The delay guarantee is a challenge to meet different real-time requirements in applications of backpressure-based wireless multihop networks, and therefore, researchers are interested in the possibility of providing bounded end-to-end delay. In this paper, a new cross-layer control algorithm with worst case delay guarantees is proposed. The utility maximization algorithm is developed using a Lyapunov optimization framework. Virtual queues that ensure the worst case delay of nondropped packets are designed. It is proved through rigorous theoretical analyses and verified by simulations that the time average overall utility achieved by the new algorithm can be arbitrarily close to the optimal solution with finite queue backlogs. The simulation results evaluated with Matlab show that the proposed algorithm achieves higher throughput utility with fewer data dropped compared with the existing work.

With the exponential increase in wireless multihop networks in the last two decades, increasingly sophisticated approaches that target resource allocation, congestion control, routing, and scheduling have been developed. Among the various policies that have been developed, the backpressure scheduling/routing policy, which was first proposed in the seminal work by Tassiulas and Ephremides [

Besides throughput utility, end-to-end delay is another important long-term performance metric of the backpressure style algorithms, and it is crucial to many essential applications. As applications with real-time requirements are being developed, it is necessary to design backpressure-based algorithms that provide bounded worst case delay guarantees. Backpressure algorithms usually bear poor delay performance mainly attributed to the following three reasons. First, the slow startup process to form a stable queue backlog gradient from the source to the destination causes large initial end-to-end delay. Second, unnecessarily long or looped paths form owing to the fluctuation of the queue backlog. Finally, the absence of consistent backpressure towards the destination can cause large latency in networks with short-lived or low-rate flows. In [

The key contributions of this paper can be summarized as follows.

The paper proposes a two-phase algorithm which can provide a bound on the worst case end-to-end delay of individual sessions by designing a novel virtual delay queue structure.

By transforming the stochastic control problem into a deterministic optimization problem using the Lyapunov drift-plus-penalty technique, we design a joint congestion control, routing, and scheduling algorithm.

The performance in terms of utility optimality and network stability of the algorithm is demonstrated with rigorous theoretical analyses. It is shown that the proposed algorithm can achieve a time average throughput utility that can be arbitrarily close to the optimal value, with queue backlogs being bounded by constants.

The remainder of this paper is organized as follows. Section

Consider a multihop wireless network consisting of several nodes. Let the network be modeled by a directed connectivity graph

The system is assumed to run in a time-slotted fashion. Nodes in the network communicate using only one channel.

The data backlog queue for session

The

In this paper, we redesign the

Any algorithm that maintains bounded

For all time slots

Fix any slot

Similar to the design of the utility function in [

The Lyapunov optimization technique is applied to solve

The algorithm CCWD is based on the drift-plus-penalty framework [

Assume that

The theorem is proved by induction.

(1) According to the induction principle, if

(2) According to the induction principle, if

(3) According to the induction principle, if

One has

The drift-plus-penalty function (

In the simulations, the commonly used greedy maximal scheduling (GMS) method is used for schedulable link set generation for each algorithm under comparison. This method is widely used for implementing backpressure-based centralized algorithms under sophisticated networks [

For simulations, a network with 20 nodes randomly distributed in a square of 1600 m^{2} is considered. A transmission is successful if a receiver is within the transmission range of its sender and outside the range of other concurrent senders. The transmission or interference range of a node is 15 m. There are four unicast sessions with randomly chosen sources and destinations. Data of each session is injected into the transport layer with the same rate in each slot at the source nodes. Parameter

In this section, the performance of CCWD is compared with that of an existing method called NeelyOpportunistic, which too can provide bounded worst case delay. NeelyOpportunistic is proposed in [

Throughput utility versus average data arrival rate.

Time average number of dropped packets versus average data arrival rate.

According to the analyses in Section

Throughput utility versus

Time average size of

Time average size of

Time average size of

This paper proposed a two-phase throughput utility maximization algorithm which provides worst case delay guarantees using a new

The authors declare that they have no competing interests.

This work was supported by the National Natural Science Foundation of China under Grant no. 2013CB329003, the National Natural Science Foundation of China under Grant no. 61307016, and Natural Science Foundation of Liaoning Province under Grant no. 2014020193.