Up to a decade ago, most research in queueing was concerned with descriptive aspects, i.e. mathematical characteristics and structure such as steady-state queue length probability distributions, waiting time distributions, average queue length, and busy and idle periods analysis. However, in real life the operator of a queueing system is also concerned with design and control. The operator wants to maximize his profit or minimize his costs. For this reason, optimization problems in queueing have received much attention during the past few years. In this paper, a queueing system with two service stations is considered. Arrivals to each station from outside follow a Poisson process. The service time at each station is an exponentially distributed random variable with mean depending on the state of the system, defined as the number of customers at each station at time t. A customer served at either of the stations leaves the system or goes to the other station with specified probabilities. A linear programming model is constructed to find a policy or a decision rule that specifies the service rate to be used at each station as a function of the state of the system to minimize a given objective cost function. The solution has applications in maintenance, business and lime-shared computer systems.