliding windows are widely used to facilitate effective event stream processing, it is greatly challenged when the event sources are distributed and asynchronous. To address this challenge, we first show that the snapshots of the asynchronous event streams within the sliding window form a convex distributive lattice (denoted by Lat-Win). Then we propose an algorithm to maintain Lat-Win at runtime. The Lat-Win maintenance algorithm is implemented and evaluated on the open-source context-aware middleware we developed. The evaluation results first show the necessity of adopting sliding windows over asynchronous event streams. Then they show the performance of detecting specified predicates within Lat-Win, even when faced with dynamic changes in the computing environment.

💡 Research Summary

The paper addresses the problem of applying sliding windows to distributed, asynchronous event streams, a scenario common in sensing, monitoring, and context‑aware applications. While sliding windows are a well‑known technique for reducing processing load in stream systems, their use becomes non‑trivial when event sources do not share a global clock and messages experience arbitrary but finite delays. The authors model the system as n non‑checker processes that generate local states and events, together with a single checker process that collects these states. Using Lamport’s “happen‑before” relation and vector clocks, they define consistent global states (CGS) as vectors of local states that are pairwise concurrent. It is known that the set of all CGSs, ordered by the transitive closure of the one‑step predecessor relation, forms a distributive lattice (denoted LAT).

The key theoretical contribution is the proof that, when an n‑dimensional sliding window (the Cartesian product of per‑stream windows of uniform size w) is imposed, the CGSs that lie entirely inside this window also form a lattice, called Lat‑Win. Moreover, Lat‑Win is a convex sub‑lattice of the original LAT and retains distributivity. The proof shows that the meet (component‑wise minimum) and join (component‑wise maximum) of any two CGSs inside the window remain CGSs, guaranteeing closure under lattice operations.

Based on this property, the authors design an online maintenance algorithm for Lat‑Win. The algorithm keeps two anchor CGSs: C_min (the minimal element with no predecessors in Lat‑Win) and C_max (the maximal element with no successors). When a new local state arrives from process i, the oldest state in that process’s window is evicted, and the window slides forward. The algorithm first “grows” Lat‑Win by adding all new CGSs that contain the fresh state and are reachable from C_max, then “prunes” Lat‑Win by removing all CGSs that contain the evicted state and are reachable from C_min. Because growth and pruning are dual operations in a distributive lattice, the updates to C_min and C_max are symmetric and can be performed in O(n) time per event, making the approach suitable for high‑throughput streams.

The implementation is carried out on MIPA, an open‑source context‑aware middleware developed by the authors. A smart‑office case study is used: a user’s location updates (from a mobile device) and meeting‑room sensor readings are streamed to the checker process, which must detect the composite predicate “the user is in the meeting room while a presentation is ongoing.” Experiments vary window size, event rates, and message delays. Results show that using the sliding window reduces processing overhead by more than 99 % compared with processing the full streams, while predicate detection accuracy remains around 95 %. The algorithm successfully maintains Lat‑Win as the window slides, adding new CGSs and discarding stale ones without violating lattice properties.

The paper contributes (1) a formal proof that sliding windows preserve the lattice structure of consistent global snapshots in asynchronous systems, (2) an efficient, online algorithm for maintaining this lattice in real time, and (3) a practical evaluation demonstrating substantial performance gains and high detection accuracy in a realistic pervasive‑computing scenario. The work opens avenues for future research on adaptive window sizing, heterogeneous window dimensions, handling multiple concurrent predicates, and scaling the approach to larger distributed cloud environments.