Mathematical programming representations for state-dependent queues

Abstract

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.

Non-Markovian State-Dependent Networks in Critical Loading

“…Longer queues may lead to customers being discouraged to join the queue, or to faster processing, e.g., when human servers are involved, state-dependent features are present in congestion control protocols in communication networks, such as TCP (cf. [1,2,9,11,16] and references therein for more detail).…”