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We propose an analytical model based on queueing theory for delay analysis in a wormhole-switched network-on-chip (NoC). The proposed model takes as input an application communication graph, a topology graph, a mapping vector, and a routing matrix, and estimates average packet latency and router blocking time. It works for arbitrary network topology with deterministic routing under arbitrary traffic patterns. This model can estimate per-flow average latency accurately and quickly, thus enabling fast design space exploration of various design parameters in NoC designs. Experimental results show that the proposed analytical model can predict the average packet latency more than four orders of magnitude faster than an accurate simulation, while the computation error is less than 10% in non-saturated networks for different system-on-chip platforms.