can someone please show me step by step how to solve this markov chain problem?

thanks

For a switch with N inputs and N with only queuing at the inputs. We assume: At the beginning of each time slot, there is an arrival at each input, and this arrival is destined to output i with probability 1/N for all i -At the end of each time slot the switch transfers packets from inputs to outputs as follows: it sends one packet at each output that has at least one packet destined to it, and it drops, i.e. removes from the input queues and discards, all unserved packets. (Note that since two packets arriving at two inputs may want to go to the same output, only one of them can be transferred, the other will be discarded.) 1) For N = 2, let X1 be the number of packets destined to output 1 and X2 be the number of packets destined to output 2 at a time slot. Argue that (X1, X2) can be modeled as a MC. 2) Draw the transition diagram of this MC and specify the transition probabilities. 3) Find the stationary distribution of this MC. How many packets on average are transferred from the inputs to the outputs at watch time slot? 4) What you found before is called the aggregate switch throughput. Divide by N = 2 to find the per input switch throughput. Now you will attempt to find the switch throughput for any N. 5) Let Ik = 1 if the k' output has a packet destined to it at the current time slot. The aggregate switch throughput is clearly equal to the expected number of outputs which have at least one packet destined to them. 6) Find the aggregate and the per input switch throughput using the Ik's. Hint: Think what _=1 1, represents. Also, think if the Ik's are symmetric or not