Scheduling is a critical and challenging resource allocation mechanism for multihop wireless networks. It is well known that scheduling schemes that favor links with larger queue length can achieve high throughput performance. However, these queue-length-based schemes could potentially suffer from large (even infinite) packet delays due to the well-known last packet problem, whereby packets belonging to some flows may be excessively delayed due to lack of subsequent packet arrivals. Delay-based schemes have the potential to resolve this last packet problem by scheduling the link based on the delay the packet has encountered. However, characterizing throughput-optimality of these delay-based schemes has largely been an open problem in multihop wireless networks (except in limited cases where the traffic is single-hop.) In this paper, we investigate delay-based scheduling schemes for multihop traffic scenarios with fixed routes. We develop a scheduling scheme based on a new delay metric, and show that the proposed scheme achieves optimal throughput performance. Further, we conduct simulations to support our analytical results, and show that the delay-based scheduler successfully removes excessive packet delays, while it achieves the same throughput region as the queue-length-based scheme.
algorithm, called Queue-length-based Back-Pressure (Q-BP), that has been shown to be throughputoptimal, i.e., it can stabilize the network under any feasible load. This paper focuses on the settings with fixed routes, where the Q-BP algorithm becomes a scheduling algorithm. Since the development of Q-BP, there have been numerous extensions that have integrated it in an overall optimal cross-layer framework.
Further, easier-to-implement queue-length-based scheduling schemes have been developed and shown to be throughput-efficient (see [2] and references therein). Some recent attempts [3]- [5] focus on designing real-world wireless protocols using the ideas behind these algorithms.
While these queue-length-based schedulers have been shown to achieve excellent throughput performance, they are usually evaluated under the assumption that flows have an infinite amount of data and keep injecting packets into the network. However, in practice, when accounting for multiple time scales [6]- [8], there also exist other types of flows that have a finite number of packets to transmit, which can result in the well-known last packet problem: consider a queue that holds the last packet of a flow, then the packet does not see any subsequent packet arrivals, and thus the queue length remains very small and the link may be starved for a long time, since the queue-length-based schemes give a higher priority to links with a larger queue length. In such a scenario with flow-level dynamics, it has also been shown in [6] that the queue-length-based schemes may not even be throughput-optimal.
Recent works in [9]- [14] have studied the performance of delay-based scheduling algorithms that use Head-of-Line (HOL) delays instead of queue lengths as link weights. One desirable property of the delaybased approach is that they provide an intuitive way around the last packet problem. The schedulers give a higher priority to the links with a larger weight as before, but now the weight (i.e., the HOL delay) of a link increases with time until the link is scheduled. Hence, if the link with the last packet is not scheduled at this moment, it is more likely to be scheduled in the next time. However, the throughput of the delay-based scheduling schemes is not fully understood, and has only been established for limited cases with single-hop traffic.
The delay-based approach was introduced in [9] for scheduling in Input-Queued switches. The results have been extended to wireless networks for single-hop traffic, providing throughput-optimal delay-based MaxWeight scheduling algorithms [11], [12], [15]. It has also been shown that delay-based schemes with appropriately chosen weight parameters provide good Quality of Service (QoS) [10], and can be used as an important component in a cross-layer protocol design [14]. The performance of the delay-based MaxWeight scheduler has been further investigated in a single-hop network with flow-level dynamics [13]. The results show that, when flows arrive at the base station carrying a finite amount of data, the delay-based MaxWeight scheduler achieves optimal throughput performance while its queue-length-based June 4, 2018 DRAFT counterpart does not.
It should be noted that even for the multihop wireless networks with fixed routes, the scheduling problem is both important and challenging. There are many existing works focusing on such scenarios with fixed routes (see [16]- [18] for examples). However, in multihop wireless networks, the throughput performance of these delay-based schemes has largely been an open problem. To the best of our knowledge, even with the assumption of fixed routes, there are no prior works that employ delay-based algorithms to address the important issue of throughput-optimal scheduling in multihop wireless networks.
Indeed, the problem becomes much more challenging in the multihop scenario. In [12], the key idea in showing throughput-optimality of the delay-based MaxWeight scheduler is to exploit the following property: after a finite time, there exists a linear relation between queue lengths and HOL delays in the fluid limits (which we formally define in Section III-A), where the ratio is the mean arrival rate.
Hence, the delay-based MaxWeight scheme is basically equivalent to its queue-length-based counterpart, and thus achieves the optimal throughput. This property holds for the single-hop traffic. Since given that the exogenous arrival processes follow the Strong Law of Large Numbers (SLLN) and the fluid limits exist, the arrival processes are deterministic with constant rates in the fluid limits. However, such a linear relation does not necessarily hold for the multihop traffic, since at a non-source (or relay) node, the arrival process may not satisfy SLLN and the packet arrival rate may not even be a constant, depending on the underlying schedulers dynamics. To this end, we investigate delay-based scheduling schemes that achieve optimal throughput performance in multihop
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