Poisson Process& Exponential Distribution& Memoryless Property

Consider the queuing system in the figure, where packets whose service is completed by Server 1 and 2 go to Server 3. The service time of Server 1, 2, and 3 is exponential with rate fi = 1 pks/s, 112 = 2 pkt/s and 13 = 3 pkt/s, respectively. At time t=0, packet A arrives in the buffer of Server 1 (which was empty), and Server 2 has two packets in its buffer (Packet B and C). A 1 3 BC 2 (a) Compute the probability that A exits the system before any other packets move to server 3. (b) Compute the probability that C exits the system before any other packets move to server 3. (c) Suppose b) is the next chain of events that happened (packet C exited the system while packets A and B are being served at server 1 and 2 respectively), compute the expected time I needed by Packet A to exist the system. Consider the queuing system in the figure, where packets whose service is completed by Server 1 and 2 go to Server 3. The service time of Server 1, 2, and 3 is exponential with rate fi = 1 pks/s, 112 = 2 pkt/s and 13 = 3 pkt/s, respectively. At time t=0, packet A arrives in the buffer of Server 1 (which was empty), and Server 2 has two packets in its buffer (Packet B and C). A 1 3 BC 2 (a) Compute the probability that A exits the system before any other packets move to server 3. (b) Compute the probability that C exits the system before any other packets move to server 3. (c) Suppose b) is the next chain of events that happened (packet C exited the system while packets A and B are being served at server 1 and 2 respectively), compute the expected time I needed by Packet A to exist the system