can someone please show me step by step how to solve this problem on little's law?

thanks

You have a system where customers arrive following a poisson process with mean rate of 1 customers per second. At the end of the queue there is one clerk that serves the clients with an exponential distribution service time and a mean service time: 1/,u. A customer's bribe x is arandom variable with an arbitrary pdf b(x) and cdf 30:). The system operates in the following manner: each new arrival offers a non-negative bribe to clerk. Based on his bribe, each customer is placed ahead of all those customers with bribes less than it and behind customers with bribe greater than it. new customers that arrive are placed behind or in front of him following the same rule. If we enforce a policy that says if a new customer gives a bribe bigger than the one the customer being served gave, the customer being served is ejected from service and placed back in queue and the service is offered to the new customer with the higher bribe. Note; Assume that arrival times, service times, and bribes are all independent random variables for each customer and independent of the values for other customers. Let T(x) be the average time spent in the system (queue plus service), for a customer whose bribe is x. We compute T(x) for such a customer: a) Using Little's law show that the expected number of customers that were in the queue before this customer arrived and had a bribe equal or larger than it is given by: I: T001!) (y)dy b) Using Little's law show that the expected number of customers that arrive in the queue after this customer arrived and had a bribe larger than )1 is given by: I: T{x)lb(y)dy c) Using a) and b) show that; Tot) = i+ f: renews); +i fT(x)}lb(y)dy d) Prove that; Tot) = im where p = Ma and not) is a solution to equation in part c