Multi-channel Assignment and Link Scheduling for Prioritized Latency-Sensitive Applications

Abstract

Current wireless networks mainly focus on delay-tolerant applications while demands for latency-sensitive applications are rising with VR/AR technologies and machine-to-machine IoT applications. In this paper we consider multi-channel, multi-radio scheduling at the MAC layer to optimize for the performance of prioritized, delay-sensitive demands. Our objective is to design an interference-free schedule that minimizes the maximum weighted refresh time among all edges, where the refresh time of an edge is the maximum number of time slots between two successive slots of that edge and the weights reflect given priorities. In the single-antenna unweighted case with k channels and n transceivers, the scheduling problem reduces to the classical edge coloring problem when $k \ge \lfloor n/2 \rfloor$ and to strong edge coloring when $k=1$, but it is neither edge coloring nor strong edge coloring for general k. Further, the priority requirement introduces extra challenges. In this paper we provide a randomized algorithm with an approximation factor of $\tilde{O}\left( \max \left\{ \sqrt{\varDelta _p }, \frac{\varDelta _p}{\sqrt{k}} \right\} \log m \right)$ in expectation, where $\varDelta _p$ denotes the maximum degree of the unweighted multi-graph, which is formed by duplicating each edge $e_i$ for $w_i$ times ($w_i$ is $e_i$’s integral priority value), and m is the number of required link communications ($f(n) \in \tilde{O}(h(n))$ means that $f(n) \in O\left( h(n) \log ^k(h(n)) \right)$ for some positive constant k. The results are generalized to the multi-antenna settings. We evaluate the performance of our methods in different settings using simulations).

Appendices

A Appendix: Omitted Proof

1.1 A.1 Proof on Schedule Periodicity

Given any infinite schedule S with a finite maximum refresh time, we can find a periodic schedule with max refresh time for each edge $e_i$ no worse than that in S. Let the max refresh time of all edges in S be L. Consider the family of all possible schedules of the edges of G with no interference with length L. The number of these schedules is finite.

Now, let’s construct a periodic schedule $S'$ from S. We divide S into sub-schedules of length L each. Since the configuration of these sub-schedules of length L is finite and S is infinitely long, there exists a subschedule M that repeats at some point in S. Extract the subschedule of S that starts from the first appearance of M and ends right before the second appearance of M. We now repeat this sub-schedule periodically and call it $S'$.

Since each sub-schedule has length L, any edge $e_i$ appears at least once in each sub-schedule. Thus, all the gap between two successive time slots of the same edge $e_i$ in $S'$ also happens in the original schedule S. Hence, the constructed periodic schedule has a maximum refresh time for each edge $e_i$ which is no worse than that in the original schedule S.    $\square$

Fig. 3.

Unit disk network with random node placement. The node degree is kept similar or increases when the scale of network increases to thousand of edges.

B Evaluation

In this section, we evaluate our unweighted and weighted channel assignment algorithms under different scenarios in the single antenna case. Without loss of generality, we can assume that the smallest weight is 1 and all other weights are rounded to integer values. We consider model networks such as random node placement and perturbed grid placement with unit disk communication capacity, and also a real testbed network (denoted the Tmote network) which consists of 48 TMotes in a building that uses the ChipCon CC2420 radio. We vary network parameters such as node degree, the number of channels, weight distributions and measure the performance of our algorithms using the maximum fresh time divided by maximum (weighted) degree and $\varDelta _p$ as the metric. For each network, we ran our algorithm 50 times to compute the average performance.

The network topology in Fig. 3 is constructed by throwing random nodes with a uniform circular range in a 2D unit square. This imitates random node placement in the wild. For each evaluation, we generate 50 networks. In Fig. 3.a, we increase the number of nodes in the unit square from 50 to 600 while keeping the average degrees the same (by scaling down the communication range of each node), so every node continues to have a similar number of interfering counterparts even when the network scale increases. The almost flat slopes of curves indicate that our algorithm still works as efficiently for large graphs as for small graphs when those graphs have similar densities. Besides, the result shows that when we have a reasonable number of channels, our algorithm can efficiently assign channels to a large network while keeping the latency low. In Fig. 3b, we increase the number of nodes but keep the communication range the same, i.e., when the number of nodes increases, the network becomes denser. That means a lot of implicit interferences occur. Therefore, the maximum refresh time increases unavoidably. Still, when we have a reasonable number of channels, our algorithm can keep the max refresh time moderate.

Fig. 4.

Visualization of the network topologies

Fig. 5.

Performance of weighted channel assignment on perturb grid and Tmote network with varying number of channels and weight distributions.

Random node placement often leads to many small holes in the network. To make the network more robust, perturbed grid placement is preferred which gives a more stable node degree among the network while reducing the number of gaps inside. Therefore, we often see an almost grid placement in real-world sensor networks. In order to evaluate on such wireless networks, we use a perturbed $7\times 7$ grid placement network shown in Fig. 4a and also a Tmote network as shown in Fig. 4b. In the Tmote network, these nodes are deployed on walls and ceilings of a building. We collect traces of 3,600,000 packet transmissions using IEEE 802.15.4 standard for each pair of nodes. With the transmission traces, we define two nodes are connected if and only if the packet reception rate of its link is over $90\%$.

In Fig. 5, we evaluate our algorithm on these two networks when weight distributions are uniform and power-law. In both networks, our algorithm can efficiently use channels to reduce the refresh time. However, when the weight distribution is power-law, the benefit diminishes because some implicit interference is unavoidable. Note that some edges have very high priorities and they contribute to the weighted degree which makes the maximum weighted degree pretty high. The ratio of the maximum weighted degree to the total weight is 0.32 for the perturbed grid and it is 0.12 for the Tmote network. The node with the maximum weighted degree creates more unavoidable interferences in the perturbed grid. Hence, the performance of the Tmote network is better than the one of the perturb grid. On the other hand, for both networks under the uniform distribution, the ratios are the same, 0.06, which is quite small and leaves room for improvement of our algorithm. When we vary the number of channels from one to two, our algorithm improves the most. It is almost twice as better than the case of only one channel.