Queuing Theory

1) Queuing Theog: Two transmission links are used to buffer/send incoming packets to a receiver. The link speeds are 6 Mbps (6x105) and 8 Mbps (8x105), respectively, and the packet arrival rate is 2,000 packets/second with an average length of 500 bytes (exponentially distributed). Packets are evenly split between the links if both are busy (with innite buffering), and packet inter-arrival times are exponential. M Packet service times are exponentially-distributed (due to random lengths), convert link speeds from Mbps to average packets/second. & What is average number of packets waiting for transmission in the system, i.e., at both links? L What is probability an incoming packet experiences no buffering delay, i.e., both links empty? Q What is the average system delay for an incoming packet? U . What is the probability that the average packet transmission time at the rst link exceeds 2.5 ms? L If both links are replaced by a faster link running at a combined 6+8= 14 Mbps (14x105), what is the average system wait time for packets? What is the reason for this improvement or decrease