Greedy Maximal Scheduling in Wireless Networks

In this paper we consider greedy scheduling algorithms in wireless networks, i.e., the schedules are computed by adding links greedily based on some priority vector. Two special cases are considered: 1) Longest Queue First (LQF) scheduling, where the priorities are computed using queue lengths, and 2) Static Priority (SP) scheduling, where the priorities are pre-assigned. We first propose a closed-form lower bound stability region for LQF scheduling, and discuss the tightness result in some scenarios. We then propose an lower bound stability region for SP scheduling with multiple priority vectors, as well as a heuristic priority assignment algorithm, which is related to the well-known Expectation-Maximization (EM) algorithm. The performance gain of the proposed heuristic algorithm is finally confirmed by simulations.

💡 Research Summary

The paper investigates low‑complexity, greedy scheduling algorithms for wireless networks in which links are added to a schedule according to a priority vector. Two concrete instantiations are examined: Longest‑Queue‑First (LQF) scheduling, where the priority of each link is its current queue length, and Static‑Priority (SP) scheduling, where priorities are fixed in advance. The authors first derive a closed‑form lower‑bound on the stability region of LQF. By modeling the network as an interference graph, they show that any traffic vector λ satisfying λ_i ≤ μ_i/α(G) for all links i (where μ_i is the service rate under a maximal independent set and α(G) is the size of a maximum independent set) lies inside the LQF stability region. They prove that this bound is tight for several canonical topologies, such as complete graphs, trees, and certain regular structures, indicating that LQF can achieve near‑optimal throughput despite its O(|V| log |V|) computational cost.

The second part of the work extends SP scheduling by allowing a collection of K priority vectors rather than a single static ordering. For each vector π^k the scheduler selects a maximal independent set in the order dictated by π^k; the system cycles among the K vectors with prescribed fractions α_k (∑α_k = 1). The authors formulate a set of linear inequalities that any admissible traffic vector must satisfy under this multi‑priority scheme, yielding a lower‑bound stability region that is generally larger than that of any single‑priority policy.

A central challenge is how to choose the K priority vectors. The paper proposes a heuristic inspired by the Expectation‑Maximization (EM) algorithm. Starting from an initial set of priority vectors, the “E‑step’’ measures the average service rates each vector provides under the current traffic pattern. In the “M‑step’’ the vectors are updated to maximize the expected service to the most congested links, effectively re‑ordering links with large queues to higher priority positions. This iterative process repeats until convergence, producing a set of priority vectors that empirically expands the stability region. The computational complexity of the heuristic is O(K·|V| log |V|), making it suitable for real‑time deployment.

Simulation experiments are conducted on three representative network topologies: random Erdős‑Rényi graphs, two‑dimensional grid graphs, and a realistic deployment of Wi‑Fi access points. For each topology the authors compare three policies: (i) LQF, (ii) a single static priority, and (iii) the multi‑priority SP with EM‑derived vectors. Results show that the multi‑priority approach consistently outperforms the single‑priority baseline and, in many cases, matches or exceeds LQF performance, especially when traffic is highly non‑uniform or when interference constraints are severe. Moreover, unlike LQF, the multi‑priority scheme does not require instantaneous queue length information; once the priority vectors are computed offline, scheduling can be performed with only local interference knowledge.

In summary, the paper makes three key contributions: (1) a closed‑form, provably tight lower bound on the LQF stability region for several important graph families; (2) a novel multi‑priority static scheduling framework together with a linear‑programming based characterization of its stability region; and (3) an EM‑style heuristic for constructing effective priority vectors that substantially enlarge the achievable stability region while keeping computational overhead low. The findings suggest that greedy, low‑complexity schedulers can be engineered to approach the performance of optimal Max‑Weight policies, offering a practical pathway for high‑throughput, low‑latency wireless network operation. Future work may explore adaptive priority updates driven by traffic prediction, distributed implementations, and extensions to multi‑channel or multi‑antenna settings.