Consider a "modified M$/$M$/1\text{'}$ queueing model, where the interarrival time of customers follows an exponential distribution with rate $1$ and the service time follows an exponential distribution with rate u$.$ Different than the conventional M$/$M$/1$ queue, this "modified M$/$M$/1"$ model assumes that each customer, at arrival, will decide not to join the queue with a probability of $1-9,$ for some q: $0<$ a $<1,$ if the server is busy in service. Otherwise, if the server is idle, the customer will always join the system. Formulate the balance equations to calculate the steady$-$state probabilities for this modified queueing model. $($Providing these equations and their derivations is sufficient. There is no need to solve these equations$).$