The rapid increase in Internet traffic is forcing packet routers to grow in capacity to meet the demand. Optical packet routers with less buffering and a greater degree of optical transparency are actively being researched as a way to improve energy efficiency and capacity scaling over traditional electronic routers. Since it is difficult to buffer packets in the optical domain, in this paper we analyze the performance of a hybrid optoelectronic packet router. The router architecture has multiple optical switch planes and a shared electronic buffer to resolve output-port contention. By using multiple ports on the switch planes for each input and output fiber, and by using some switch-plane ports to inter-connect the planes, we can achieve a relatively low packet loss ratio in a router with no buffer. In this case, most traffic can be switched using only the through optical paths of the router without entering the shared buffer. The shared electronic buffer is primarily used to reduce the packet drop ratio under periods of heavy loads and occasionally for optical regeneration of a packet.We run extensive simulations to evaluate the performance of the router with varying number of switch plane ports, number of connections to the electronic buffer, and number of interconnections between the switch planes. We show that the router can provide good throughput, with realistic on-off bursty traffic and asynchronous packet arrivals.