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In this paper we present modeling and simulation of multiple-hop all-optical packet routing based on the pulse- position modulation header processing (PPM-HP) scheme in ultrafast optical packet switching network. Optical core node employing PPM-HP requires a dedicated routing table based on PPM scheme that will result in significantly reduced number of routing table entries. In this scheme, the header address correlation, using optical AND gates, is carried out by employing only a single bit-wise for each entry rather than a multiple-bit stream as in the existing systems thus resulting in reduced header processing time and avoiding the slow gain-recovery of AND gates. The reduced routing table also offers embedding multiple transmitting modes (unicast, multicast, broadcast) in optical layer and improves core network scalability where the number of core/edge nodes could be altered without the need for changing the number of routing table entries. The simulation results for the optical signal-to-noise ratio (OSNR) of packets at each hop are presented and compared with the theoretical calculations.