STOCHASTIC PROCESS

lQuestion 3 A service station has one petrol pump. Cars arrive at the station according to a Poisson process at a mean rate of 15 per hour. However, if the pump is ahead},r being used, these potential customers may balk {drive on to another service station). In particular, if there are already 11 cars in the service station, the probability that an arriving potential customer will hall: is 11,13 for n = 1,2, 3. The time required to service a car has an exponential distribution with a mean of four minutes. {a} Assimie that this system is modelled by a hirthanddeath process. IGive the birth and death. parameters. (13] Develop the steadystate equilibrium equations. {c} Solve these equations to nd the steadystate probabilities pg, 1}], Pg, . . . {d} Find the expected time spent in the system for those cars that stay