In a multihop wireless network, wireless interference is a crucial factor in the maximum multiflow (MMF) problem, which studies the maximum throughput between multiple pairs of sources and sinks with a link schedule to support it. In this paper, we observe that network coding could help to decrease the impact of wireless interference, and thus propose a framework to study the MMF problem for multihop wireless networks with network coding. Firstly, a network model is established to describe the new conflict relations and schedulability modified by network coding. Next, we formulate the MMF problem to compute the maximum throughput of multiple unicast flows supported by the multihop wireless network with network coding, and show that its capacity region could be enlarged by performing network coding. Finally, we show that determining the capacity region of a multihop wireless network with network coding is an NP-hard problem, and thus propose a greedy heuristic algorithm, called coding-first collecting (CFC), to determine a capacity subregion of the network. We also show that finding an optimal hyperarc schedule to meet a given link demand function is NP-hard, and propose a polynomial algorithm, called coding-first scheduling (CFS), to find an approximate fractional hyperarc schedule in the multihop wireless network with network coding. A numerical analysis of a grid wireless network and a random wireless network is presented to demonstrate the efficiencies of the CFC algorithm and the CFS algorithm based on the framework.

It has been shown that virtual output queuing (VOQ) and a sophisticated scheduling algorithm enable an input-queued switch to achieve 100% throughput for independent arrival process. Several of the scheduling algorithms that have been proposed can be classified as either iterative scheduling algorithms or symmetric crossbar arbitration algorithms. i-OCF (oldest-cell-first) and TSA (two step arbiter) are well-known examples of iterative scheduling algorithms and symmetric crossbar arbitration algorithms, respectively. However, there are drawbacks in using these algorithms. i-OCF takes long time to find completely a conflict-free match between input ports and output ports because it requires multiple iterations. If i-OCF cannot find a conflict-free match completely, the switch throughput falls. TSA has the possibility that it finds a conflict-free match faster than i-OCF because it does not need any iterations. However, TSA suffers from the starvation problem. In this paper, we propose a new scheduling algorithm. It uses two schedulers, which we call scheduler 1 and scheduler 2, in parallel. After cells were transmitted, the information that input port i granted the offer from output port j in scheduler 2 is mapped to scheduler 1 if and only if input port i has at least one cell destined for output port j. If the information is moved, input port i and output port j are matched in scheduler 1 at the beginning of the next time slot. Our proposed algorithm uses one scheduler based on TSA and the other scheduler based on i-OCF. Numerical results show that the proposed scheduling algorithm does not require multiple iterations to find a conflict-free match completely and suffer from the starvation problem for both uniform and bursty traffic.

This paper evaluates the throughput performance of a switch architecture for broadband networks that is capable of switching variable-length packets. The structure is connectionless, so that no bandwidth reservation takes place before the user packet, or datagram, is transferred. The interconnection network is assumed to be internally non-blocking and provided with input queues. A previous approximated throughput analysis of the proposed system has been carried out under the hypothesis that the length of the offered packets is uniformly distributed. In this work we perform an exact throughput analysis and we show how the actual throughput of the system can be expressed analytically with a simple closed form. Moreover, we consider a more general case of packet length distributed as a truncated exponential. In this way it is possible to account for cases in which short packets are more frequent than long packets or, conversely, long packets are more frequent than short ones. The minimum throughput of the system is obtained when packets are uniformly distributed; a better performance is obtained when short (long) packets are more frequent than long (short) ones.