Reversibility in Queueing Models

In stochastic models for queues and their networks, random events evolve in time. A process for their backward evolution is referred to as a time reversed process. It is often greatly helpful to view a stochastic model from two different time directions. In particular, if some property is unchanged under time reversal, we may better understand that property. A concept of reversibility is invented for this invariance. Local balance for a stationary Markov chain has been used for a weaker version of the reversibility. However, it is still too strong for queueing applications. We are concerned with a continuous time Markov chain, but dose not assume it has the stationary distribution. We define reversibility in structure as an invariant property of a family of the set of models under certain operation. The member of this set is a pair of transition rate function and its supporting measure, and each set represents dynamics of queueing systems such as arrivals and departures. We use a permutation {\Gamma} of the family menmbers, that is, the sets themselves, to describe the change of the dynamics under time reversal. This reversibility is is called {\Gamma}-reversibility in structure. To apply these definitions, we introduce new classes of models, called reacting systems and self-reacting systems. Using those definitions and models, we give a unified view for queues and their networks which have reversibility in structure, and show how their stationary distributions can be obtained. They include symmetric service, batch movements and state dependent routing.Comment: Submitted for publicatio

Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective

In this paper we present and analyze a queueing-theoretical model for autonomous mobility-on-demand (MOD) systems where robotic, self-driving vehicles transport customers within an urban environment and rebalance themselves to ensure acceptable quality of service throughout the entire network. We cast an autonomous MOD system within a closed Jackson network model with passenger loss. It is shown that an optimal rebalancing algorithm minimizing the number of (autonomously) rebalancing vehicles and keeping vehicles availabilities balanced throughout the network can be found by solving a linear program. The theoretical insights are used to design a robust, real-time rebalancing algorithm, which is applied to a case study of New York City. The case study shows that the current taxi demand in Manhattan can be met with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi fleet). Finally, we extend our queueing-theoretical setup to include congestion effects, and we study the impact of autonomously rebalancing vehicles on overall congestion. Collectively, this paper provides a rigorous approach to the problem of system-wide coordination of autonomously driving vehicles, and provides one of the first characterizations of the sustainability benefits of robotic transportation networks.Comment: 10 pages, To appear at RSS 201

Incentives for Quality through Endogenous Routing

We study how rework routing together with wage and piece rate compensation can strengthen incentives for quality. Traditionally, rework is assigned back to the agent who generates the defect (in a self routing scheme) or to another agent dedicated to rework (in a dedicated routing scheme). In contrast, a novel cross routing scheme allocates rework to a parallel agent performing both new jobs and rework. The agent who passes quality inspection or completes rework receives the piece rate paid per job. We compare the incentives of these rework allocation schemes in a principal-agent model with embedded quality control and routing in a multi-class queueing network. We show that conventional self routing of rework can never induce first-best effort. Dedicated routing and cross routing, however, strengthen incentives for quality by imposing an implicit punishment for quality failure. In addition, cross routing leads to workload allocation externalities and a prisoner’s dilemma, thereby creating highest incentives for quality. Firm profitability depends on capacity levels, revenues, and quality costs. With ample capacity, dedicated routing and cross routing both achieve first-best profit rate, while self routing does not. With limited capacity, cross routing generates the highest profit rate when appraisal, internal failure, or external failure costs are high, while self routing performs best when gross margins are high. When the number of agents increases, the incentive power of cross routing reduces monotonically and approaches that of dedicated routing.queueing networks; routing; Nash equilibrium; quality control; piece rate; epsilon equilibrium.

Cloud Enabled Emergency Navigation Using Faster-than-real-time Simulation

State-of-the-art emergency navigation approaches are designed to evacuate civilians during a disaster based on real-time decisions using a pre-defined algorithm and live sensory data. Hence, casualties caused by the poor decisions and guidance are only apparent at the end of the evacuation process and cannot then be remedied. Previous research shows that the performance of routing algorithms for evacuation purposes are sensitive to the initial distribution of evacuees, the occupancy levels, the type of disaster and its as well its locations. Thus an algorithm that performs well in one scenario may achieve bad results in another scenario. This problem is especially serious in heuristic-based routing algorithms for evacuees where results are affected by the choice of certain parameters. Therefore, this paper proposes a simulation-based evacuee routing algorithm that optimises evacuation by making use of the high computational power of cloud servers. Rather than guiding evacuees with a predetermined routing algorithm, a robust Cognitive Packet Network based algorithm is first evaluated via a cloud-based simulator in a faster-than-real-time manner, and any "simulated casualties" are then re-routed using a variant of Dijkstra's algorithm to obtain new safe paths for them to exits. This approach can be iterated as long as corrective action is still possible.Comment: Submitted to PerNEM'15 for revie

Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multi-hop routing is more advantageous than single-hop routing