2,031 research outputs found
Stationary distributions of the multi-type ASEP
We give a recursive construction of the stationary distribution of multi-type
asymmetric simple exclusion processes on a finite ring or on the infinite line
. The construction can be interpreted in terms of "multi-line diagrams" or
systems of queues in tandem. Let be the asymmetry parameter of the system.
The queueing construction generalises the one previously known for the totally
asymmetric () case, by introducing queues in which each potential service
is unused with probability when the queue-length is . The analysis is
based on the matrix product representation of Prolhac, Evans and Mallick.
Consequences of the construction include: a simple method for sampling exactly
from the stationary distribution for the system on a ring; results on common
denominators of the stationary probabilities, expressed as rational functions
of with non-negative integer coefficients; and probabilistic descriptions
of "convoy formation" phenomena in large systems.Comment: 54 pages, 4 figure
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
Energy Sharing for Multiple Sensor Nodes with Finite Buffers
We consider the problem of finding optimal energy sharing policies that
maximize the network performance of a system comprising of multiple sensor
nodes and a single energy harvesting (EH) source. Sensor nodes periodically
sense the random field and generate data, which is stored in the corresponding
data queues. The EH source harnesses energy from ambient energy sources and the
generated energy is stored in an energy buffer. Sensor nodes receive energy for
data transmission from the EH source. The EH source has to efficiently share
the stored energy among the nodes in order to minimize the long-run average
delay in data transmission. We formulate the problem of energy sharing between
the nodes in the framework of average cost infinite-horizon Markov decision
processes (MDPs). We develop efficient energy sharing algorithms, namely
Q-learning algorithm with exploration mechanisms based on the -greedy
method as well as upper confidence bound (UCB). We extend these algorithms by
incorporating state and action space aggregation to tackle state-action space
explosion in the MDP. We also develop a cross entropy based method that
incorporates policy parameterization in order to find near optimal energy
sharing policies. Through simulations, we show that our algorithms yield energy
sharing policies that outperform the heuristic greedy method.Comment: 38 pages, 10 figure
Performance modelling with adaptive hidden Markov models and discriminatory processor sharing queues
In modern computer systems, workload varies at different times and locations. It is important to model the performance of such systems via workload models that are both representative and efficient. For example, model-generated workloads represent realistic system behaviour, especially during peak times, when it is crucial to predict and address performance bottlenecks. In this thesis, we model performance, namely throughput and delay, using adaptive models and discrete queues. Hidden Markov models (HMMs) parsimoniously capture the correlation and burstiness of workloads with spatiotemporal characteristics. By adapting the batch training of standard HMMs to incremental learning, online HMMs act as benchmarks on workloads obtained from live systems (i.e. storage systems and financial markets) and reduce time complexity of the Baum-Welch algorithm. Similarly, by extending HMM capabilities to train on multiple traces simultaneously it follows that workloads of different types are modelled in parallel by a multi-input HMM. Typically, the HMM-generated traces verify the throughput and burstiness of the real data. Applications of adaptive HMMs include predicting user behaviour in social networks and performance-energy measurements in smartphone applications. Equally important is measuring system delay through response times. For example, workloads such as Internet traffic arriving at routers are affected by queueing delays. To meet quality of service needs, queueing delays must be minimised and, hence, it is important to model and predict such queueing delays in an efficient and cost-effective manner. Therefore, we propose a class of discrete, processor-sharing queues for approximating queueing delay as response time distributions, which represent service level agreements at specific spatiotemporal levels. We adapt discrete queues to model job arrivals with distributions given by a Markov-modulated Poisson process (MMPP) and served under discriminatory processor-sharing scheduling. Further, we propose a dynamic strategy of service allocation to minimise delays in UDP traffic flows whilst maximising a utility function.Open Acces
Regularities and Irregularities in Order Flow Data
We identify and analyze statistical regularities and irregularities in the
recent order flow of different NASDAQ stocks, focusing on the positions where
orders are placed in the orderbook. This includes limit orders being placed
outside of the spread, inside the spread and (effective) market orders. We find
that limit order placement inside the spread is strongly determined by the
dynamics of the spread size. Most orders, however, arrive outside of the
spread. While for some stocks order placement on or next to the quotes is
dominating, deeper price levels are more important for other stocks. As market
orders are usually adjusted to the quote volume, the impact of market orders
depends on the orderbook structure, which we find to be quite diverse among the
analyzed stocks as a result of the way limit order placement takes place.Comment: 10 pages, 9 figure
Dynamic traffic equilibria with route and departure time choice
This thesis studies the dynamic equilibrium behavior in traffic networks and it is motivated by rush-hour congestion. It is well understood that one of the key causes of traffic congestion relies on the behavior of road users. These do not coordinate their actions in order to avoid the creation of traffic jams, but rather make choices that favor only themselves and not the community. An equilibrium occurs when everyone is satisfied with his own choices and would not benefit from changing them. We focus on dynamic mathematical models where the congestion delay of a road varies over time, depending on the amount of traffic that has crossed it up to that specific moment and independently on the pattern of traffic that will cross it at a later time. We mainly consider settings with arbitrary network topologies where users choose both the route and departure time and we tackle questions such as the followings: - Does an equilibrium always exist? - Can there be different equilibria? - How can an equilibrium behavior be computed? - How can one set tolls on roads so that, in an equilibrium, there is no congestion and social welfare is maximized
An integrated method for short-term prediction of road traffic conditions for intelligent transportation systems applications
The paper deals with the short-term prediction of road traffic conditions within Intelligent Transportation Systems applications. First, the problem of traffic modeling and the potential of different traffic monitoring technologies are discussed. Then, an integrated method for short-term traffic prediction is presented, which integrates an Artificial Neural Network predictor that forecasts future states in standard conditions, an anomaly detection module that exploits floating car data to individuate possible occurrences of anomalous traffic conditions, and a macroscopic traffic model that predicts speeds and queue progressions in case of anomalies. Results of offline applications on a primary Italian motorway are presented
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