A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic (Q2572396)

The paper considers a sequence of networks indexed by \(r\). Description for the \(r\)th network is as follows. For \(i = 1,2\), customers of Class \(i\) arrive according to a Poisson process with rate \(\lambda _i^r \) and have independent exponential service times at server 1 with parameter \(\mu _i^r \). Class 1 customers, after being served by server 1, leave the system. Class 2 customers, after being served by server 1, proceed to Buffer 3 and are redesignated as Class 3 customers. There they are served by Server 2. They have i.i.d. exponential service times with parameter \(\mu _3^r \). After service, these customers leave the system. All inter-arrival and service times are assumed to be mutually independent and all buffers have infinite capacity. The system starts empty. The paper studies the problem of asymptotically optimal control in heavy traffic. It considers linear holding cost and an infinite horizon discounted cost criterion.