5. As pictured below, fixed length datagrams destined for crossbar switch output

Question

5. As pictured below, fixed length datagrams destined for crossbar switch output ports X, Y, and Z queue at the switch's input ports. Due to the switch's crossbar architecture (text Figure 4.8), during each time slot at most one datagram can be transferred to a given output port in a time slot, but different output ports can receive datagrams from different input ports. Assuming that non-empty input ports that can transfer datagrams must transfer datagrams -output port X-+ crossbar switchOut -output port Y- -output port Z-+ (a) Determine the minimal number of time slots needed to transfer the datagrams shown from the input ports to the output ports (optimal scheduling) and list, in order, thet (b) Determine the maximum number of time slots needed to transfer the datagrams shown from the input ports to the output ports (worst-case scheduling) and list, in order, the transfers that achieve this maximum.

Explanation / Answer

(a) The minimum number of time slots needed is three. In first time slot, the transfers are YZ_. where _ denotes that nothing is transmiited. In second time slot, the transfer is XYZ and in third time slot the transfer is XY_.

(b).The maximum number of time slots needed is seven where the transfers are Y_ _, _ Z _, _ _ Z, X _ _, _ Y _, _ _ Y, X _ _.

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