[16 marks] At the lunch rush of a hawkerstyle food hall. customers wall: by a certain stall with one server according to a Poisson process with rate 21] per minute. If there is either only one person being served or no one being served. then a customer goes to the stall with probability pf for some p E (U, 1]. Once there are k. 33 1 people waiting to be served (so {k + l} in the system]. then arriving customers join the queue with probability pkflt + 1}. {Everyone knows a long queue signies a good stall.) The time from when a customer orders to when they receive their food is exponentially distributed with mean 913 seconds. For t 23 i], let X; be the number of customers in the system {that is, those waiting for service or in service} t minutes into the lunch rush. (a) Model {Xrltgn as a continuous time Markov chain and specify its generator. fb] Find the values of p where {xrltgn has a stationary distribution rr = {anjzm and for those values of p, write down a simple formula (i.e.. no innite sums] for an