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

thanks

Cansider a roller coaster. The roller coaster lasts for 1 minute and we will discretize time such that one-time slot equals 1 minute. During a ride, one new customer arrives with probability p1, two new customers arrives with probability p2, and with probability 1 p1 p2 there are no new customers. Customers wait in line in a rst-come rst-served manner {no line cutting}. Assume the line can be innitely large. A customer thatjust nished hisa'her ride, may choose to repeat the ride. Because the ride is quite intense, customers choose not to repeat the ride with probability q; with probability 1 q they choose to have one more ride. If a customer chooses not to repeat the ride, the customer departs and the next one rides the roller coaster. Notice that customer arrivals and departures are independent in the various time slots. 1] Draw the state transition diagram for the first 4 states of this D'IMC. Note: This is an innite state Markov chain. Camputing the average time spent on the roller coaster {waiting in the line and going on the ride}, W, from the iri's, the stationary distribution, can be cumbersome. So, another method of solving for W is using the following equation Xn+1 =Xn_anin +111\" where : X\": number of customers in the system at the beginning of the at]:1 time slot th 6.\": indicates if there are customers in the system at the beginning of the n time slot D\": number of departures at the end of the nth time slot A\": number of arrivals during the int]:1 time slot 2] Write the distributions ofDn and An. 3] Express P (X 3 D), the probability that there are customers in the system, in terms of p1 , p2 and q. 4) Square both sides of Equation {1), take expectations and then let n > no to obtain the average number of customers. 5) Compute W 'om the average number of customers as seen by a departure. 6] What is the stability condition of this queue