Show me the steps to solve 1) Consider a queue \(\mathrm{M}/\mathrm{M}/1\) with buffering capacity K (i.e.\(\mathrm{M}/\mathrm{M}/1/\mathrm{K}\)). The queue multiplexes the traffic of ten users, each generating 256 bits per second of traffic. The link service rate is 16 message per second, each message consists of four packets on average, and each packet is 516 bits length. Find the blocking probability and the expected waiting time if \(\mathrm{K}=4\).2) Compare the mean delay and mean waiting time performance of the two queueing systems represented as \( M / M /1\) and \( M / M /2\). Note that both systems have the same service rate \(\mu=1\) and arrival time rate, \(\lambda=1/2\)(i.e. for M/M/2, the \(\left.\mu^{\prime}=\mu /2 ight)\).3) Consider a Telecommunication network system that respects the \( M / M /1\) queueing system in which packets arrive at the system with arrival rate of 125 packets per second (pps) and served at service rate of 1000 packets per second. Determine the probability of having n packets in the system and the probability of having more than 10 packets in the system. 4) A company has two 1 Megabit/second lines connecting two of its sites. Suppose that packets for these lines arrive according to a Poisson process at a rate of 150 packets per second, and that packets are exponentially distributed with mean 10 kbits. When both lines are busy, the system queues the packets and transmits them on the first available line. Find the probability that a packet has to wait in queue.