42. Customers arrive to a single server system according to a Poisson process with rate . An...

42. Customers arrive to a single server system according to a Poisson process with rate λ. An arrival that finds the server idle immediately begins service; an arrival that finds the server busy waits. When the server completes a service it then simultaneously serves all those customers who are waiting. The time it takes to serve a group of size i is a random variable with density function , . If is the number of customers in the nth service batch, is a Markov chain. If it is, give its transition probabilities; if it is not, tell why not.