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Consider a single packet switch with a finite number of packet buffers shared between several output queues. An arriving packet is lost if no free buffer is available, as in the CIGALE network. It has been observed by simulation that if load increases too much, congestion may occur, i.e., throughput declines; it appears that the busiest link's queue tends to hog the buffers. Therefore, we will limit the queue length and when the queue is full the packet will be dropped. We expect that this restricted buffer sharing policy will avoid congestion under conditions of heavy load. A queueing model of a packet switch is defined and solved by local balance. Loss probability is evaluated, and values of queue limit to minimize loss are found; they depend on load. A Square-Root rule is introduced to make the choice of queue limit independent of load. For a sample switch, with three output links, a comparison is made between performance under different buffer sharing policies; it is shown that restricted sharing prevents congestion by making throughput an increasing function of load.