(a) A supermarket has two (regular) checkout stations served by two equally qualified staffs, Carmen and Chloe. When a customer arrives and finds any cashier idle, his/her checkout starts right away. If both Carmen and Chloe are busy, the customer waits in a single First-In-First-Out queue with unlimited capacity. After checking out, the customer leaves the supermarket immediately. Define the system state at time t as [Q(t), C(t)], where Q(t) = number of customers waiting in the queue C(t) = number of customers in service at the checkout stations (0, 1, 2) Let [q, c] be the current state of the system. Define events and write the corresponding state transitions.(b) Now, suppose that the supermarket adds one express checkout station, which is served by a senior staff, Ada. The express checkout station has its own First-In-First-Out queue for at most 5 customers waiting in the queue. A customer can be served by any one of the 3 cashiers, but will be served by Ada if she is available. If all 3 cashiers are busy, the customer waits in the express queue if it is not full and its current length is shorter than (but not equal to) the length of the regular queue, otherwise, the customer joins the regular queue. Assume that customers will never switch to another queue. When Ada finishes serving a customer, she takes the first one from the express queue, if any, and if the express queue is empty but the regular queue is not, she takes the first customer from the regular queue. Similarly, if either Carmen or Chloe finishes serving a customer, she takes the first customer from the regular queue, if any, and if the regular queue is empty but the express queue is not, she takes the first customer from the express queue. After checking out, the customer leaves the supermarket immediately. Define the system state at time t as [E(t), Q(t), A(t), C(t)], where E(t) = number of customers waiting in the express queue (0 to 5) Q(t) = number of customers waiting in the regular queue A(t) = number of customers in service at Ada's (express) checkout station (0, 1) C(t) = number of customers in service at the regular checkout stations (0, 1, 2) Let [e, q, a, c] be the current state of the system. Define events and write the corresponding state transitions