Mathematical programming representations for state-dependent queues

Discrete-event dynamic systems with feedback, where the behavior of the system depends on the system state, are difficult to model due to the uncertainties and dependencies of system performance on the system state. Service systems, in particular, tend to exhibit this behavior where servers may work faster (or slower) when facing an increasingly long line of impatient customers. A common example is a state-dependent queue where the service rate depends on the queue size, which can change during service. In this paper, we present a mathematical programming representation for the sample path dynamics of a state-dependent queue, and illustrate its application in sensitivity analysis.