Exclusive Queueing Process with Discrete Time

In a recent study [C Arita, Phys. Rev. E 80, 051119 (2009)], an extension of the M/M/1 queueing process with the excluded-volume effect as in the totally asymmetric simple exclusion process (TASEP) was introduced. In this paper, we consider its discrete-time version. The update scheme we take is the parallel one. A stationary-state solution is obtained in a slightly arranged matrix product form of the discrete-time open TASEP with the parallel update. We find the phase diagram for the existence of the stationary state. The critical line which separates the parameter space into the regions with and without the stationary state can be written in terms of the stationary current of the open TASEP. We calculate the average length of the system and the average number of particles

A Fixed-Point Algorithm for Closed Queueing Networks

In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)

When Backpressure Meets Predictive Scheduling

Motivated by the increasing popularity of learning and predicting human user behavior in communication and computing systems, in this paper, we investigate the fundamental benefit of predictive scheduling, i.e., predicting and pre-serving arrivals, in controlled queueing systems. Based on a lookahead window prediction model, we first establish a novel equivalence between the predictive queueing system with a \emph{fully-efficient} scheduling scheme and an equivalent queueing system without prediction. This connection allows us to analytically demonstrate that predictive scheduling necessarily improves system delay performance and can drive it to zero with increasing prediction power. We then propose the \textsf{Predictive Backpressure (PBP)} algorithm for achieving optimal utility performance in such predictive systems. \textsf{PBP} efficiently incorporates prediction into stochastic system control and avoids the great complication due to the exponential state space growth in the prediction window size. We show that \textsf{PBP} can achieve a utility performance that is within $O(\epsilon)$ of the optimal, for any $\epsilon>0$, while guaranteeing that the system delay distribution is a \emph{shifted-to-the-left} version of that under the original Backpressure algorithm. Hence, the average packet delay under \textsf{PBP} is strictly better than that under Backpressure, and vanishes with increasing prediction window size. This implies that the resulting utility-delay tradeoff with predictive scheduling beats the known optimal $[O(\epsilon), O(\log(1/\epsilon))]$ tradeoff for systems without prediction

Reachability Analysis of Communicating Pushdown Systems

The reachability analysis of recursive programs that communicate asynchronously over reliable FIFO channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability problem restricted to eager runs (i.e., runs where messages are either received immediately after being sent, or never received). The problem is EXPTIME-complete in the decidable case. The second result is a doubly exponential time algorithm for bounded context analysis in this setting, together with a matching lower bound. Both results extend and improve previous work from La Torre et al