can anyone help me with this question with step by step process

Consider a simple barber shop with two (2) "service chairs" each served by a separate hair stylist, and one (1) "waiting chair." Stylist 1 is more experienced and when there is no customer in the shop, an arriving customer automatically goes to stylist 1 to be served. Customers to this barber shop arrive with exponential arrival events depending on the state of the system. If the system is empty or only one stylist is busy (i.e. when there is 0 or 1 customer in the shop), customers arrive at rate . Once both stylists are busy, arrival rate reduces to 0.75. Once there are three customers in the system, an incoming customer decides to turn away. In addition, the hair stylists service rate follows an exponential rate depending on the state of the system. Both stylists work at service rates of 1 and 2 respectively when there is only one customer in the system. However, when there are 2 customers in the system, the stylists speed up their rates to 1.11 and 1.32 respectively. Also, when there are 3 customers in the system, the stylists work at rates of 1.21 and 1.42 respectively. If is estimated to be 5 customers per hour, and 1 and 1 are estimated to be 5 customers and 3 customers per hour respectively; ( 50 points) a) Draw and label a state space diagram, showing all states and the rates of transition between states. b) Write a complete set of balance equations c) Solve your system of equations to determine the long run probability of the system being in each possible state d) What is the average number of jobs in the system at any point in time? e) What would be the effect on the state probabilities if the arrival rate increases to 6 customers per hour? Consider a simple barber shop with two (2) "service chairs" each served by a separate hair stylist, and one (1) "waiting chair." Stylist 1 is more experienced and when there is no customer in the shop, an arriving customer automatically goes to stylist 1 to be served. Customers to this barber shop arrive with exponential arrival events depending on the state of the system. If the system is empty or only one stylist is busy (i.e. when there is 0 or 1 customer in the shop), customers arrive at rate . Once both stylists are busy, arrival rate reduces to 0.75. Once there are three customers in the system, an incoming customer decides to turn away. In addition, the hair stylists service rate follows an exponential rate depending on the state of the system. Both stylists work at service rates of 1 and 2 respectively when there is only one customer in the system. However, when there are 2 customers in the system, the stylists speed up their rates to 1.11 and 1.32 respectively. Also, when there are 3 customers in the system, the stylists work at rates of 1.21 and 1.42 respectively. If is estimated to be 5 customers per hour, and 1 and 1 are estimated to be 5 customers and 3 customers per hour respectively; ( 50 points) a) Draw and label a state space diagram, showing all states and the rates of transition between states. b) Write a complete set of balance equations c) Solve your system of equations to determine the long run probability of the system being in each possible state d) What is the average number of jobs in the system at any point in time? e) What would be the effect on the state probabilities if the arrival rate increases to 6 customers per hour