Transient state analysis of the shortest queueing system

In this paper, we consider a queueing systems with two parallel servers. Each server has a queue with infinite capacity. Customers arrive according to a Possion process and join the shortest queue. The service times of customers are independent and have generally distributed. If both queues have equal length, the new arrival with equal probability joins any of a queue. Jockeying between the queues is not allowed. Using Markov skeleton processes theory, we derive the transient joint queue length distribution of customers in the system, and show that it is the minimal nonnegative solution of a backward equation.