Stability and asymptotic optimality of opportunistic schedulers in wireless systems

Abstract

We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based [9], Proportionally Best [1] or Potential Improvement [4] are stable under the maximum stability conditions, whereas Relative-Best [10] or the cµ-rule are not. (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. In particular, we show that simple priority-index policies with a myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.

Application-level scheduling with deadline constraints

“…Our model also differs from flow-level scheduling. In typical flow-level scheduling studies [8,9,16], flow-level dynamics and packet-level dynamics are mixed together, i.e., packetlevel scheduling decisions must take into account flow-level statistics (e.g., delay or residual file size [9]). In contrast, our model can be viewed as a simplification that decouples flow-level scheduling from packet-level scheduling.…”

“…In contrast, our model can be viewed as a simplification that decouples flow-level scheduling from packet-level scheduling. The benefit of such simplification is that we can provide rigorous delay guarantees (in comparison, existing flow-level studies focus only on stability and throughput optimality [8,9,16]). …”

“…For example, consider the following Less-Resource-First (LRF) policy: all users are eligible for service and at each timeslot, and the BS gives priorities to the users that require less resource to be served. For identical-file-size systems, LRF can be viewed as a work-conserving enhancement of the Best-Rate policy in [8]. One can show that the LRF policy also dominates FOO and hence is asymptotically optimal in the single-class case.…”

“…Under such multi-state channels and general arrival models, although recently-developed optimization-based approaches to wireless control have been very successful for maximizing long-term throughput and stability [7][8][9], they are of limited capability in maximizing capacity subject to deadline constraints. For instance, the Delay-driven MaxWeight [9] policy is shown to be throughput optimal for flow-level scheduling, but may perform poorly in the case with deadline constraints.…”

Laxity-based opportunistic scheduling with flow-level dynamics and deadlines

“…Similar to the packet-level scheduling, a critical issue is to guarantee stability if possible. Recent results show that the maximum stable region can be easily achieved by applying some simple rules such as Best-Rate (BR) rule [4]. Other papers investigate policies for minimizing the average transmission delay.…”