At a highway service station vehicles approach the pumps on a long service road and for the next available fuel pump. There are 10 pumps. On filling their vehicle, drivers take their vehicle to a pay kiok. On compliting payment, driver may exit the service satation or choose to stop to use the air and water, refreshmnet, shopping and toilet facilities.

Vehicle arrive at the service station at a rate of 100 per hour and spend an average of five minutes at the pump before driving to a pay kiosk. The average service time at a pay kiosk is 30 Seconds. vehicle arrive at the service station randomly with a Poisson distribution. All service rates have a negative exponential distribution.

Calculate

a) the pump facility utilization

b) the probability there are no cars at the pumps

c) the aveage time from joining the queue to leaving the pumps

d) the probsbilty that there is at least one car but not more than five carsqueuing for the pumps at any one time.

e) the kiosk facility utilisation

f) the average time from joining the queue for the kiosk to leaving the kiosk

g) the probality that there are at least two cars in the queue for the kiosk at any given time