Optimal Control of a Two-stage Tandem Queuing System with Flexible Servers

We consider the optimal control of two parallel servers in a two-stage tandem queuing system with two flexible servers+ New jobs arrive at station 1, after which a series of two operations must be performed before they leave the system+ Holding costs are incurred at rate h1 per unit time for each job at station 1 and at rate h2 per unit time for each job at station 2+ The system is considered under two scenarios; the collaborative case and the noncollaborative case+ In the prior, the servers can collaborate to work on the same job, whereas in the latter, each server can work on a unique job although they can work on separate jobs at the same station+ We provide simple conditions under which it is optimal to allocate both servers to station 1 or 2 in the collaborative case+ In the noncollaborative case, we show that the same condition as in the collaborative case guarantees the existence of an optimal policy that is exhaustive at station 1+ However, the condition for exhaustive service at station 2 to be optimal does not carry over+ This case is examined via a numerical study+ Probability in the Engineering and Informational Sciences, 16, 2002, 453–469+ Printed in the U+S+A+