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This paper introduces packet chaining, a simple and effective method to increase allocator matching efficiency and hence network performance, particularly suited to networks with short packets and short cycle times. Packet chaining operates by chaining packets destined to the same output together, to reuse the switch connection of a departing packet. This allows an allocator to build up an efficient matching over a number of cycles, like incremental allocation, but not limited by packet length. For a 64-node 2D mesh at maximum injection rate and with single-flit packets, packet chaining increases network throughput by 15% compared to a conventional single-iteration separable iSLIP allocator, outperforms a wavefront allocator, and gives comparable throughput with an augmenting paths allocator. Packet chaining achieves this performance with a cycle time comparable to a single-iteration separable allocator. Packet chaining also reduces average network latency by 22.5%. Finally, packet chaining increases IPC up to 46% (16% average) for application benchmarks because short packets are critical in a typical cache-coherent CMP. These are considerable improvements given the maturity of network-on-chip routers and allocators.