# is this two dimensional markov chain correct for this queueing system?

the problem that i have two single server station with no queuing space a customer goes to station 1 if it is available else it goes to station 2 if it is available or it will be lost output from station 1 goes to station 2 if it is empty or blocking occurs and will stay in station 1 til station 2 become available. if customer visits station 2 first he will be served for two consecutive service times and then leave the system .

so to model this i consider that the first station will have 3 states 0(empty),1(customer get service),b(customer finish the service and blocked in station 1)

and 4 states for station 2 : 0(empty),1(customer from station 1 get service at station 2),a(customer initially go to station 2 and get his first service time ) , B(customer initially go to station 2 and get his second service time)

so is this model correct or it can be simplified more better .

• Isn't the state [customer in service, customer queued for second station] for station 1 feasible? this could occur if a new customer appears while the customer is waiting for the second station to open up. – Dave Jan 3 '14 at 20:17
• as I understand it station 1 is blocked if the customer is waiting for station 2. @Dave – Verena Haunschmid Jan 3 '14 at 21:33
• i want to be sure that is there an extra case of second station that can be removed or it is correct – M_F Jan 3 '14 at 22:17