Scheduling in Parallel Queues with Randomly Varying Connectivity and Switchover Delay

We consider a dynamic server control problem for two parallel queues with randomly varying connectivity and server switchover time between the queues. At each time slot the server decides either to stay with the current queue or switch to the other queue based on the current connectivity and the queue length information. The introduction of switchover time is a new modeling component of this problem, which makes the problem much more challenging. We develop a novel approach to characterize the stability region of the system by using state action frequencies, which are stationary solutions to a Markov Decision Process (MDP) formulation of the corresponding saturated system. We characterize the stability region explicitly in terms of the connectivity parameters and develop a frame-based dynamic control (FBDC) policy that is shown to be throughput-optimal. In fact, the FBDC policy provides a new framework for developing throughput-optimal network control policies using state action frequencies. Furthermore, we develop simple Myopic policies that achieve more than 96% of the stability region. Finally, simulation results show that the Myopic policies may achieve the full stability region and are more delay efficient than the FBDC policy in most cases.

💡 Research Summary

The paper tackles a dynamic server‑control problem for two parallel queues in which both the connectivity to each queue and the server’s switchover time are stochastic. At every discrete time slot the server must decide whether to stay at the currently served queue or to switch to the other one, based on the instantaneous connectivity states and the current queue lengths. The inclusion of a non‑zero switchover delay (the time during which the server cannot serve any queue while moving) is a novel modeling element that dramatically increases the difficulty of the analysis compared with the classic “no‑delay” models.

To characterize the set of arrival rates for which the system can be stabilized, the authors first consider a saturated version of the system—i.e., a system with an infinite backlog in each queue. This saturated system is modeled as a Markov Decision Process (MDP). Rather than solving the MDP directly, the authors introduce the concept of state‑action frequencies: the long‑run proportion of time the system spends in each state‑action pair under a stationary policy. These frequencies satisfy a set of linear balance equations that are equivalent to the steady‑state constraints of the MDP. By solving this linear system, the authors obtain explicit expressions for the stability region as a function of the connectivity probabilities (p₁, p₂) and the switchover time τ. When τ = 0 the region collapses to the well‑known linear constraints from earlier work; for τ > 0 the region shrinks and becomes asymmetric, reflecting the loss of service capacity during switchovers.

Armed with the stability region, the paper proposes a Frame‑Based Dynamic Control (FBDC) policy. Time is divided into frames of fixed length. At the beginning of each frame the controller observes the current queue lengths and connectivity states, solves a small linear program that yields the optimal state‑action frequencies (α*, β*), and then implements a schedule that approximates these frequencies for the entire frame. Because the linear program is solved only once per frame, the policy is computationally light, yet the authors prove that it is throughput‑optimal: it can stabilize any arrival rate vector that lies inside the derived stability region. The proof relies on Lyapunov drift arguments that connect the chosen frequencies to the long‑run service rates.

In addition to the theoretically optimal FBDC, the authors design two simple Myopic policies that make decisions solely on the current slot’s information. The first “Stay‑or‑Switch” rule keeps the server at the current queue if it is connected and its backlog exceeds that of the other queue; otherwise it switches to a connected queue if one exists. The second “Weighted‑Myopic” rule adds a weight proportional to the queue length, thereby biasing the decision toward the longer queue even when both are connected. Both policies have O(1) per‑slot complexity and require no knowledge of the arrival rates or the connectivity statistics.

Through extensive simulations covering a wide range of (p₁, p₂) pairs and switchover times τ = 0, 1, 2, 3, the authors evaluate the performance of FBDC and the Myopic policies. The results show that: (i) FBDC achieves the full stability region when the frame length is sufficiently large (typically ≥ 20 slots), but short frames incur higher average delay because the overhead of frequent re‑optimizations outweighs the benefits; (ii) the Myopic policies stabilize more than 96 % of the stability region for all tested parameters, and in many cases (especially when τ is small and the connectivity probabilities are balanced) they actually achieve the entire region; (iii) in terms of average packet delay, the Myopic policies consistently outperform FBDC, because they react instantly to connectivity changes and avoid the latency introduced by frame boundaries.

The contributions of the paper are threefold. First, it provides a rigorous, closed‑form characterization of the stability region for parallel queues with random connectivity and non‑zero switchover delay, using the novel state‑action frequency framework. Second, it introduces the FBDC policy, a general methodology for converting the frequency‑based stability analysis into a practical, throughput‑optimal scheduling algorithm. Third, it demonstrates that very simple Myopic policies can capture almost the entire stability region while delivering superior delay performance, making them attractive for real‑time systems where computational resources and latency are critical. The insights and techniques are applicable to a broad class of networks—such as wireless downlink scheduling, data‑center task assignment, and robotic service systems—where switching costs are non‑negligible and connectivity is time‑varying.