This work studies computation tree logic (CTL) model checking for finite-state Markov decision processes (MDPs) over the space of their distributions. Instead of investigating properties over states of the MDP, as encoded by formulae in standard probabilistic CTL (PCTL), the focus of this work is on the associated transition system, which is induced by the MDP, and on its dynamics over the (transient) MDP distributions. CTL is thus used to specify properties over the space of distributions, and is shown to provide an alternative way to express probabilistic specifications or requirements over the given MDP. We discuss the distinctive semantics of CTL formulae over distribution spaces, compare them to existing non-branching logics that reason on probability distributions, and juxtapose them to traditional PCTL specifications. We then propose reachability-based CTL model checking algorithms over distribution spaces, as well as computationally tractable, sampling-based procedures for computing the relevant reachable sets: it is in particular shown that the satisfaction set of the CTL specification can be soundly under-approximated by the union of convex polytopes. Case studies display the scalability of these procedures to large MDPs.

Queue overflow of a dynamic queue system gives rise to the information loss (or packet loss) in the communication buffer or the decrease of throughput in the transportation network. This paper investigates a stochastic optimal control problem for dynamic queue systems when imposing probability constraints on queue overflows. We reformulate this problem as a Markov decision process (MDP) with safety constraints. We prove that both finite-horizon and infinite-horizon stochastic optimal control for MDP with such constraints can be transformed as a linear program (LP), respectively. Feasibility conditions are provided for the finite-horizon constrained control problem. Two implementation algorithms are designed under the assumption that only the state (not the state distribution) can be observed at each time instant. Simulation results compare optimal cost and state distribution among different scenarios, and show the probability constraint satisfaction by the proposed algorithms.